PHYSICSCET-2014

MODEL QUESTIONS AND ANSWERS

NUCLEAR

PHYSICS

CET-2014MODEL QUESTIONS AND ANSWERS

NUCLEAR

PHYSICS

CET-2014IMPORTANT FORMULE TO BE REMEMBERED

CET-2014IMPORTANT FORMULE TO BE REMEMBERED

CET-20141. Identify the correct statement withregards to nuclear densitya) It is directly proportional to cube rootof mass number.b) It is inversely proportional to cube rootof mass number.c) It is directly proportional to massnumber.d) It is independent of mass number.

1. Identify the correct statement withregards to nuclear densitya) It is directly proportional to cube rootof mass number.b) It is inversely proportional to cube rootof mass number.c) It is directly proportional to massnumber.d) It is independent of mass number.

CET-2014

CET-2014

2. Compared to radius of an atom,radius of the nucleus isapproximately

a) 1% b) 0.1%

c) 0.01% d) 0.0001%

2. Compared to radius of an atom,radius of the nucleus isapproximately

a) 1% b) 0.1%

c) 0.01% d) 0.0001%

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3. If mP and mN are the massesof a proton and a neutronrespectively and u denoteatomic mass unit, then

3. If mP and mN are the massesof a proton and a neutronrespectively and u denoteatomic mass unit, then

CET-2014a) mP is slightly less than 1u but mN is

slightly greater than 1ub) mP is slightly greater than 1u butmN is slightly less than 1uc) Both mP and mN are slightly greaterthan 1ud) Both mP and mN are slightly lessthan 1uANSWER: OPTION-C)

a) mP is slightly less than 1u but mN isslightly greater than 1u

b) mP is slightly greater than 1u butmN is slightly less than 1uc) Both mP and mN are slightly greaterthan 1ud) Both mP and mN are slightly lessthan 1uANSWER: OPTION-C)

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4.The smallest ratio of number ofneutrons to number of protons amongthe known nuclei is

a)1 / 2 b) 3 / 4 c) 1 d) 0

ANS: 0. Since in case of hydrogennucleus will have only one proton

4.The smallest ratio of number ofneutrons to number of protons amongthe known nuclei is

a)1 / 2 b) 3 / 4 c) 1 d) 0

ANS: 0. Since in case of hydrogennucleus will have only one proton

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5. If the radius of Al-27nucleus is 3.6fm, then theradius of Te-125 nucleus is

a) 6fm b)7.2fm

c) 10.8fm d) 8fm

5. If the radius of Al-27nucleus is 3.6fm, then theradius of Te-125 nucleus is

a) 6fm b)7.2fm

c) 10.8fm d) 8fm

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CET-2014

6. Which one among thefollowing conservationlaw is generally violated innuclear reactions

6. Which one among thefollowing conservationlaw is generally violated innuclear reactions

CET-2014a) Law of conservation of mass

b) Law of conservation of energy

c) Law of conservation of linearmomentum

d) Law of conservation of totalangular momentum

a) Law of conservation of mass

b) Law of conservation of energy

c) Law of conservation of linearmomentum

d) Law of conservation of totalangular momentum

CET-20147) Which one among the followingstatement is truea) Proton is a spin ½ particle and neutronis spin zero particle.b) Proton is a spin zero particle andneutron is spin ½ particle.c) Both proton and neutron are spin ½particles.d) Both proton and neutron are spin zeroparticles.

7) Which one among the followingstatement is truea) Proton is a spin ½ particle and neutronis spin zero particle.b) Proton is a spin zero particle andneutron is spin ½ particle.c) Both proton and neutron are spin ½particles.d) Both proton and neutron are spin zeroparticles.

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8. If EL, EM and EH denotethe binding energy pernucleon for light, moderateand heavy nuclei, then whichone among the followingstatements is true

8. If EL, EM and EH denotethe binding energy pernucleon for light, moderateand heavy nuclei, then whichone among the followingstatements is true

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La) E E and E < E

M M H

Lb) E E and E > E

M M H

Lc) E E and E < E

M M H

Lc) E E and E < E

M M H

Ld) E E and E > E

M M H

CET-20149. Nuclear force isa) Charge dependent but spinindependent.b) Charge dependent and spindependent.c) Charge independent and spinindependent.d) Charge independent and spindependent.

9. Nuclear force isa) Charge dependent but spinindependent.b) Charge dependent and spindependent.c) Charge independent and spinindependent.d) Charge independent and spindependent.

CET-201410. The mass number A of an atomis equal to difference between 5times the number of protons and 3times the number of neutrons in thenucleus. Then

a) A=2Z b) A=2Z+2c) A=2Z-2 d) A=2Z+4

10. The mass number A of an atomis equal to difference between 5times the number of protons and 3times the number of neutrons in thenucleus. Then

a) A=2Z b) A=2Z+2c) A=2Z-2 d) A=2Z+4

CET-2014

5 3

2

)

A Z N Z N Z N

A Z N Z

optiona

5 3

2

)

A Z N Z N Z N

A Z N Z

optiona

CET-201411) The graph of logR against logA,where R is the radius of the nucleusand A is the mass number is

a)a straight line with slope equal to 1b)a straight line with slope equal to 1/3c)a straight line with slope equal to 3d)a non-linear curve.

11) The graph of logR against logA,where R is the radius of the nucleusand A is the mass number is

a)a straight line with slope equal to 1b)a straight line with slope equal to 1/3c)a straight line with slope equal to 3d)a non-linear curve.

CET-20141

30

0

1log log log

3

R R A

R R A

13

0

0

1log log log

3

R R A

R R A

0

1; log

3y mx C m and C R

CET-201412) The nucleus of an element willhave half the radius as that ofsulphur-32. The element could be

a) b) c) d)

12) The nucleus of an element willhave half the radius as that ofsulphur-32. The element could be

a) b) c) d)4

2H e

8

4Be 12

6C 16

8O

CET-20141

30

R R A

1 3 33

1 1 22 1

2 2 1

132 4

2

R A RA A

R A R

.

1 3 33

1 1 22 1

2 2 1

132 4

2

R A RA A

R A R

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13) Three-fourths of the radioactivenuclei present in a radioactive sampledecay in 3/4s. The half-life of thesample is

a)1s b)1/2s c) 3/4s d) 3/8s

13) Three-fourths of the radioactivenuclei present in a radioactive sampledecay in 3/4s. The half-life of thesample is

a)1s b)1/2s c) 3/4s d) 3/8s

CET-2014

• The correct answer is option d)

2

0

1 1

4 2

3 32 ; 2

4 8

N

N

t T Therefore T T s

• The correct answer is option d)

2

0

1 1

4 2

3 32 ; 2

4 8

N

N

t T Therefore T T s

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14) A nucleus of an atom with massnumber A initially at rest, emits an α-particle with kinetic energy E. Thekinetic energy of the recoil nucleus is

a) b) c) d)

14) A nucleus of an atom with massnumber A initially at rest, emits an α-particle with kinetic energy E. Thekinetic energy of the recoil nucleus is

a) b) c) d)4

AE

A 4

AE 4

4

E

A

4E

A

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2 2

4( )

4

4 4 4

4 4 4recoil nucl

m v Mv

mv v v mass no of nucleons

M A

KE M v A

KE m v A A

Correct option is c)

2 2

4( )

4

4 4 4

4 4 4recoil nucl

m v Mv

mv v v mass no of nucleons

M A

KE M v A

KE m v A A

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15) A radioactive nucleus emits n α-particles per sec. If the number of atomsat that time instant is N, then its mean-lifeisa) b) c) d)

15) A radioactive nucleus emits n α-particles per sec. If the number of atomsat that time instant is N, then its mean-lifeisa) b) c) d)N

n

n

NNn

1

Nn

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1

dNactivity N

dt

n N

n

NN

n

Therefore the correct answer is option a)

1

dNactivity N

dt

n N

n

NN

n

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16) In nuclear reactor if 4.7 gram of isconsumed per sec and the energy released perfission of is 200MeV, then the amount ofenergy released in MeV in t second is

a) b) c) d)

16) In nuclear reactor if 4.7 gram of isconsumed per sec and the energy released perfission of is 200MeV, then the amount ofenergy released in MeV in t second is

a) b) c) d)A

40N t A4N t

N

4At N

40At

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235g of Uranium-235 contains NA atoms.Therefore 4.7g contains

Therefore the correct option is b)

200E ntMeV

4.7235 50

A AN N

n atoms

235g of Uranium-235 contains NA atoms.Therefore 4.7g contains

Therefore the correct option is b)

4.7235 50

A AN N

n atoms

200 450

AA

NE t N t

CET-2014

17) Two nuclei whose radii are in theratio 2:3. Their masses areapproximately in the ratio

a) 4:9 b) 8:27 c) 16:81 d) 2:3

17) Two nuclei whose radii are in theratio 2:3. Their masses areapproximately in the ratio

a) 4:9 b) 8:27 c) 16:81 d) 2:3

CET-2014

The correct answer is option b)

CET-201418) A radioactive element with atomic numberZ and mass number A emits an α-particle andthe daughter nucleus emits a β-particle to yieldan element with atomic number Z’ and massnumber A’ . Then

a) b)

c) d)

18) A radioactive element with atomic numberZ and mass number A emits an α-particle andthe daughter nucleus emits a β-particle to yieldan element with atomic number Z’ and massnumber A’ . Then

a) b)

c) d)

4 2A A and Z Z

4 1A A and Z Z

4 3A A and Z Z

3 1A A and Z Z

CET-201419) In successive radioactivedisintegration ,

the sequence of particles emitted are

a) b) c) d)

4

1 1 1

A A A A

Z Z Z ZX Y Y Q

19) In successive radioactivedisintegration ,

the sequence of particles emitted are

a) b) c) d)

4

1 1 1

A A A A

Z Z Z ZX Y Y Q

, , , , , , , ,

CET-2014

: 4; 2

: 4

1 1

, 4, 1 )

emission A A A Z Z Z

emission A A A A

Z Z Z Z

A Z A Z option b

The correct sequence is

: 4; 2

: 4

1 1

, 4, 1 )

emission A A A Z Z Z

emission A A A A

Z Z Z Z

A Z A Z option b

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20) A heavy nucleus at rest breaksinto two fragments which fly off withvelocities 27:8. The ratio of radii ofthe fragments

a) 9:4 b) 4:9 c) 3:2 d) 2:3

20) A heavy nucleus at rest breaksinto two fragments which fly off withvelocities 27:8. The ratio of radii ofthe fragments

a) 9:4 b) 4:9 c) 3:2 d) 2:3

CET-20141 1 2 2

1 2

2 1

1 1

2 2

1 13 31 1

2 2

8

27

8

27

8 2

27 3

m v m v

m v

m v

A m

A m

R A

R A

The correct option is d)

1 1 2 2

1 2

2 1

1 1

2 2

1 13 31 1

2 2

8

27

8

27

8 2

27 3

m v m v

m v

m v

A m

A m

R A

R A

CET-2014

21) Radius of the nucleus of an atom isequal to the sum of the radii of andthe element could be

a) b) c) d)

8

4Be 27

13Al

21) Radius of the nucleus of an atom isequal to the sum of the radii of andthe element could be

a) b) c) d)105

47Ag 70

30Zn 35

17Cl 125

52Te

CET-2014

The correct option is d)

1 2

1 1 13 3 3

0 0 1 0 2

1 1 1 1 13 3 3 3 3

1 2

3

8 27 2 3 5

5 125

R R R

R A R A R A

A A A

A

The correct option is d)

1 2

1 1 13 3 3

0 0 1 0 2

1 1 1 1 13 3 3 3 3

1 2

3

8 27 2 3 5

5 125

R R R

R A R A R A

A A A

A

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22) An α-particle of energy is scatteredthrough 1800 by a fixed uranium nucleus.The distance of closest approach is of theorder of

a)1fm b) 10fm c) 100fm d) 1000fm

22) An α-particle of energy is scatteredthrough 1800 by a fixed uranium nucleus.The distance of closest approach is of theorder of

a)1fm b) 10fm c) 100fm d) 1000fm

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0

0

29

6

199 15

6

1 92 2

4

1 92 2

4

1849 10

2.65 10184 1.6 10

9 10 10 12.65 10

initial

initial

e eKE

r

e er

KE

e

e

m fm

The correct answer is option a)

0

0

29

6

199 15

6

1 92 2

4

1 92 2

4

1849 10

2.65 10184 1.6 10

9 10 10 12.65 10

initial

initial

e eKE

r

e er

KE

e

e

m fm

CET-201423) Binding energy per nucleon for twonuclei Pn and Q2n are x and y respectively.The amount of energy released in thereaction Pn+ Pn = Q2n will be

a) 2x-y b) n.(2x-y)c) 2n.(2x-y) d) 2n.(x-y)

23) Binding energy per nucleon for twonuclei Pn and Q2n are x and y respectively.The amount of energy released in thereaction Pn+ Pn = Q2n will be

a) 2x-y b) n.(2x-y)c) 2n.(2x-y) d) 2n.(x-y)

CET-2014

tan

2 2

2

reac ts productE BE BE

n x ny

n x y

The correct answer is option d)

tan

2 2

2

reac ts productE BE BE

n x ny

n x y

CET-2014

24) A radioactive nucleus emits 3 α-particlesand 5β-particles. The ratio of number ofneutrons to that of protons will be

a) b)

c) d)

24) A radioactive nucleus emits 3 α-particlesand 5β-particles. The ratio of number ofneutrons to that of protons will be

a) b)

c) d)

6

A Z

Z

11

1

A Z

Z

1

A Z

Z

9

6

A Z

Z

CET-2014

3 4 12

3 2 5 1 1

11

1

A A A

Z Z Z

no of neutrons A Z A Z

no of protons Z Z

The correct answer is option b)

3 4 12

3 2 5 1 1

11

1

A A A

Z Z Z

no of neutrons A Z A Z

no of protons Z Z

CET-201425) The time taken by a radioactiveelement with half-life T to reduce from N0atoms to N is t. the time taken by it toreduce from N0 atoms to N / 8 is

a) 3t b) t+3T c) t+4T d) t+2T

25) The time taken by a radioactiveelement with half-life T to reduce from N0atoms to N is t. the time taken by it toreduce from N0 atoms to N / 8 is

a) 3t b) t+3T c) t+4T d) t+2T

CET-2014• Time taken by the radioactive element

to reduce from N0 to N = t• Time taken by the radioactive element

to reduce from N to N / 8 =3T• Therefore total time taken = t+3T

The correct answer is option a)

• Time taken by the radioactive elementto reduce from N0 to N = t

• Time taken by the radioactive elementto reduce from N to N / 8 =3T

• Therefore total time taken = t+3T

The correct answer is option a)

CET-2014

26) After t second, the number of atomsof a radioactive element with half-life Tdisintegrated is seven times the numberof atoms remaining. Then time t must be

a) 7T b) 8T c) 3T d) 4T

26) After t second, the number of atomsof a radioactive element with half-life Tdisintegrated is seven times the numberof atoms remaining. Then time t must be

a) 7T b) 8T c) 3T d) 4T

CET-2014

0 00 3

78 2

3

N NN N N N

t T

The correct answer is option c)

0 00 3

78 2

3

N NN N N N

t T

CET-2014

27) Singly ionized Li7 and doubly ionizedBe8 are moving in an uniform externalelectric field. The ratio of acceleration ofsingly ionized Li7 to that of doubly ionizedBe8 is

a) 7:8 b) 1:2 c) 4:7 d) 7:16

27) Singly ionized Li7 and doubly ionizedBe8 are moving in an uniform externalelectric field. The ratio of acceleration ofsingly ionized Li7 to that of doubly ionizedBe8 is

a) 7:8 b) 1:2 c) 4:7 d) 7:16

CET-2014

1 1 2 1 2

2 2 1 2 1

8 4

2 7 7

F qE ma

qa E

ma q m q A e

a q m q A e

The correct answer is option c)

1 1 2 1 2

2 2 1 2 1

8 4

2 7 7

F qE ma

qa E

ma q m q A e

a q m q A e

CET-2014

28) In the fusion reaction of two hydrogento produce a deuterium, the third particleemitted is

a)Neutrino b) antineutrinoc) electron d) positron

28) In the fusion reaction of two hydrogento produce a deuterium, the third particleemitted is

a)Neutrino b) antineutrinoc) electron d) positron

CET-2014

29) No of atoms disintegrate in half of thehalf-life time is nearly

a) 25% b) 30% c) 35% d) 40%

29) No of atoms disintegrate in half of thehalf-life time is nearly

a) 25% b) 30% c) 35% d) 40%

CET-2014

0 01 0 0

20.707 70%

1.412. sin 30%

N NN N of N

no of atoms di tegrated

The correct answer is option b)

0 01 0 0

20.707 70%

1.412. sin 30%

N NN N of N

no of atoms di tegrated

CET-201430) Three radioactive elements A, B and Cinitially contain 8N0 , 2 N0 and N0 number ofatoms respectively. Half–lives of elements A, Band C are T, 2T and 4T respectively. After atime t all three elements will left with equalnumber of atoms. Then the time t must beequal to

a) T b) 2T c) 3T d) 4T

30) Three radioactive elements A, B and Cinitially contain 8N0 , 2 N0 and N0 number ofatoms respectively. Half–lives of elements A, Band C are T, 2T and 4T respectively. After atime t all three elements will left with equalnumber of atoms. Then the time t must beequal to

a) T b) 2T c) 3T d) 4T

CET-2014

0 0 0

2 4

3 1 2 4

8 2

2 2 2

2 2 2

4

A B C

t t tT T T

t t tT T T

N N N

N N N

t T

The correct answer is option d)

0 0 0

2 4

3 1 2 4

8 2

2 2 2

2 2 2

4

A B C

t t tT T T

t t tT T T

N N N

N N N

t T