1. 1
   Thorium-232, $^{232}_{90}\mathrm{Th}$, found in some granite rocks, decays by alpha emission to an isotope of radium. This radium nuclide then decays by β⁻ emission to an isotope of actinium (proton number 89).

   (a)

   What are the nucleon number and proton number of the radium nuclide formed by the alpha decay?

   [1 mark]

   • AA = 230, Z = 88
   • BA = 228, Z = 92
   • CA = 232, Z = 89
   • DA = 228, Z = 88

   (b)

   Which particles are emitted when the radium nuclide undergoes β⁻ decay?

   [1 mark]

   • AAn electron and a neutrino
   • BAn electron and an antineutrino
   • CA positron and a neutrino
   • DA helium nucleus and a gamma photon

   (c)

   Write the nuclear equation for the β⁻ decay of the radium nuclide.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The mass of a helium-4 nucleus is 4.001506 u. The mass of a free proton is 1.007276 u and the mass of a free neutron is 1.008665 u.

   (a)

   What is the mass defect of the helium-4 nucleus?

   [1 mark]

   • A0.0076 u
   • B4.0015 u
   • C0.0304 u
   • D4.0319 u

   (b)

   Which nuclide has the greatest binding energy per nucleon?

   [1 mark]

   • A$^{56}_{26}\mathrm{Fe}$
   • B$^{2}_{1}\mathrm{H}$
   • C$^{4}_{2}\mathrm{He}$
   • D$^{235}_{92}\mathrm{U}$

   (c)

   Calculate the binding energy per nucleon of helium-4, in MeV.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student uses a Geiger–Müller tube and counter to investigate a small radioactive sample. With the sample removed, the average count rate over 10 minutes is 30 counts per minute. With the sample in place, the recorded count rates are: 830 counts per minute at the start; 430 counts per minute after 3.0 hours; 230 counts per minute after 6.0 hours; 130 counts per minute after 9.0 hours; and 80 counts per minute after 12.0 hours.

   (a)

   Determine the half-life of the sample.

   [3 marks]

   (b)

   The student predicts that after 24 hours the counter will record no counts at all. Evaluate this prediction, including an estimate of the recorded count rate after 18 hours.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A factory makes aluminium sheet with a target thickness of 1.0 mm. To monitor the thickness continuously, a radioactive source is placed on one side of the moving sheet and a detector on the other side, and the count rate is recorded. Three sources are available: polonium-210, an alpha emitter with a half-life of 138 days; strontium-90, a beta emitter with a half-life of 29 years; and cobalt-60, a gamma emitter with a half-life of 5.3 years. Beta particles from the strontium source are partly absorbed by 1 mm of aluminium, and are fully absorbed by about 5 mm.

   (a)

   Compare the ionising and penetrating abilities of alpha, beta and gamma radiation, and explain the differences in terms of the nature of each radiation.

   [6 marks]

   (b)

   Evaluate which of the three sources is most suitable for monitoring the thickness of the aluminium sheet.

   [6 marks]

   Total for question 4: 12 marks

End of questions