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MINISTRY OF EDUCATION, SINGAPORE in collaboration with UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CENTRE INDEX NUMBER NUMBER ITITJ \11 0 - """"""'" - - PHYSICS 9646/03 E """""= Paper 3 Longer Structured Ouestions October/November 2010 m- \II 2 hours Candidates answer on the Question Paper. ,J..-= />"' == """"""'" No Additional Materials are required. \11 READ THESE INSTRUCTIONS FIRST Write your Centre number, index number and name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. 00 not use staples, paper clips , highlighlers. glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. You are advised to spend about one hour on each section . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets r I at the end of each question or pari question . For Examiner's Use 1 2 3 4 5 6 7 a Total This document consists of 23 printed pages and 1 blank page . /" ..... " lA'I (1-01 Singapore Examinallons and Assessment Board UN of International Examinations © UCLES & MOE 2010 DC (NF/SW) 33256 [Turn over

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Page 1: 9646/03 - A Level Tuitiona-leveltuition.com/wp-content/uploads/2011/12/2010-A... · 2013. 10. 3. · 9646/03. E ,J~ m """""= Paper 3 Longer Structured Ouestions October/November 2010

MINISTRY OF EDUCATION SINGAPORE in collaboration with UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE General Certificate of Education Advanced Level Higher 2

CANDIDATE NAME

CENTRE INDEX NUMBER NUMBER ITITJ

11

0 - -

shy PHYSICS 964603E

J~ = Paper 3 Longer Structured Ouestions OctoberNovember 2010mshy

II 2 hours

o~ Candidates answer on the Question Paper J-=gt== No Additional Materials are required

11

~

READ THESE INSTRUCTIONS FIRST

Write your Centre number index number and name on all the work you hand in Write in dark blue or black pen on both sides of the paper You may use a soft pencil for any diagrams graphs or rough working 00 not use staples paper clips highlighlers glue or correction fluid

Section A Answer all questions

Section B Answer any two questions

You are advised to spend about one hour on each section

At the end of the examination fasten all your work securely together The number of marks is given in brackets r I at the end of each question or pari question

For Examiners Use

1

2

3

4

5

6

7

a

Total

This document consists of 23 printed pages and 1 blank page

lAI(1-01 Singapore Examinallons and Assessment Board ~41 UN IVER~ITI of CAM~RIJGE ~ International Examinations

~ copy UCLES amp MOE 2010 DC (NFSW) 33256 [Turn over

Data

speed of light in free space

permeability of free space

permittivity of free space

elementary charge

the Planck constant

unified atomic mass constant

rest mass of electron

rest mass of proton

molar gas constant

the Avogadro constant

the Boltzmann constant

gravitational constant

acceleration of free fall

e UClES s MOE 2010

2

c =300 x 108 rns

fLo = 4n x 10-7 H rn

Bo =885 x 10- 12 Fm- 1

(136n)) x 10-9 Fm- 1

e = 160 x 10-19 C

h = 663 x 10-34 J s

u = 166 x 10- 27 kg

me = 911 x 10-3 1 kg

m = 167 x 10-27 kgp

R = 831 J K-1 rnor

NA = 602 x 1023 mol- 1

k = 138 x 10-23 J K- 1

G =667 x 10-11 N m2 kg- 2

29 = 981 ms-

9646 03l0lNl0

3

Formulae

uniformly accelerated motion s =ut + ~at2

work done onby a gas w =p1V

hydrostatic pressure p =pgh

cent =_ Gmgravitational potential r

displacement of particle in shm x = Xo sin cot

velocity of particle in shrn II = Vo cos cot

mean kinetic energy of a molecule of an ideal gas E = ~kT

resistors in series

resistors in parallel 1R = 1R1 + 1R2 +

Qelectric potential V= ~-

4rrco

atternatinq currenVvoltage x = Xosin cot

transmission coefficient T ~ exp(-2kd)

sn2m(U - E)h kwere = h2

radioactive decay x = Xoexp(- At)

A = 0693decay constant t ~

e UCLES amp MOE 2010 9646103l0IN10 [Turn over

--- - - - -

- - -- - - - -

- - - -

- - - - - - - -- - - - - -

- - - - - -

4

Section A

Answer all the questions in this section

1 (a) State what is meant by tatent heat of vaporisation

[2)

(b) A student carries out an experiment to determine the specific latent heat of vaporisation of water

Water is boiled in a beaker by means of an electric heater as shown in Fig 11

to power supply

beaker

- --

---

- -water -y I I I f--shy

-

Fig 11

The power P supplied to the heater is measured When the water is boiling at a constant rate the mass m of water evaporated in 50 minutes is determined

Data for the power P and the mass m for two different values of P are shown in Fig 12

PIW mig

140 141

95 82

Fig 12

copy UCLES s MOE 2010 9646J0310N10

For Examme(s

Use

5

(i) Suggest why in order to obtain a reliable result for the specific latent heat the mass m is determined for two different values of P

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[1J

(ii) Calculate the value for the specif ic latent heat L of vaporisation

L = J g-1 3]

For EXEminels

Use

964 6030N l 0 [TUrn over e UCLES 8 MOE 20 10

2

6

A small ball of mass m is fixed to one end of a light rigid rod The ball is made to move at constant speed around the circumference of a vertical circle with centre at C as shown in Fig21

ball mass m --- - - - - shy

light rod ----I a72m

cmiddot -----shyFig21

When the rod is vertical with the ball above C the tension T in the rod is given by

T 2mg

where 9 is the acceleration of free fall

(a) (i) Explain why the centripetal force on the ball is greater than 2 mg

[11

(ii) State in terms of mg the magnitude of the centripetal force

centripetal force = (1 J

(iii) Determine the magnitude of the tension in terms of mg in the rod when the rod is vertical with the ball below point C

tension = [1]

copyUCLES ampMOE 2010 964603QNl0

For ExamIners

Use

7

(b) The distan ce from the centre of the ball to point Cis 072 m

Use your answer in (a)(ii) to dete rmine for the ball

(0 the angular speed

angular speed = rads-1 [3]

(ii) the linear speed

linear speed = m 5- 1 [2]

(c) The ball has a constant angular speed

(i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C

[2]

(II) Calculate the work done in (I) for a ball of mass 240 g

work done = J [2)

For Examiners

Use

copy UCLES s MOE 2010 964603l0N110 [Tu rn over

8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

Page 2: 9646/03 - A Level Tuitiona-leveltuition.com/wp-content/uploads/2011/12/2010-A... · 2013. 10. 3. · 9646/03. E ,J~ m """""= Paper 3 Longer Structured Ouestions October/November 2010

Data

speed of light in free space

permeability of free space

permittivity of free space

elementary charge

the Planck constant

unified atomic mass constant

rest mass of electron

rest mass of proton

molar gas constant

the Avogadro constant

the Boltzmann constant

gravitational constant

acceleration of free fall

e UClES s MOE 2010

2

c =300 x 108 rns

fLo = 4n x 10-7 H rn

Bo =885 x 10- 12 Fm- 1

(136n)) x 10-9 Fm- 1

e = 160 x 10-19 C

h = 663 x 10-34 J s

u = 166 x 10- 27 kg

me = 911 x 10-3 1 kg

m = 167 x 10-27 kgp

R = 831 J K-1 rnor

NA = 602 x 1023 mol- 1

k = 138 x 10-23 J K- 1

G =667 x 10-11 N m2 kg- 2

29 = 981 ms-

9646 03l0lNl0

3

Formulae

uniformly accelerated motion s =ut + ~at2

work done onby a gas w =p1V

hydrostatic pressure p =pgh

cent =_ Gmgravitational potential r

displacement of particle in shm x = Xo sin cot

velocity of particle in shrn II = Vo cos cot

mean kinetic energy of a molecule of an ideal gas E = ~kT

resistors in series

resistors in parallel 1R = 1R1 + 1R2 +

Qelectric potential V= ~-

4rrco

atternatinq currenVvoltage x = Xosin cot

transmission coefficient T ~ exp(-2kd)

sn2m(U - E)h kwere = h2

radioactive decay x = Xoexp(- At)

A = 0693decay constant t ~

e UCLES amp MOE 2010 9646103l0IN10 [Turn over

--- - - - -

- - -- - - - -

- - - -

- - - - - - - -- - - - - -

- - - - - -

4

Section A

Answer all the questions in this section

1 (a) State what is meant by tatent heat of vaporisation

[2)

(b) A student carries out an experiment to determine the specific latent heat of vaporisation of water

Water is boiled in a beaker by means of an electric heater as shown in Fig 11

to power supply

beaker

- --

---

- -water -y I I I f--shy

-

Fig 11

The power P supplied to the heater is measured When the water is boiling at a constant rate the mass m of water evaporated in 50 minutes is determined

Data for the power P and the mass m for two different values of P are shown in Fig 12

PIW mig

140 141

95 82

Fig 12

copy UCLES s MOE 2010 9646J0310N10

For Examme(s

Use

5

(i) Suggest why in order to obtain a reliable result for the specific latent heat the mass m is determined for two different values of P

bullbull bull bull bull bull bull bull bullbullbullbullbullbullbull bull bull bull bull bull r 0 bullbullbullbull bullbull bull bull bull bull bullbullbullbullbullbullbullbull bull bull bull bull bull bullbullbull bull bull bull bull bull bull bull - bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bullbull bull bull bull bull bull bull bullbull bullbullbull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull ~ bull bullbull bull bull bull

[1J

(ii) Calculate the value for the specif ic latent heat L of vaporisation

L = J g-1 3]

For EXEminels

Use

964 6030N l 0 [TUrn over e UCLES 8 MOE 20 10

2

6

A small ball of mass m is fixed to one end of a light rigid rod The ball is made to move at constant speed around the circumference of a vertical circle with centre at C as shown in Fig21

ball mass m --- - - - - shy

light rod ----I a72m

cmiddot -----shyFig21

When the rod is vertical with the ball above C the tension T in the rod is given by

T 2mg

where 9 is the acceleration of free fall

(a) (i) Explain why the centripetal force on the ball is greater than 2 mg

[11

(ii) State in terms of mg the magnitude of the centripetal force

centripetal force = (1 J

(iii) Determine the magnitude of the tension in terms of mg in the rod when the rod is vertical with the ball below point C

tension = [1]

copyUCLES ampMOE 2010 964603QNl0

For ExamIners

Use

7

(b) The distan ce from the centre of the ball to point Cis 072 m

Use your answer in (a)(ii) to dete rmine for the ball

(0 the angular speed

angular speed = rads-1 [3]

(ii) the linear speed

linear speed = m 5- 1 [2]

(c) The ball has a constant angular speed

(i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C

[2]

(II) Calculate the work done in (I) for a ball of mass 240 g

work done = J [2)

For Examiners

Use

copy UCLES s MOE 2010 964603l0N110 [Tu rn over

8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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3

Formulae

uniformly accelerated motion s =ut + ~at2

work done onby a gas w =p1V

hydrostatic pressure p =pgh

cent =_ Gmgravitational potential r

displacement of particle in shm x = Xo sin cot

velocity of particle in shrn II = Vo cos cot

mean kinetic energy of a molecule of an ideal gas E = ~kT

resistors in series

resistors in parallel 1R = 1R1 + 1R2 +

Qelectric potential V= ~-

4rrco

atternatinq currenVvoltage x = Xosin cot

transmission coefficient T ~ exp(-2kd)

sn2m(U - E)h kwere = h2

radioactive decay x = Xoexp(- At)

A = 0693decay constant t ~

e UCLES amp MOE 2010 9646103l0IN10 [Turn over

--- - - - -

- - -- - - - -

- - - -

- - - - - - - -- - - - - -

- - - - - -

4

Section A

Answer all the questions in this section

1 (a) State what is meant by tatent heat of vaporisation

[2)

(b) A student carries out an experiment to determine the specific latent heat of vaporisation of water

Water is boiled in a beaker by means of an electric heater as shown in Fig 11

to power supply

beaker

- --

---

- -water -y I I I f--shy

-

Fig 11

The power P supplied to the heater is measured When the water is boiling at a constant rate the mass m of water evaporated in 50 minutes is determined

Data for the power P and the mass m for two different values of P are shown in Fig 12

PIW mig

140 141

95 82

Fig 12

copy UCLES s MOE 2010 9646J0310N10

For Examme(s

Use

5

(i) Suggest why in order to obtain a reliable result for the specific latent heat the mass m is determined for two different values of P

bullbull bull bull bull bull bull bull bullbullbullbullbullbullbull bull bull bull bull bull r 0 bullbullbullbull bullbull bull bull bull bull bullbullbullbullbullbullbullbull bull bull bull bull bull bullbullbull bull bull bull bull bull bull bull - bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bullbull bull bull bull bull bull bull bullbull bullbullbull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull ~ bull bullbull bull bull bull

[1J

(ii) Calculate the value for the specif ic latent heat L of vaporisation

L = J g-1 3]

For EXEminels

Use

964 6030N l 0 [TUrn over e UCLES 8 MOE 20 10

2

6

A small ball of mass m is fixed to one end of a light rigid rod The ball is made to move at constant speed around the circumference of a vertical circle with centre at C as shown in Fig21

ball mass m --- - - - - shy

light rod ----I a72m

cmiddot -----shyFig21

When the rod is vertical with the ball above C the tension T in the rod is given by

T 2mg

where 9 is the acceleration of free fall

(a) (i) Explain why the centripetal force on the ball is greater than 2 mg

[11

(ii) State in terms of mg the magnitude of the centripetal force

centripetal force = (1 J

(iii) Determine the magnitude of the tension in terms of mg in the rod when the rod is vertical with the ball below point C

tension = [1]

copyUCLES ampMOE 2010 964603QNl0

For ExamIners

Use

7

(b) The distan ce from the centre of the ball to point Cis 072 m

Use your answer in (a)(ii) to dete rmine for the ball

(0 the angular speed

angular speed = rads-1 [3]

(ii) the linear speed

linear speed = m 5- 1 [2]

(c) The ball has a constant angular speed

(i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C

[2]

(II) Calculate the work done in (I) for a ball of mass 240 g

work done = J [2)

For Examiners

Use

copy UCLES s MOE 2010 964603l0N110 [Tu rn over

8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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--- - - - -

- - -- - - - -

- - - -

- - - - - - - -- - - - - -

- - - - - -

4

Section A

Answer all the questions in this section

1 (a) State what is meant by tatent heat of vaporisation

[2)

(b) A student carries out an experiment to determine the specific latent heat of vaporisation of water

Water is boiled in a beaker by means of an electric heater as shown in Fig 11

to power supply

beaker

- --

---

- -water -y I I I f--shy

-

Fig 11

The power P supplied to the heater is measured When the water is boiling at a constant rate the mass m of water evaporated in 50 minutes is determined

Data for the power P and the mass m for two different values of P are shown in Fig 12

PIW mig

140 141

95 82

Fig 12

copy UCLES s MOE 2010 9646J0310N10

For Examme(s

Use

5

(i) Suggest why in order to obtain a reliable result for the specific latent heat the mass m is determined for two different values of P

bullbull bull bull bull bull bull bull bullbullbullbullbullbullbull bull bull bull bull bull r 0 bullbullbullbull bullbull bull bull bull bull bullbullbullbullbullbullbullbull bull bull bull bull bull bullbullbull bull bull bull bull bull bull bull - bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bullbull bull bull bull bull bull bull bullbull bullbullbull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull ~ bull bullbull bull bull bull

[1J

(ii) Calculate the value for the specif ic latent heat L of vaporisation

L = J g-1 3]

For EXEminels

Use

964 6030N l 0 [TUrn over e UCLES 8 MOE 20 10

2

6

A small ball of mass m is fixed to one end of a light rigid rod The ball is made to move at constant speed around the circumference of a vertical circle with centre at C as shown in Fig21

ball mass m --- - - - - shy

light rod ----I a72m

cmiddot -----shyFig21

When the rod is vertical with the ball above C the tension T in the rod is given by

T 2mg

where 9 is the acceleration of free fall

(a) (i) Explain why the centripetal force on the ball is greater than 2 mg

[11

(ii) State in terms of mg the magnitude of the centripetal force

centripetal force = (1 J

(iii) Determine the magnitude of the tension in terms of mg in the rod when the rod is vertical with the ball below point C

tension = [1]

copyUCLES ampMOE 2010 964603QNl0

For ExamIners

Use

7

(b) The distan ce from the centre of the ball to point Cis 072 m

Use your answer in (a)(ii) to dete rmine for the ball

(0 the angular speed

angular speed = rads-1 [3]

(ii) the linear speed

linear speed = m 5- 1 [2]

(c) The ball has a constant angular speed

(i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C

[2]

(II) Calculate the work done in (I) for a ball of mass 240 g

work done = J [2)

For Examiners

Use

copy UCLES s MOE 2010 964603l0N110 [Tu rn over

8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

Page 5: 9646/03 - A Level Tuitiona-leveltuition.com/wp-content/uploads/2011/12/2010-A... · 2013. 10. 3. · 9646/03. E ,J~ m """""= Paper 3 Longer Structured Ouestions October/November 2010

5

(i) Suggest why in order to obtain a reliable result for the specific latent heat the mass m is determined for two different values of P

bullbull bull bull bull bull bull bull bullbullbullbullbullbullbull bull bull bull bull bull r 0 bullbullbullbull bullbull bull bull bull bull bullbullbullbullbullbullbullbull bull bull bull bull bull bullbullbull bull bull bull bull bull bull bull - bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bullbull bull bull bull bull bull bull bullbull bullbullbull bull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull bull bull bull bull bull bullbull bull bull bull bull bull ~ bull bullbull bull bull bull

[1J

(ii) Calculate the value for the specif ic latent heat L of vaporisation

L = J g-1 3]

For EXEminels

Use

964 6030N l 0 [TUrn over e UCLES 8 MOE 20 10

2

6

A small ball of mass m is fixed to one end of a light rigid rod The ball is made to move at constant speed around the circumference of a vertical circle with centre at C as shown in Fig21

ball mass m --- - - - - shy

light rod ----I a72m

cmiddot -----shyFig21

When the rod is vertical with the ball above C the tension T in the rod is given by

T 2mg

where 9 is the acceleration of free fall

(a) (i) Explain why the centripetal force on the ball is greater than 2 mg

[11

(ii) State in terms of mg the magnitude of the centripetal force

centripetal force = (1 J

(iii) Determine the magnitude of the tension in terms of mg in the rod when the rod is vertical with the ball below point C

tension = [1]

copyUCLES ampMOE 2010 964603QNl0

For ExamIners

Use

7

(b) The distan ce from the centre of the ball to point Cis 072 m

Use your answer in (a)(ii) to dete rmine for the ball

(0 the angular speed

angular speed = rads-1 [3]

(ii) the linear speed

linear speed = m 5- 1 [2]

(c) The ball has a constant angular speed

(i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C

[2]

(II) Calculate the work done in (I) for a ball of mass 240 g

work done = J [2)

For Examiners

Use

copy UCLES s MOE 2010 964603l0N110 [Tu rn over

8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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2

6

A small ball of mass m is fixed to one end of a light rigid rod The ball is made to move at constant speed around the circumference of a vertical circle with centre at C as shown in Fig21

ball mass m --- - - - - shy

light rod ----I a72m

cmiddot -----shyFig21

When the rod is vertical with the ball above C the tension T in the rod is given by

T 2mg

where 9 is the acceleration of free fall

(a) (i) Explain why the centripetal force on the ball is greater than 2 mg

[11

(ii) State in terms of mg the magnitude of the centripetal force

centripetal force = (1 J

(iii) Determine the magnitude of the tension in terms of mg in the rod when the rod is vertical with the ball below point C

tension = [1]

copyUCLES ampMOE 2010 964603QNl0

For ExamIners

Use

7

(b) The distan ce from the centre of the ball to point Cis 072 m

Use your answer in (a)(ii) to dete rmine for the ball

(0 the angular speed

angular speed = rads-1 [3]

(ii) the linear speed

linear speed = m 5- 1 [2]

(c) The ball has a constant angular speed

(i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C

[2]

(II) Calculate the work done in (I) for a ball of mass 240 g

work done = J [2)

For Examiners

Use

copy UCLES s MOE 2010 964603l0N110 [Tu rn over

8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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7

(b) The distan ce from the centre of the ball to point Cis 072 m

Use your answer in (a)(ii) to dete rmine for the ball

(0 the angular speed

angular speed = rads-1 [3]

(ii) the linear speed

linear speed = m 5- 1 [2]

(c) The ball has a constant angular speed

(i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C

[2]

(II) Calculate the work done in (I) for a ball of mass 240 g

work done = J [2)

For Examiners

Use

copy UCLES s MOE 2010 964603l0N110 [Tu rn over

8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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8

3 Force-fields may be represented using lines that have direction I For Examiners

Use(a) State

(i) what is meanl by a field of force

1]

(ii) how using lines of force changes in the strength of a force-field are represented

bull ~ bullbull bullbullbullbull ~ bullbull ~ bull bullbull e bullbull ~ bullbullbullbull ~ bullbull bull bullbullbullbullbullbull ~ ~ bull bull bull bull ~ ~ bullbullbullbullbull bull bullbullbullbullbullbullbullbull bull bull bull bullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbullbull bull bullbullbullbullbull bull bullbullbullbullbullbullbull bullbullbullbullbullbullbullbullbull bullbull bullbullbullbullbullbullbull bullbullbullbull bull bull bullbullbullbullbullbull bull bullbull bull bullbullbull bull

[2]

(b) Conventionally arrows on field lines define the direction of a force acting on an object

State the property of the object that experiences a force in this direction for

(i) a gravitational field

[1]

(ii) an electric field bull

[1]

(iii) a magnetic field

[1]

copy UCLES amp MOE 2010 9646J0301N10

9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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9

(c) Explain how an electric field and a magnetic field may be used for the velocity selection For of charged particles You may draw a diagram if you wish I Examiners

Use

[4]

copy UCLES amp MOE 2010 9646103101N10 [Turn over

4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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4

10

A circuit consists of three resistors Rl R2 and R3 and two switches A and B as shown in Fig 41

I-------------Oy-------

B

Fig 41

The resistance between terminals X and Y is measured for different settings of the switches A and B The results are shown in Fig 42

switch A switch 8 resistance between X and Y Q

open open

closed closed

open closed open

closed

12 10 6 6

Fig 42

(a) Determine the resistance of

(i) resistor R1

resistance = Q [1]

(ii) resistor R2 bull

resistance = Q [1]

(iii) resistor R3

resistance = Q [1]

(b) Switch A is now closed and switch B is open

Calculate the resistance between terminals X and Z

resistance = Q f2]

copy UCLES amp MOE 2010 964603l0N1 0

For Exammers

Use

11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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11

5 (a) By reference to the photoelectric effect state what is meant by the work function of a For surface Examine(s

Use

[1)

(b) Light of wavelength 540 nm is incident on a metal surface having a work function of 25eV

Determine whether electrons are emitted from the suriace

[4]

(c) Exptain whether your conclusion In (b) Is aHected by the intensity of light incident on the surface

[2]

copy UCLES s MOE 2010 964603lON10 [Turn over

12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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12

Section 8

Answer two questions from this section

6 (a) Define force

[2)

(b) A light helical spring is suspended vertically from a fixed point as shown in Fig 61

spring

mass

Fig 61

DiHerent masses are suspended from the spring The weight Wof the mass and the length L of the spring are noted

The variation with weight Waf the length L is shown in Fig 62

~ - =shy ~ l~+ H-1++++1

- 1-H--1-H- - _ T-I -H-fmiddot~~+-HH-t+++l--f--HH-+-H--I middot+H- I + 1 )+++1--1-shy +-1

H --t-middot+++ Io-Irl-+-+-H-+-I-t-H-+-++ + H --HH+-Ishy -shy - - - shy -shy

-t-1--j-+-t-+-I-+-+-H-+-I-I-t--I++-++H -l-+ + middot -- - shy - -- - - --I--H-+HH

-H-l-+-tshy - -shy - f++++l--- JtEE=etiJ - 1-

- -++-I + -1--H-+-+-I-H-f+-1-1-H--iHH+++I- H-l- shyH- -H-H - I-HH-+-1--f-+-I-t-H-+-++ I-+-1

4 +++-+-iH-+-+++-+--~-++-++++-H-+-+-++++-+-iH-+-++++-+-+-i+-l--++++t-+-i-+-H

J~ 1-~ H- I-+-I++++~H 4 I j H -+-f-+-I--+--H-+-H--+-1

H --f-+ + +-I-H-++f-I 1 I shy Irl i I ~

53 4

WIN

H-+-+-HH-++-I_ l-l I+-t-+H-+-H-H-+-I--t-shy

Fig 62

copyUCLES ampMOE 2010 964603l0Nl0

For Examiners

Use

13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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13

(i) On Fig 62 show clearly the area of the graptl that represents energy stored in the spring when the weight on the spring is increased from zero to 50N (1)

(Ii) For a spring undergoing an elastic change the force per unit extension of the spring is known as the force constant k

Show that the energy E stored in Ihe spring for an extension x of the spring is given by Ihe expression

E = ~kx2

[2]

Question 6 continues on the next page

FOf

Examiners Use

9646f03l0 fNf10 [Turn overcopy UClES amp MOE 2010

14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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14

(c) A mass of weight 40N is suspended from the spring in (b)

When the mass is stationary it is then pulled downwards a distance of DaDem and held stationary

(i) Determine the total length of the spring

length = cm [1 J

(ii) For the increase in extension of osocrn determine the magnitude of the change in

1 the gravitational potential energy of the mass

change = J [2)

2 the elastic potential energy of the spring

change = J [3]

(Iii) Use your answers in (ii) to show that the work done to cause the additional extension of D80em is 40 x 10-3 J

[1)

copy UCLES s MOE 2010 964603IONI10

I FOI

Examiners Use

15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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15

(d) The mass in (c) is now released The mass performs simple harmonic motion

(i) State the total energy of oscillation of the mass

energy = J [1j

(il) Calculate for the mass

1 its maximum speed

speed = m S-l [2]

2 the frequency of oscillation

frequency = Hz [3]

(e) The spr ing in (d) is assumed to be light In practice the spring will have some mass

Assuming that the spring constant k is unchanged suggest and explain the effect on the freque ncy of osci llation 01 having a spring with mass

bullbull bull bull bullbull bull bull bull bull bullbull bullbullbullbullbullbull bullbullbullbullbull bullbullbullbull bullbull bullbullbullbullbullbullbullbull bullbull bull bull bullbull bull bull bull bullbull bull bull l bull bull bull bull bull bull bull bull bull bullbull bull 6 bullbullbullbullbull bull bullbullbullbull bull bull bullbull bull bull bull bullbull bull bullbullbullbull bullbullbull bull bullbullbullbullbullbullbullbull bullbull bullbullbull bullbull bull bull bull bull bull bullbullbull bull bullbull bull bull bull bullbullbull bull bullbull bull bull bull bull bull bull bull bullbull bull bull

~ ~

[2)

I For Examlllers

Use

[Turn over9646f030fNf10copy UCLES amp MOE 2010

7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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7

16

(a) Explain what is meant by a progressive transverse wave

progressive

transverse _

(3]

(b) Slate how a polarised transverse wave differs from an unpolarised transverse wave

[2)

(c) Light is polarised when it passes through a sheet of material known as polaroid

The component of the displacement of the wave in the direction of polarisation produced by the polaroid tS unaffected as the wave passes through the polaroid The -component normal to the direction of polarisation is completely absorbed by the polaroid

Two sheets of polaroid P and Q are placed close to each other Their directions of polarisation are parallel to one another as shown in Fig 71

polaroid Qpolaroid P

polarised light unpolarised

incident light amplitude A intensity I

direction of polarisation

Fig 71

copy UCLES amp MOE 2010 9646030N10

For Examiners

Use

17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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17

A parallel beam of light passes through polaroid P The beam after passing through polaroid P has amplitude A and intensity I

The beam then passes through polaroid Q

For the light transmitted through polaroid Q state

(i) the amplitude (in terms of Al

amplitude =

(ii) the in-tensity (in terms 01 l)

intensity =

(iii) the relation between the answers to (i) and (ii)

[2]

(d) The polaroid Q in (c) is now rotated about the axis of the light beam as shown in Fig 72

polaroid P

unpolarised

light

Fig 72

The plane of polaroid Q remains parallel to the plane of polaroid P

The angle between the direction of polarisation of polaroid P and of polaroid 0 is e

Complete Fig 73 to show the amplitude in terms of A and the intensity in terms 01 I for angle (I equal to 180deg 90deg and 60deg

angle 0 amplitude intensity

180deg

90deg ~ ~ ~

60deg -

Fig 73 [3]

For Examme(s

Use

copy UCLES amp MOE 2010 9646f030Nll 0 [Turn over

18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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18

(e) (i) State the principle of superposition

3

(ii) A sound wave passes into a pipe that is open at both ends 85 shown in Fig 74

wall of pioe

I incident sound wave

67cm

Fig 74

The sound wave travels along the axis of the pipe

Explain the formation 01 a stationary (standing) wave In the pipe

[2J

(1) The frequency of the sound wave in (e)(ii) is gradually increased from a low value

A loud sound is heard in the pipe for the first time at a frequency of 250 Hz

The length of the pipe is 67cm

(i) On Fig 74 mark all the positions of

1 the displacement antinodes (use the letter A)

2 the displacement nodes (use the letter N) [1 J

(ii) Calculate a value for the speed of sound in the pipe

1speed = ms- [2J

e UCLES amp MOE 2010 964603l0Nl0

For Examlne(s ~

19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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19

(g) An alternative more reliable method of measuring the speed of sound shows that the I For value in (f)(ii) is an underestimate Examine(s

Use

This underestimate cannot be attributed to the uncertainty in the measurement of either the frequency or the length of the pipe

State and explain what can be deduced about the positions of either the nodes or the antinodes of the stationary wave in the pipe

[2]

copy UCl ES amp MOE 2010 9646f030NI10 [Turn over

20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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20

8 (a) An unstable nucleus of nucleon number (mass number) A undergoes a-decay as illustrated in Fig 8 1

stationary nucleus nucleon number A

before decay 0 v V

o ~

after decay o daughter a-particle nucleus

Fig81

The nucleus is stationary before the decay

After the decay the initial speed of the a-particle is Vand that of the daughter nucleus is v

(i) State an equation in terms of A v and V to represent conservation of linear momentum for this decay

bull bull bull bull bull bull bull bull ~ v-

[2J

(il) Show that the ratio

initial kinetic energy of a-particle

initial kinetic energy of daughter nucleus

is equal to (~A - 1)

(3]

UCLES ampMOE 2010 9646103l0Nl0

For Examiners

Use

21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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21

(b) Data for the a-decay of bismuth-212 (2~~Bi) to form thallium-2G8 e~~TI ) are given in Fig 82

nucleus

bismu lh-212 thallium-208 helium-4

-

mass of nucleus u

2119459 2079374

40015 -

For Examiners

Use

Fig 82

(i) Use the data of Fig 82 to calculate to two places of decimals the energy released during the decay

energy = MeV 4]

(ii) Use your answer in (i) to show that based on the expression in (a)(ii) the energy of the a -particle is 642 MeV

[2]

964 603 01NJ10 [Turn over copy UCLES amp MOE 2010

22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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22

(e) In practice the a-particle is found to have an energy of 610MeV rather than 6 42 MeV as calculated in (b)(ii)

Suggest

(i) an explanation for the difference in energy

[1]

(ii) why it is likely that the thallium nucleus and the a-particle do not move off in opposite directions

[3)

(d) Some data for the half-lives and decay constants of bismuthmiddot212 and thallium-208 are given in Fig 83

nucleus half-life I s decay constant S-1 --__ - - - shy

bismuthmiddot212 19 x 10-4

thallium-2G8 190 37 x 10- 3

_ ~ ~

Fig 63

(I) Complete Fig 83 by calculating tne half-life of bismuthmiddot212

[1 J

copy UCLES s MOE 2010 964603lOIN10

Fot amp1Jmlners

Use

23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0

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23

(ii) Initially a radioact ive source contains N nuclei of bismuth-212 For

ExaminersAfter two hours it is found that the number of bismuth-212 nuclei has reduced to j Use approximately ~N However although bismuth-212 decays to form thallium-20B the number of thallium nuclei is much less than ~N

Suggest an explanation for these observations

[4]

copy UGLES s MOE 2010 964603l0Nl0