Ten original structured questions in the style of Paper 4, covering the whole of Nuclear physics: mass defect and binding energy, E = mc², fusion and fission energy, and the random exponential law of radioactive decay. The later questions tie a decay's mass change to its energy. Each is tagged with its lessons; attempt them all, then reveal the worked solutions.
A helium-4 nucleus is made of 2 protons and 2 neutrons. Use: proton mass = 1.00728 u, neutron mass = 1.00867 u, helium-4 nucleus mass = 4.00151 u.
(a) State what is meant by the mass defect of a nucleus. [1]
(b) Calculate the mass defect of the helium-4 nucleus, in u. [2]
(c) Calculate the binding energy, in MeV. [2]
(d) Calculate the binding energy per nucleon, in MeV. [2]
(e) State what the binding energy per nucleon tells you about the nucleus. [2]
Show how the conversion 1 u ≡ 931 MeV comes from E = mc².
(a) Calculate the energy equivalent of a mass of 1 u, in joules. [2]
(b) Convert this energy to MeV, and compare with 931 MeV. [2]
(c) State why mass and energy are treated as equivalent in nuclear physics. [2]
The binding energy per nucleon rises steeply for light nuclei, peaks near iron (A ≈ 56), then falls slowly toward the heaviest nuclei.
(a) State which nuclei are the most stable, and why. [2]
(b) Explain, using the curve, why energy is released when a heavy nucleus undergoes fission. [3]
(c) Explain why energy is released when two light nuclei undergo fusion. [2]
(d) State one reason fusion is hard to achieve on Earth. [1]
A deuterium and a tritium nucleus fuse: ²₁H + ³₁H → ⁴₂He + ¹₀n. Masses (u): ²₁H = 2.01410, ³₁H = 3.01605, ⁴₂He = 4.00260, n = 1.00867.
(a) Calculate the change in mass for the reaction, in u. [2]
(b) Calculate the energy released, in MeV. [2]
(c) Calculate the energy released, in joules. [2]
(d) State what happens to this energy. [2]
The Sun radiates energy at a power of 3.8 × 10²⁶ W, all of it coming from a loss of mass.
(a) State the relation between the power radiated and the rate of mass loss. [1]
(b) Calculate the mass lost by the Sun each second. [3]
(c) Suggest why this enormous rate barely changes the Sun's mass over a human lifetime. [2]
A radioactive source contains 5.0 × 10²₀ undecayed nuclei of a nuclide whose decay constant is 2.0 × 10⁻⁸ s⁻¹.
(a) State what is meant by the decay constant. [1]
(b) Calculate the activity of the source, in Bq. [2]
(c) Calculate the half-life of the nuclide, in seconds. [2]
(d) State and explain how the activity changes as time passes. [3]
A radioactive nuclide has a half-life of 8.0 days.
(a) Calculate its decay constant, in day⁻¹. [2]
(b) State the fraction of the original nuclei remaining after 24 days. [2]
(c) Calculate the fraction remaining after 20 days. [3]
(d) State whether the half-life depends on how much of the sample is left. [1]
A sample of a nuclide of half-life 15 hours has an initial activity A₀.
(a) Calculate the time for the activity to fall to A₀/16. [2]
(b) Calculate the decay constant, in hour⁻¹. [2]
(c) Calculate the time for the activity to fall to 10% of A₀. [3]
(d) State why a measured count rate is usually less than the activity. [1]
Carbon-14 has a half-life of 5730 years. A living sample has a C-14 activity of 0.25 Bq per gram of carbon. An old wooden artefact reads 0.0625 Bq per gram.
(a) State the assumption that makes carbon dating possible. [1]
(b) Calculate the age of the artefact using the number of half-lives. [3]
(c) Confirm the age using N = N₀e⁻λᵗ. [3]
(d) Suggest one reason very old samples cannot be dated this way. [1]
Radium-226 decays by alpha emission to radon: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Masses (u): Ra-226 = 226.0254, Rn-222 = 222.0176, He-4 = 4.0026. The half-life of radium-226 is 1600 years.
(a) Show that the nucleon and proton numbers balance in the equation. [2]
(b) Calculate the change in mass, in u. [2]
(c) Calculate the energy released, in MeV and in joules. [3]
(d) Calculate the decay constant of radium-226, in s⁻¹ (1 year = 3.15 × 10⁷ s). [2]
(e) State whether the energy released per decay changes as the sample ages, and why. [2]
Mark this once you have attempted all ten questions and checked your working against the solutions. Revealing the solutions alone does not count.