Nuclear instabilityAQA A-Level Physics: Subtopic test

1. 1
   Stable nuclei lie in a narrow band on a graph of neutron number N against proton number Z. For light nuclei the band follows the line N = Z, and for heavier nuclei it curves towards larger values of N than Z. Nuclei that lie outside the band are unstable and decay.

   (a)

   Carbon-14 (Z = 6, N = 8) lies above the stable band. Which decay mode is most likely?

   [1 mark]

   • AAlpha decay
   • Bβ⁻ decay
   • Cβ⁺ decay
   • DElectron capture

   (b)

   Which row correctly gives the changes in N and Z in β⁺ decay?

   [1 mark]

   • AN decreases by 1 and Z increases by 1
   • BN decreases by 2 and Z decreases by 2
   • CN and Z do not change
   • DN increases by 1 and Z decreases by 1

   (c)

   Uranium-238 is a heavy nucleus which decays by alpha emission. Explain, using the graph, why alpha emission suits heavy nuclei and what effect it has on N and Z.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Potassium-40 (⁴⁰₁₉K) is a radioactive isotope found in rocks and in the human body. It decays in two ways: by β⁻ emission to calcium-40, and by electron capture to argon-40.

   (a)

   Which equation correctly represents the β⁻ decay of potassium-40?

   [1 mark]

   • A$^{40}_{19}\mathrm{K} \to {}^{40}_{20}\mathrm{Ca} + {}^{0}_{-1}\mathrm{e} + \bar{\nu}_e$
   • B$^{40}_{19}\mathrm{K} \to {}^{40}_{18}\mathrm{Ar} + {}^{0}_{+1}\mathrm{e} + \nu_e$
   • C$^{40}_{19}\mathrm{K} \to {}^{36}_{17}\mathrm{Cl} + {}^{4}_{2}\mathrm{He}$
   • D$^{40}_{19}\mathrm{K} \to {}^{40}_{20}\mathrm{Ca} + {}^{0}_{-1}\mathrm{e} + \nu_e$

   (b)

   Which statement describes electron capture?

   [1 mark]

   • AA neutron captures an electron and becomes a proton
   • BThe nucleus captures an electron and emits a gamma photon
   • CA proton captures an inner-shell electron and becomes a neutron, and a neutrino is emitted
   • DA proton captures an inner-shell electron and the proton number increases by 1

   (c)

   Write a balanced equation for the electron capture of potassium-40 to argon-40.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Technetium-99m (⁹⁹ᵐTc) is a source of gamma radiation used in medical diagnosis. It is produced in a hospital by the decay of molybdenum-99, and the technetium-99m nucleus is left in an excited state that decays to the ground state of technetium-99 by emitting a single gamma photon of energy 140 keV. The half-life of technetium-99m is 6.0 hours.

   (a)

   Calculate the wavelength of the gamma photons emitted by technetium-99m.

   [3 marks]

   (b)

   Explain why technetium-99m is well suited to use as a source in medical diagnosis.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Radium-226 (Z = 88, N = 138), cobalt-60 (Z = 27, N = 33) and carbon-11 (Z = 6, N = 5) are all unstable and lie outside the band of stable nuclei. Cobalt-60 decays by β⁻ emission to an excited state of nickel-60, which reaches its ground state by emitting two gamma photons one after the other, of energies 1.17 MeV and 1.33 MeV.

   (a)

   Explain, with reference to the graph of N against Z, how the position of each nuclide relative to the stable band determines its mode of decay, giving the changes in N and Z. Include a balanced equation for one decay.

   [6 marks]

   (b)

   Write an equation for the β⁻ decay of cobalt-60 to nickel-60, state the energy of the excited state of nickel-60 above its ground state, and calculate the wavelength of the 1.33 MeV gamma photon.

   [6 marks]

   Total for question 4: 12 marks

End of questions