atomic and nuclear option sl

8/17/2019 Atomic and Nuclear Option SL

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1. This question is about the photoelectric effect.

In an experiment to investigate the photoelectric effect, light of frequency f is incident on the

metal surface A, shown in the diagram below. A potential difference is applied between A and B.

The photoelectric current is measured by a sensitive ammeter. (ote! the complete electrical

circuit is not shown."

#hen the frequency of the light is reduced to a certain value, the current measured by the

ammeter becomes $ero. %xplain how %instein&s photoelectric theory accounts for this

observation.

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IB Questionbank Physics 1


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2. This question is about atomic spectra.

'iagram shows some of the energy levels of the hydrogen atom. 'iagram ) is a representation

of part of the emission spectrum of atomic hydrogen. The lines shown represent transitions

involving the *+.- e level.

(a" 'educe that the energy of a photon of wavelength /01 nm is .12 e.

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(b" (i" 3n diagram 1, draw an arrow to show the electron transition between energy

levels that gives rise to the emission of a photon of wavelength /01 nm. 4abel this

arrow with the letter A.(1)

(ii" 3n diagram 1, draw arrows to show the electron transitions between energy levels



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that give rise to the emission of photons of wavelengths 11 nm, +0 nm and

nm.

4abel these arrows with the letters B, 5 and '.(1)

(c" %xplain why the lines in the emission spectrum of atomic hydrogen, shown in diagram 2, become closer together as the wavelength of the emitted photons decreases.

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(Total 8 marks)

3. This question is about radioactive decay.

Iodine6) (I6)" is an unstable radioisotope with proton number 0+. It undergoes beta plus

decay to form an isotope of tellurium (Te".

(a" 7tate the reaction for the decay of the I6) nuclide.

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(b" The graph below shows how the activity of a sample of iodine6) changes with time.

(i" 7tate the half6life of iodine6)

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(1)

(ii" 5alculate the activity of the sample at ) days.

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(iii" A sample of an un8nown radioisotope has a half6life twice that of iodine6) and

the same initial activity as the sample of iodine6). 3n the axes opposite, draw a

graph to show how the activity of the sample would change with time.

4abel this graph 9.(1)

(iv" A second sample of iodine6) has half the initial activity as the original sample of

iodine6). 3n the axes opposite, draw a graph to show how the activity of this

sample would change with time. 4abel this graph :.(1)

(Total 8 marks)


(a" 7tate what is meant by the photoelectric effect.

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(b" 4ight of frequency 1.; < -

=$ is incident on the surface of a metal in a photocell.

The surface area of the metal is 2.- < - */

m) and the intensity of the light is

. < - *+

# m *)

.

(i" 'educe that the maximum possible photoelectric current in the photocell is ).; nA.

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(ii" The maximum 8inetic energy of photoelectrons released from the metal surface is

.) e. 5alculate the value of the wor8 function of the metal.

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(Total 5 marks)

5. This question is about the de Broglie hypothesis.

(a" 7tate the de Broglie hypothesis.

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(b" 'etermine the de Broglie wavelength of a proton that has been accelerated from rest

through a potential difference of .) 8.

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(c" %xplain why a precise 8nowledge of the de Broglie wavelength of the proton implies that

its position cannot be observed.

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(Total 6 marks)


itrogen6+ (

(+

; " is an isotope that is used in medical diagnosis. The decay constant of

nitrogen6+ is .) < - *+

s *

.

(a" (i" 'efine decay constant .

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(ii" A sample of nitrogen6+ has an initial activity of 1-- Bq. The sample cannot be

used for diagnostic purposes if its activity becomes less than 0- Bq. 'etermine

the time it ta8es for the activity of the sample to fall to 0- Bq.

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(b" (i" 5alculate the half6life of nitrogen6+

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(ii" 3utline how the half6life of a sample of nitrogen6+ can be measured in a

laboratory.

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(c" itrogen6+ undergoes >? decay. 3utline the experimental evidence that suggests another

particle, the neutrino, is also emitted in the decay.

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(Total 9 marks)

7. This question is about the wave nature of matter.



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(a" 'escribe the de Broglie hypothesis.

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(2)

(b" 3utline an experiment to verify the de Broglie hypothesis.

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(c" 7how that the de Broglie wavelength of electrons accelerated from rest through a

potential difference of 0- is .-


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9. This question is about β ? (positron" decay.

(a" In a β ? decay, a positron is emitted along with a neutrino, and a 6ray photon.

Although the energy spectrum for 6rays involved is discrete, the energy spectrum for the

positrons is continuous.

(i" 7tate the difference between a discrete energy spectrum and a continuous energy

spectrum.

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(ii" %xplain how the existence of the neutrino accounts for the continuous nature of the

positron energy spectrum.

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(b" 7odium6)) is a radioisotope used in nuclear medicine that undergoes β ? decay.

The half6life of sodium6)) is )./ years.

A sample of sodium6)) has an initial activity of /.) < -2 Bq.

(i" 'efine decay constant.

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(ii" 5alculate the decay constant of sodium6)).

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(iii" 5alculate the activity of the sample of sodium6)) after 1.- years.



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(Total 8 marks)

10. This question is about fundamental interactions.

(a" 7tate an exchange particle for

(i" the wea8 interaction.

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(ii" the electromagnetic interaction.

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(b" 5omment, with reference to the mass of the exchange particles, on the range of the wea8

and electromagnetic interactions.

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(c" 'escribe the process represented by the Ceynman diagram below.

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(d" 7tate what is meant by a virtual particle.

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(e" %xplain how the =eisenberg uncertainty principle for energy and time applies to the

interaction in (c".

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(f" The uncertainty in the time for the electromagnetic interaction between two electrons is

./ < - */

s. 'etermine the uncertainty in the energy of the virtual photon.

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(Total 10 marks)


(a" In the photoelectric effect, electrons are emitted from a metal surface almost immediately

after light is incident on the surface, i.e. without any time delay. %xplain this observationwith reference to %instein&s theory of the photoelectric effect.

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(b" The graph shows the variation with incident light frequency f of the maximum 8inetic

energy E D of the emitted electrons.

Ese the graph to

(i" estimate the wor8 function of the metal surface.

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(ii" calculate the maximum speed of the emitted electrons for incident light of

frequency 0.- < -0

=$.

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(Total 6 marks)



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12. This question is about quantum aspects of the electron.

(a" The energy of electrons in atoms is said to be quanti$ed. 7tate what is meant by quanti$ed

energy.

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(b" An electron that is confined to move in a region of length L can only have energies given

by the equation

E n F)

))

G1 mL

nh

where n is a positive integer.

Cor L F .- < - *-

m, use the equation above to

(i" calculate that the smallest difference between the allowed energies of the electron

is 0.1 < - *1

H.

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(ii" determine the wavelength of the photon whose energy is 0.1 < - *1

H.

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(c" art of the emission spectrum of hydrogen is shown in the diagram.

7uggest whether this spectrum can be explained by the model in (b".

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(Total 8 marks)


(a" The decay constant for a particular isotope is λ F -.-1 s *

. A sample of the isotope

initially contains ).- < -)

nuclei of this isotope.

(i" 'efine decay constant .

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(ii" %stimate the number of nuclei that will decay in the first second.

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(b" The graph shows the variation with time t of the activity A of a sample containing

radioactive material that consists of two different isotopes. %ach isotope decays into a

stable daughter isotope.

(i" Ese the graph to explain how it may be deduced that the sample contains more than

one isotope.

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(ii" 3ne of the isotopes in the sample has a half6life that is shorter than -.)- s. Ese the

graph to estimate the half6life of the other isotope. %xplain your wor8ing.

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(Total 6 marks)

14. This question is about wave*particle duality.

(a" In the photoelectric effect, electrons are not emitted from the surface of a metal if the

frequency of the incident light is below a certain value called the threshold frequency.

(i" %xplain, with reference to the %instein model of the photoelectric effect, the

existence of the threshold frequency.

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(4)

(ii" 7tate, with reference to your answer in (a"(i", the reason why the threshold

frequency is different for different metals.

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(b" 4ight of frequency .- < -0

=$ is incident on the surface of a metal. The wor8 function



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of the metal is +.) < - *2

H.

(i" 7how that the maximum 8inetic energy of the emitted electrons is +. < - *2

H.

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(ii" 'etermine the de Broglie wavelength of the electrons in (b"(i".

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(Total 10 marks)



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15. This question is about the spectrum of atomic hydrogen.

(a" The diagram represents the principal lines in the visible spectrum of atomic hydrogen.

3utline how the spectrum can be produced and observed in the laboratory.

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(b" 5alculate the difference in energy in e between the energy levels in the hydrogen atom

that give rise to the red line in the spectrum.

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(Total 5 marks)


(a" A nucleus of a radioactive isotope of gold (Au612" emits a neutrino in the decay to a

nucleus of an isotope of platinum (t".

In the nuclear reaction equation below, state the name of the particle X and identify the

nucleon number A and proton number Z of the nucleus of the isotope of platinum.

v X A Z ++→ tAu12;2

X ! ................................................................................................................................

A! ................................................................................................................................

Z ! ................................................................................................................................(2)

(b" The half6life of Au612 is 1.1 minutes. A freshly prepared sample of the isotope has an

activity of ) Bq.

(i" 5alculate the decay constant of Au612.

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(ii" 'etermine the activity of the sample after ).- min.

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(Total 5 marks)


(a" In the photoelectric effect, electrons are emitted from a metallic surface only if thewavelength of the light incident on the surface is below a certain value called the

threshold wavelength.

%xplain this observation.

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(b" A monochromatic source of power +.- # emits light of wavelength ./- < - *;

m. All of

the light is incident on a metal surface and causes electrons to be emitted at a rate of

.- < --

s *

. The threshold wavelength of the metal is 0.0- < - *;

m.

5alculate the

(i" photoelectric current.

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(ii" wor8 function of the metal.

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(iii" the ratio of the rate of electron emission to the rate at which the photons are

incident on the metal.

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(c" 4ight from a different source is incident on the metal in (b". The new source has power

/.- # and emits light of wavelength 2.-- < - *;

m.

7tate the effect of these changes, if any, on your answer to (b"(i".

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(Total 10 marks)



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18. This question is about quantum aspects of the electron.

The graph shows the variation with distance x of the wavefunction Ψ of an electron at a

particular instant of time. The electron is confined within a region of length ).- < - *-

m.

(a" 7tate what is meant by the wavefunction of an electron.

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(b" Esing data from the graph estimate, for this electron,

(i" its momentum.

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(ii" the uncertainty in its momentum.

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(Total 5 marks)

19. This question is about nuclear energy levels and radioactive decay.

The diagram shows some of the nuclear energy levels of the boron isotope B()

0 and the carbon

isotope 5()

/ . 'ifferences in energy between the levels are indicated on the diagram. A particular

beta decay of boron and a gamma decay of carbon are mar8ed on the diagram.

(a" 5alculate the wavelength of the photon emitted in the gamma decay.

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(b" 5alculate the maximum 8inetic energy of the electron emitted in the beta decay indicated.

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(c" %xplain why the electrons emitted in the indicated beta decay of boron do not always

have the 8inetic energy calculated in (b".

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(Total 5 marks)


(a" A clean metal surface in a vacuum is illuminated with monochromatic light, resulting in

the emission of electrons from the surface.



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(i" 3n the axes, s8etch a graph to show how the maximum 8inetic energy K of the

electron varies with the intensity I of the light.

(1)

(ii" %xplain the shape of the graph you have drawn.

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(b" The wavelength of the incident light in (a" is -- nm. The maximum 8inetic energy of the

emitted electrons is ). e. 'etermine the wor8 function of the metal.

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(Total 7 marks)



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21. This question is about the wave nature of matter and quantum energy states.

(a" 'escribe what is meant by the de Broglie hypothesis.

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(b" An electron is confined to one dimension in a JboxK of length L. The de Broglie waves

associated with the particle form standing waves in the box with wavelengths given by

n

L)

where n is F , ), +, etc.

7how that the energy levels E n for the particle are given by E n F"1( )

))

mL

hn

where h is

lanc8&s constant.

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(c" The electron ma8es a transition from the energy state given by n F to n F ). The length

L F .+ < - *2

m. 5alculate the

(i" energy of the photon emitted.

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(ii" wavelength of the photon emitted.



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(2)(Total 9 marks)

22. This question is about nuclear physics and radioactive decay.

(a" 'efine the decay constant of a radioactive nuclide.

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(b" (i" lutonium6)+2 (u6)+2" has a half6life of ). < - years. 7how that the decay

constant of u6)+2 is approximately + < - *0

year *

.

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(ii" 5alculate the time ta8en for the activity of a freshly6prepared sample of u6)+2 to

fall to -. L of its initial value.

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(Total 4 marks)



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23. This question is about quantum physics and electrons.

(a" hotons of frequency ).< -0

=$ stri8e the surface of uranium and electrons are emitted

from the surface. The wor8 function of uranium is +./ e.

(i" 7how that the maximum 8inetic energy of the emitted electrons is about 0.- e.

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(ii" %xplain what change to this energy would occur if the light intensity was doubled.

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(b" The de Broglie wavelength of an electron with energy 0.- 8e is M.

(i" 'etermine M.

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(ii" A student ma8es the statement JThe electron wavelength is not real, it is Nust a

mathematical construction. %lectrons are particles and never waves.K 3utline

evidence which suggests that the student&s statement is not correct.

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(c" 3utline how the

(i" Jelectron in a boxK model accounts for the existence of discrete energy levels in the

hydrogen atom.

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(ii" line spectra of atomic hydrogen provide evidence for electron energy levels in the

atom.

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(Total 14 marks)



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A nucleus of the isotope iodine6) (I6)" (proton number 0+" may undergo positive beta

decay to a nucleus of an isotope 9.

(a" 7tate the nuclear reaction equation for this decay.

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(b" The half6life of iodine6) is .) days. A freshly prepared sample of the isotope has an

activity of 1- Bq. 'etermine the activity of the sample after /.- days.

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(Total 6 marks)

25. This question is about wave6particle duality.

(a" 'escribe the de Broglie hypothesis.

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(2)



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(b" An electron is accelerated from rest through a potential difference of )0- . 'etermine

the associated de Broglie wavelength of the accelerated electron.

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(Total 6 marks)

26. This question is about line spectra.

(a" 4ight is emitted from a gas discharge tube. 3utline briefly how the visible line spectrum

of this light may be obtained.

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(b" The table below gives information relating to three of the wavelengths in the line

spectrum of atomic hydrogen.

Wavelength 10!9

m "hoton energ# 10!19

$

11- .-/

/0/ +.-+

1/ .-2

'educe that the photon energy for the wavelength of 1/ × -O2

m is .-2 × -O2

H.

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(c" The diagram below shows two of the energy levels of the hydrogen atom, using data from



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the table above. An electron transition between these levels is also shown.

(i" 3n the diagram above, construct the other energy level needed to produce the

energy changes shown in the table above.

(1)

(ii" 'raw labelled arrows to represent the energy changes for the two other

wavelengths shown in the table above.(1)

(Total 6 marks)


In an experiment to investigate the photoelectric effect, light of frequency f is incident on the

metal surface A shown in the diagram below. A potential difference is applied between A andelectrode B. The photoelectric current is measured by the microammeter. ( Note: the complete

electrical circit is not sho!n."

(a" Indicate on the diagram the polarity of A and of B.(1)



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(b" The frequency f of the light is reduced and it is found that there is a frequency f -, the

threshold frequency, below which the microammeter does not indicate a current. %xplain

how %instein&s photoelectric theory accounts for this observation.

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(c" The potential difference between A and B is now reversed. Cor a particular frequency of

the light, the potential difference is changed until there is $ero current in the circuit. The

graph below shows the variation of frequency f of the light with the potential difference,

# s, for $ero current.

%xplaining your wor8ing, use the graph to determine the

(i" threshold frequency.

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(ii" wor8 function, in e, of the metal.

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(Total 8 marks)

atomic and nuclear option sl

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