Topic 7 Revision [143 marks]

1. Which Feynman diagram shows beta-plus (β ) decay?+

2. The average binding energy per nucleon of the nucleus is 7.5 MeV. What is thetotal energy required to separate the nucleons of one nucleus of ?

A. 53 MeV

B. 60 MeV

C. 113 MeV

D. 173 MeV

158 O

158 O

3. Two pure samples of radioactive nuclides X and Y have the same initial number ofatoms. The half-life of X is .

After a time equal to 4 half-lives of X the ratio is .

What is the half-life of Y?

A.

B.

C.

D.

T 12

number of atoms of Xnumber of atoms of Y

18

0.25T 12

0.5T 12

3T 12

4T 12

The energy-level diagram for an atom that has four energy states is shown.

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4. The energy-level diagram for an atom that has four energy states is shown.

What is the number of different wavelengths in the emission spectrum of this atom?

A. 1

B. 3

C. 6

D. 7

5. A detector, placed close to a radioactive source, detects an activity of 260 Bq. Theaverage background activity at this location is 20 Bq. The radioactive nuclide has a half-life of 9 hours.

What activity is detected after 36 hours?

A. 15 Bq

B. 16 Bq

C. 20 Bq

D. 35 Bq

6. Element X decays through a series of alpha (α) and beta minus (β ) emissions. Whichseries of emissions results in an isotope of X?

A. 1α and 2βB. 1α and 4βC. 2α and 2βD. 2α and 3β

–

–

–

–

–

7. 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

Three of the fundamental forces between particles are

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8. Three of the fundamental forces between particles are

I. strong nuclear

II. weak nuclear

III. electromagnetic.

What forces are experienced by an electron?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

9. What is correct about the Higgs Boson?

A. It was predicted before it was observed.

B. It was difficult to detect because it is charged.

C. It is not part of the Standard Model.

D. It was difficult to detect because it has no mass.

10. Identify the conservation law violated in the proposed reaction.

p + p → p + n + µ

A. Strangeness

B. Lepton number

C. Charge

D. Baryon number

+ + + 0 +

11a.

The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (β–) decay to form a stableboron (B) nuclide.

Identify the missing information for this decay.

The initial number of nuclei in a pure sample of beryllium-10 is N . The graph shows how the

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11b.

The initial number of nuclei in a pure sample of beryllium-10 is N . The graph shows how thenumber of remaining beryllium nuclei in the sample varies with time.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

0

11c. After 4.3 × 10 years,

Show that the half-life of beryllium-10 is 1.4 × 10 years.

6

= 7.number of produced boron nuclei

number of remaining beryllium nuclei

6

11d. Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initiallycontains 7.6 × 10 atoms of beryllium-10. State the number of remaining beryllium-10nuclei in the sample after 2.8 × 10 years.

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An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.

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11e.

An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.

State what is meant by thermal radiation.

11f. Discuss how the frequency of the radiation emitted by a black body can be used toestimate the temperature of the body.

11g. Calculate the peak wavelength in the intensity of the radiation emitted by the icesample.

11h. Derive the units of intensity in terms of fundamental SI units.

Rutherford constructed a model of the atom based on the results of the alpha

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12a. Rutherford constructed a model of the atom based on the results of the alphaparticle scattering experiment. Describe this model.

12b.

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 –

12c. 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.–

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12d.

β decay is described by the following incomplete Feynman diagram.

Draw a labelled arrow to complete the Feynman diagram.

–

12e. Identify particle V.

13a. Identify the missing information for this decay.

13b. On the graph, sketch how the number of boron nuclei in the sample varies with time.

After 4.3 × 10 years,6

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13c. After 4.3 × 10 years,

Show that the half-life of beryllium-10 is 1.4 × 10 years.

6

= 7.number of produced boron nuclei

number of remaining beryllium nuclei

6

13d. Beryllium-10 is used to investigate ice samples from Antarctica. A sample of iceinitially contains 7.6 × 10 atoms of beryllium-10. The present activity of the sample is8.0 × 10 Bq.

Determine, in years, the age of the sample.

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13e. State what is meant by thermal radiation.

Discuss how the frequency of the radiation emitted by a black body can be used to

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13f. Discuss how the frequency of the radiation emitted by a black body can be used toestimate the temperature of the body.

13g. Calculate the peak wavelength in the intensity of the radiation emitted by the icesample.

13h. The temperature in the laboratory is higher than the temperature of the ice sample.Describe one other energy transfer that occurs between the ice sample and thelaboratory.

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14a. Bohr modified the Rutherford model by introducing the condition mvr = n . Outlinethe reason for this modification.

h2π

14b. Show that the speed v of an electron in the hydrogen atom is related to the radius r ofthe orbit by the expression

where k is the Coulomb constant.

v = √ ke2

mer

14c. Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in theground state of hydrogen is given by the following expression.

r =h2

4π2kmee2

Calculate the electron’s orbital radius in (c)(ii).

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14d. Calculate the electron’s orbital radius in (c)(ii).

14e.

Rhodium-106 ( ) decays into palladium-106 ( ) by beta minus (β ) decay. Thediagram shows some of the nuclear energy levels of rhodium-106 and palladium-106. The arrowrepresents the β decay.

Explain what may be deduced about the energy of the electron in the β decay.

10645Rh 106

46Pd –

–

–

14f. Suggest why the β decay is followed by the emission of a gamma ray photon.–

14g. Calculate the wavelength of the gamma ray photon in (d)(ii).

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15a.

A positive pion decays into a positive muon and a neutrino.

The momentum of the muon is measured to be 29.8 MeV c in a laboratory reference frame inwhich the pion is at rest. The rest mass of the muon is 105.7 MeV c and the mass of theneutrino can be assumed to be zero.

For the laboratory reference frame

write down the momentum of the neutrino.

π+ → μ+ + vμ

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15b. show that the energy of the pion is about 140 MeV.

15c. State the rest mass of the pion with an appropriate unit.

16. Which statement about atomic spectra is not true?

A. They provide evidence for discrete energy levels in atoms.

B. Emission and absorption lines of equal frequency correspond to transitions betweenthe same two energy levels.

C. Absorption lines arise when electrons gain energy.

D. Emission lines always correspond to the visible part of the electromagnetic spectrum.

What gives the total change in nuclear mass and the change in nuclear binding energy

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17. What gives the total change in nuclear mass and the change in nuclear binding energyas a result of a nuclear fusion reaction?

18. The Feynman diagram shows a particle interaction involving a W boson.

Which particles are interacting?

A. U and Y

B. W boson and Y

C. X and Y

D. U and X

–

–

19a.

The Feynman diagram shows electron capture.

Deduce that X must be an electron neutrino.

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19b. Distinguish between hadrons and leptons.

20a. State and explain the nature of the particle labelled X.

20b.

Particles can be used in scattering experiments to estimate nuclear sizes.

Outline how these experiments are carried out.

Outline why the particles must be accelerated to high energies in

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20c. Outline why the particles must be accelerated to high energies inscattering experiments.

20d. State and explain one example of a scientific analogy.

20e.

Electron diffraction experiments indicate that the nuclear radius of carbon-12 is 2.7 x 10 m.The graph shows the variation of nuclear radius with nucleon number. The nuclear radius of thecarbon-12 is shown on the graph.

Plot the position of magnesium-24 on the graph.

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20f. Draw a line on the graph, to show the variation of nuclear radius with nucleon number.

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21. Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

22. A nucleus of phosphorus (P) decays to a nucleus of silicon (Si) with the emission ofparticle X and particle Y.

What are X and Y?

3015P → 30

14Si + X + Y

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

In nuclear fission, a nucleus of element X absorbs a neutron (n) to give a nucleus of

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24. In nuclear fission, a nucleus of element X absorbs a neutron (n) to give a nucleus ofelement Y and a nucleus of element Z.

X + n → Y + Z + 2n

What is and ?magnitude of the binding energy per nucleon of Ymagnitude of the binding energy per nucleon of X

total binding energy of Y and Ztotal binding energy of X

25. 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

26. Atomic spectra are caused when a certain particle makes transitions between energylevels.What is this particle?

A. Electron

B. Proton

C. Neutron

D. Alpha particle

27. The half-life of a radioactive element is 5.0 days. A freshly-prepared sample contains128 g of this element. After how many days will there be 16 g of this element left behindin the sample?

A. 5.0 days

B. 10 days

C. 15 days

D. 20 days

28. 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

The reaction p + n → p + does not occur because it violates the conservation law+ 0 + 0

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29. The reaction p + n → p + does not occur because it violates the conservation lawof

A. electric charge.

B. baryon number.

C. lepton number.

D. strangeness.

+ 0 + π0

30. A pure sample of nuclide A and a pure sample of nuclide B have the same activity attime t = 0. Nuclide A has a half-life of T, nuclide B has a half-life of 2T.

What is when t = 4T?

A. 4

B. 2

C.

D.

activity of Aactivity of B

12

14

31. 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?

32. Which of the following leads to a paradigm shift?

A. Multi-loop circuits

B. Standing waves

C. Total internal reflection

D. Atomic spectra

33a. State the quark structures of a meson and a baryon.

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33b.

A possible decay of a lambda particle ( ) is shown by the Feynman diagram.

Explain which interaction is responsible for this decay.

Λ0

33c. Draw arrow heads on the lines representing and d in the .u π−

33d. Identify the exchange particle in this decay.

33e. Outline one benefit of international cooperation in the construction or use of high-energy particle accelerators.

The first scientists to identify alpha particles by a direct method were Rutherford and Royds.

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34a.

The first scientists to identify alpha particles by a direct method were Rutherford and Royds.They knew that radium-226 ( ) decays by alpha emission to form a nuclide known as radon(Rn).

Write down the missing values in the nuclear equation for this decay.

22686 Ra

34b. Rutherford and Royds put some pure radium-226 in a small closed cylinder A. CylinderA is fixed in the centre of a larger closed cylinder B.

At the start of the experiment all the air was removed from cylinder B. The alphaparticles combined with electrons as they moved through the wall of cylinder A to form heliumgas in cylinder B.

The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.

Rutherford and Royds expected 2.7 x 10 alpha particles to be emitted during15

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34c. Rutherford and Royds expected 2.7 x 10 alpha particles to be emitted duringthe experiment. The experiment was carried out at a temperature of 18 °C. Thevolume of cylinder B was 1.3 x 10 m and the volume of cylinder A was negligible. Calculatethe pressure of the helium gas that was collected in cylinder B.

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34d. Rutherford and Royds identified the helium gas in cylinder B by observing its emissionspectrum. Outline, with reference to atomic energy levels, how an emission spectrumis formed.

34e. The work was first reported in a peer-reviewed scientific journal. Outlinewhy Rutherford and Royds chose to publish their work in this way.

The first scientists to identify alpha particles by a direct method were Rutherford and Royds.

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35a.

The first scientists to identify alpha particles by a direct method were Rutherford and Royds.They knew that radium-226 ( ) decays by alpha emission to form a nuclide known as radon(Rn).

Write down the nuclear equation for this decay.

22686 Ra

35b.

At the start of the experiment, Rutherford and Royds put 6.2 x 10 mol of pure radium-226 in asmall closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.

The experiment lasted for 6 days. The decay constant of radium-226 is 1.4 x 10 s .

Deduce that the activity of the radium-226 is almost constant during the experiment.

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Show that about 3 x 10 alpha particles are emitted by the radium-226 in 6 days.15

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35c. Show that about 3 x 10 alpha particles are emitted by the radium-226 in 6 days.15

35d.

At the start of the experiment, all the air was removed from cylinder B. The alpha particlescombined with electrons as they moved through the wall of cylinder A to form helium gas incylinder B.

The wall of cylinder A is made from glass. Outline why this glass wall had to be verythin.

35e. The experiment was carried out at a temperature of 18 °C. The volume of cylinder Bwas 1.3 x 10 m and the volume of cylinder A was negligible. Calculate the pressureof the helium gas that was collected in cylinder B over the 6 day period. Helium is a monatomicgas.

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Photons of energy 2.3eV are incident on a low-pressure vapour. The energy levels of

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36. Photons of energy 2.3eV are incident on a low-pressure vapour. The energy levels ofthe atoms in the vapour are shown

What energy transition will occur when a photon is absorbed by the vapour?

A. –3.9eV to –1.6eV

B. –1.6eV to 0eV

C. –1.6eV to –3.9eV

D. 0eV to –1.6eV

37. 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

38. 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

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39. As quarks separate from each other within a hadron, the interaction between thembecomes larger. What is the nature of this interaction?

A. ElectrostaticB. Gravitational C. Strong nuclear D. Weak nuclear

40. 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

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

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

42a. A particular K meson has a quark structure s. State the charge on this meson.u

42b. The Feynman diagram shows the changes that occur during beta minus (β ) decay.

Label the diagram by inserting the four missing particle symbols.

–

42c. Carbon-14 (C-14) is a radioactive isotope which undergoes beta minus (β ) decay tothe stable isotope nitrogen-14 (N-14). Energy is released during this decay. Explainwhy the mass of a C-14 nucleus and the mass of a N-14 nucleus are slightly different eventhough they have the same nucleon number.

–

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43a. A particular K meson has a quark structure s. State the charge, strangeness andbaryon number for this meson.

u

43b. The Feynman diagram shows the changes that occur during beta minus (β ) decay.

Label the diagram by inserting the four missing particle symbols and the direction of the arrowsfor the decay particles.

–

C-14 decay is used to estimate the age of an old dead tree. The activity of C-14 in the

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Printed for Jyvaskylan Lyseon lukio

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

43c. C-14 decay is used to estimate the age of an old dead tree. The activity of C-14 in thedead tree is determined to have fallen to 21% of its original value. C-14 has a half-lifeof 5700 years.

(i) Explain why the activity of C-14 in the dead tree decreases with time.

(ii) Calculate, in years, the age of the dead tree. Give your answer to an appropriate number ofsignificant figures.

[4 marks]