1. 1
   Iodine-131, used to treat thyroid disease, has a half-life of 8.02 days. It decays by β⁻ emission: the emitted electrons have a continuous range of kinetic energies from almost zero up to a maximum of 0.606 MeV. The daughter nucleus then usually emits a gamma photon of energy 0.364 MeV. A hospital receives a sample of iodine-131 with an activity of 4.0 × 10⁸ Bq.

   (a)

   What is the decay constant of iodine-131?

   [1 mark]

   • A1.0 × 10⁻⁶ s⁻¹
   • B1.4 × 10⁻⁶ s⁻¹
   • C8.6 × 10⁻² s⁻¹
   • D6.9 × 10⁵ s⁻¹

   (b)

   What does the continuous range of electron energies in this decay provide evidence for?

   [1 mark]

   • AThe daughter nucleus has a continuous range of energy levels
   • BThe gamma photon takes a variable share of the energy from the electron
   • CThe electrons come from different electron shells of the atom
   • DA second, undetected particle shares the energy released in each decay

   (c)

   Calculate the number of iodine-131 nuclei in the sample when it arrives.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   For light stable nuclides, such as $^{12}_{6}\mathrm{C}$ and $^{16}_{8}\mathrm{O}$, the ratio of neutrons to protons N/Z is close to 1. For heavy stable nuclides the ratio is larger: for $^{208}_{82}\mathrm{Pb}$ it is about 1.54. Carbon-14 ($^{14}_{6}\mathrm{C}$) is unstable, while sodium-22 ($^{22}_{11}\mathrm{Na}$) is unstable and decays to an isotope of neon (Z = 10); the only stable isotope of sodium is sodium-23.

   (a)

   Carbon-14 has more neutrons than the stable isotopes of carbon. Which type of decay would it be expected to undergo?

   [1 mark]

   • AAlpha
   • Bβ⁺
   • Cβ⁻
   • DGamma only

   (b)

   Why do heavy stable nuclides such as lead-208 need more neutrons than protons?

   [1 mark]

   • ANeutrons cancel the charge of some of the protons
   • BExtra neutrons add strong-force attraction without adding electrostatic repulsion
   • CThe strong nuclear force acts only between neutrons
   • DNeutrons are lighter than protons, so they reduce the mass of the nucleus

   (c)

   Suggest why sodium-22 is unstable and write the equation for its decay.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A technician measures the activity of a freshly prepared sample of a radionuclide, correcting every reading for background. The activity is 6.40 × 10⁴ Bq at the start and 1.52 × 10⁴ Bq exactly 25.0 minutes later.

   (a)

   Determine the half-life of the radionuclide.

   [3 marks]

   (b)

   The technician states: 'Because λ = 0.0575 per minute, the probability that a particular nucleus decays in the next 10 minutes is 0.575.' Evaluate this statement.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Bismuth-212 decays in two ways. In about 36% of decays it emits an alpha particle, forming thallium-208; the alpha particles are emitted with one of two kinetic energies, 6.090 MeV or 6.051 MeV, and gamma photons of energy 0.040 MeV are also detected. In about 64% of decays it undergoes β⁻ decay to polonium-212; these electrons have a continuous range of kinetic energies from zero up to 2.25 MeV. The binding energy per nucleon is about 7.8 MeV for bismuth-212, 8.8 MeV for iron-56 and 7.1 MeV for helium-4.

   (a)

   Explain how these data provide evidence for discrete nuclear energy levels and for the existence of the antineutrino.

   [6 marks]

   (b)

   Discuss the evidence for the strong nuclear force and use it to explain the shape of the binding-energy-per-nucleon curve for heavy nuclei, including why bismuth-212 can emit alpha particles.

   [6 marks]

   Total for question 4: 12 marks

End of questions