Nuclear Structure and Decay [100marks]

1. In the Rutherford-Geiger-Marsden scattering experiment it was observed that a smallpercentage of alpha particles are deflected through large angles.

Three features of the atom are

I. the nucleus is positively charged

II. the nucleus contains neutrons

III. the nucleus is much smaller than the atom.

Which features can be inferred from the observation?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

2. The following decay is observed.

µ → e + v + X

What is particle X?

A. γB.

C. Z

D. v

− −µ

v̄e

0

e

The graph shows the variation of the natural log of activity, ln (activity), against time for

[1 mark]

[1 mark]

3. The graph shows the variation of the natural log of activity, ln (activity), against time fora radioactive nuclide.

What is the decay constant, in days , of the radioactive nuclide?

A.

B.

C. 3

D. 6

–1

16

13

4. Two radioactive nuclides, X and Y, have half-lives of 50 s and 100 s respectively. Attime t = 0 samples of X and Y contain the same number of nuclei.

What is when t = 200 s?

A. 4

B. 2

C.

D.

number of nuclei of X undecayednumber of nuclei of Y undecayed

12

14

5. Alpha particles with energy E are directed at nuclei with atomic number Z. Smalldeviations from the predictions of the Rutherford scattering model are observed.

Which change in E and which change in Z is most likely to result in greater deviations from theRutherford scattering model?

Samples of different radioactive nuclides have equal numbers of nuclei. Which graph

[1 mark]

[1 mark]

[1 mark]

6. Samples of different radioactive nuclides have equal numbers of nuclei. Which graphshows the relationship between the half-life and the activity A for the samples?t 1

2

7. The diameter of a silver-108 ( ) nucleus is approximately three times that of thediameter of a nucleus of

A.

B.

C.

D.

10847 Ag

42He.73Li.115 B.2010Ne.

8. What can be used to calculate the probability of finding an electron in a particular regionof space?

A.

B.

C. The magnitude of the wave function

D. The magnitude of the (wave function)

Planck's constant4π×uncertainty in energy

Planck's constant4π×uncertainty in speed

2

9. Electron capture can be represented by the equation

p + e → X + Y.

What are X and Y?

–

In the Bohr model for hydrogen an electron in the ground state has orbit radius r and

[1 mark]

[1 mark]

[1 mark]

[1 mark]

10. In the Bohr model for hydrogen an electron in the ground state has orbit radius r andspeed v. In the first excited state the electron has orbit radius 4 r. What is the speed ofthe electron in the first excited state?

A.

B.

C.

D.

v2v4v8v

16

11. A radioactive element has decay constant (expressed in s ). The number of nuclei ofthis element at t = 0 is N. What is the expected number of nuclei that will have decayedafter 1 s?

A.

B.

C.

D.

λ –1

N (1 − e−λ)Nλ

Ne−λ

λN

12. Which of the following lists the particles emitted during radioactive decay in order ofincreasing ionizing power?

A. γ, β, αB. β, α, γ C. α, γ, βD. α, β, γ

13. An electron of mass m has an uncertainty in its position r. What is the uncertainty in thespeed of this electron?

A.

B.

C.

D.

h4πr

hr4πm

hm4πr

h4πmr

14. Which of the following, observed during a radioactive-decay experiment, provideevidence for the existence of nuclear energy levels?

I. The spectrum of alpha particle energiesII. The spectrum of beta particle energies III. The spectrum of gamma ray energies

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

What is the charge on an electron antineutrino and during what process is an electron

[1 mark]

[1 mark]

[1 mark]

[1 mark]

[1 mark]

15. What is the charge on an electron antineutrino and during what process is an electronantineutrino produced?

16a. Rutherford constructed a model of the atom based on the results of the alphaparticle scattering experiment. Describe this model.

16b.

Rhodium-106 ( ) decays into palladium-106 ( ) by beta minus (β ) decay.

The binding energy per nucleon of rhodium is 8.521 MeV and that of palladium is 8.550 MeV.

State what is meant by the binding energy of a nucleus.

10645Rh 106

46Pd –

16c. Show that the energy released in the β decay of rhodium is about 3 MeV.–

β decay is described by the following incomplete Feynman diagram.–

[1 mark]

[2 marks]

[1 mark]

[1 mark]

16d.

β decay is described by the following incomplete Feynman diagram.

Draw a labelled arrow to complete the Feynman diagram.

–

16e. Identify particle V.

This question is in two parts. Part 1 is about the oscillation of a mass. Part 2 is about nuclear

[1 mark]

[1 mark]

17a.

This question is in two parts. Part 1 is about the oscillation of a mass. Part 2 is about nuclearfission.

Part 1 Oscillation of a mass

A mass of 0.80 kg rests on a frictionless surface and is connected to two identical springs bothof which are fixed at their other ends. A force of 0.030 N is required to extend or compress eachspring by 1.0 mm. When the mass is at rest in the centre of the arrangement, the springs are notextended.

The mass is displaced to the right by 60 mm and released.

Determine the acceleration of the mass at the moment of release.

17b. Outline why the mass subsequently performs simple harmonic motion (SHM).

Calculate the period of oscillation of the mass.

[3 marks]

[2 marks]

17c. Calculate the period of oscillation of the mass.

17d.

The motion of an ion in a crystal lattice can be modelled using the mass–spring arrangement.The inter-atomic forces may be modelled as forces due to springs as in the arrangement shown.

The frequency of vibration of a particular ion is and the mass of the ion is . The amplitude of vibration of the ion is .

Estimate the maximum kinetic energy of the ion.

7 × 1012 Hz5 × 10−26 kg 1 × 10−11 m

17e. On the axes, draw a graph to show the variation with time of the kinetic energy ofmass and the elastic potential energy stored in the springs. You should addappropriate values to the axes, showing the variation over one period.

Calculate the wavelength of an infrared wave with a frequency equal to that of the

[2 marks]

[2 marks]

[3 marks]

17f. Calculate the wavelength of an infrared wave with a frequency equal to that of themodel in (b).

17g.

Part 2 Nuclear fission

A reaction that takes place in the core of a particular nuclear reactor is as shown.

In the nuclear reactor, fissions take place every second. Each fission gives rise to200 MeV of energy that is available for conversion to electrical energy. The overall efficiency ofthe nuclear power station is 32%.

Determine the mass of U-235 that undergoes fission in the reactor every day.

23592 U +1

0 n →14456 Ba +89

36 Kr + 310n

9.5 × 1019

17h. Calculate the power output of the nuclear power station.

In addition to the U-235, the nuclear reactor contains a moderator and control rods. Explain the

[1 mark]

[3 marks]

[2 marks]

17i.

In addition to the U-235, the nuclear reactor contains a moderator and control rods. Explain thefunction of the

moderator.

17j. control rods.

18a.

This question is about nuclear reactions.

A reaction that takes place in the core of a particular nuclear reactor is as shown.

State the nature of X.

23592 U + X →144

56 Ba +8936 Kr + 3X

State one form of energy that is instantaneously released in the reaction.

[3 marks]

[2 marks]

[1 mark]

18b. State one form of energy that is instantaneously released in the reaction.

18c.

In the nuclear reactor, fissions take place every second. Each fission gives rise to200 MeV of energy that is available for conversion to electrical energy. The overall efficiency ofthe nuclear power station is 32%.

Determine the mass of U-235 that undergoes fission in the reactor every day.

9.5 × 1019

18d. Calculate the power output of the nuclear power station.

In addition to the U-235, the nuclear reactor contains graphite that acts as a

[1 mark]

[3 marks]

[2 marks]

18e. In addition to the U-235, the nuclear reactor contains graphite that acts as amoderator. Explain the function of the moderator.

18f. Outline how energy released in the nuclear reactor is transformed to electrical energy.

19a.

This question is about binding energy and mass defect.

State what is meant by mass defect.

(i) Data for this question is given below.

[3 marks]

[3 marks]

[1 mark]

19b. (i) Data for this question is given below.

Binding energy per nucleon for deuterium is 1.1 MeV.

Binding energy per nucleon for helium-3 is 2.6 MeV.

Using the data, calculate the energy change in the following reaction.

(ii) The cross on the grid shows the binding energy per nucleon and nucleon number A of thenuclide nickel-62.

On the grid, sketch a graph to show how the average binding energy per nucleon varies withnucleon number A.

(iii) State and explain, with reference to your sketch graph, whether energy is released orabsorbed in the reaction in (b)(i).

(21H)

(32He)

21H +1

1 H →32 He + γ

This question is about nuclear reactions.

[6 marks]

20a.

This question is about nuclear reactions.

The nuclide U-235 is an isotope of uranium. A nucleus of U-235 undergoesradioactive decay to a nucleus of thorium-231 (Th-231). The proton number ofuranium is 92.

(i) State what is meant by the terms nuclide and isotope.

1. Nuclide:

Isotope:

2.

(ii) One of the particles produced in the decay of a nucleus of U-235 is a gamma photon. Statethe name of another particle that is also produced.

20b. The daughter nuclei of U-235 undergo radioactive decay until eventually a stableisotope of lead is reached.

Explain why the nuclei of U-235 are unstable whereas the nuclei of the lead are stable.

Nuclei of U-235 bombarded with low energy neutrons can undergo nuclear

[3 marks]

[3 marks]

20c. Nuclei of U-235 bombarded with low energy neutrons can undergo nuclearfission. The nuclear reaction equation for a particular fission is shown below.

Show, using the following data, that the kinetic energy of the fission products is about 200 MeV.

Mass of nucleus of U-235 = 235.04393 uMass of nucleus of Ba-144 = 143.922952 uMass of nucleus of Kr-89 = 88.91763 uMass of neutron = 1.00867 u

10n + 235

92 U → 14456 Ba + 89

36Kr + 310n

21a.

Part 2 Nuclear physics

(i) Define binding energy of a nucleus.

(ii) The mass of a nucleus of plutonium is 238.990396 u. Deduce that the bindingenergy per nucleon for plutonium is 7.6 MeV.

(23994 Pu)

The graph shows the variation with nucleon number A of the binding energy per

[3 marks]

[4 marks]

21b. The graph shows the variation with nucleon number A of the binding energy pernucleon.

Plutonium undergoes nuclear fission according to the reaction given below.

(i) Calculate the number x of neutrons produced.

(ii) Use the graph to estimate the energy released in this reaction.

(23994 Pu)

23994 Pu + 1

0n → 9138Sr + 146

56 Ba + x10n

21c. Stable nuclei with a mass number greater than about 20, contain more neutronsthan protons. By reference to the properties of the nuclear force and of theelectrostatic force, suggest an explanation for this observation.

[3 marks]

[4 marks]

22. A graph of the variation of average binding energy per nucleon with nucleon numberhas a maximum. What is indicated by the region around the maximum?

A. The position below which radioactive decay cannot occur

B. The region in which fission is most likely to occur

C. The position where the most stable nuclides are found

D. The region in which fusion is most likely to occur

23. What is the definition of the unified atomic mass unit?

A. the mass of a neutral atom of carbon-12

B. The mass of a neutral atom of hydrogen-1

C. the mass of a nucleus of carbon-12

D. The mass of a nucleus of hydrogen-1

112

112

24. What is the energy equivalent to the mass of one proton?

A. 9.38 × (3 × 10 ) × 10 J

B. 9.38 × (3 × 10 ) × 1.6 × 10 J

C. J

D. 9.38 × 10 × 1.6 × 10 J

8 2 6

8 2 –19

9.38×108

1.6×10−19

8 –19

25. The binding energy per nucleon of is 6 MeV. What is the energy required toseparate the nucleons of this nucleus?

A. 24 MeV

B. 42 MeV

C. 66 MeV

D. 90 MeV

114 Be

26. In the nuclear reaction X + Y → Z + W, involving nuclides X, Y, Z and W, energy isreleased. Which is correct about the masses (M) and the binding energies ( BE) of thenuclides?

14

[1 mark]

[1 mark]

[1 mark]

[1 mark]

[1 mark]

27. When an alpha particle collides with a nucleus of nitrogen-14 , a nucleus X canbe produced together with a proton. What is X?

A.

B.

C.

D.

(147 N)

188 X178 X189 X179 X

28. The mass defect for deuterium is 4×10 kg. What is the binding energy of deuterium?

A. 4×10 eV

B. 8×10 eV

C. 2×10 eV

D. 2×10 eV

–30

–7

–2

6

12

29. Patterns in graphs help scientists make predictions. What can be deduced from a graphof neutron number versus proton number for all stable nuclides?

A. The short-range nature of the strong nuclear force

B. The increase of the binding energy per nucleon with proton number

C. The existence of quarks and leptons

D. The existence of alpha decay

30. Bismuth-210 is a radioactive isotope that decays as follows.

What are the mass number and proton number of Y?

(21083 Bi)

21083 Bi −→ X → Y

β− α

31. The nuclear reaction would best be described as

A. alpha decay.B. nuclear fission.C. nuclear fusion.D. neutron capture.

21H + 3

1H → 42He+1

0n

The graph shows the relationship between binding energy per nucleon and nucleon

[1 mark]

[1 mark]

[1 mark]

[1 mark]

[1 mark]

32. The graph shows the relationship between binding energy per nucleon and nucleonnumber. In which region are nuclei most stable?

33. A unit in which mass defect can be measured is

A. MeV.B. MeV c .C. MeV c .D. MeV per nucleon.

–1

–2

34. A fission reaction for uranium is

where n is the neutron. Which of the following gives the value of the nucleon number A andproton number Z for the krypton (Kr)?

23592 U + n → 141

56 Ba + AZKr + 3n

The nuclear equation below is an example of the transmutation of mercury into gold.

[1 mark]

[1 mark]

[1 mark]

Printed for Skyline High School

© International Baccalaureate Organization 2019 International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®

35. The nuclear equation below is an example of the transmutation of mercury into gold.

The particle X is a

1. gamma-ray photon.

2. helium nucleus.

3. proton.

4. neutron.

21H + 199

80 Hg → 19779 Au + X

36. A sample contains an amount of radioactive material with a half-life of 3.5 days. After 2weeks the fraction of the radioactive material remaining is

A. 94 %.

B. 25 %.

C. 6 %.

D. 0 %.

37. The rest mass of a proton is . The energy of a proton at rest is

A.

B.

C.

D.

938 MeV c−2

9.38 J

9.38 × 108 × (3 × 108)2 J

9.38 × 108 eV

9.38 × 108 × (3 × 108)2 eV

[1 mark]

[1 mark]

[1 mark]