Radioactive decay worksheet with answers for A Level physics (free PDF download)

Problem 1 Three kinds of radiation ★★★

Imani in Mombasa revises the three types of radiation from nuclei.
1. State what an alpha particle is and the changes it causes in A and Z.
2. Then state what happens inside the nucleus in beta-minus decay and the change in Z.
3. Finally, state the changes in A and Z when a gamma photon is emitted.

Problem 2 Radium alpha decay ★★★

Radium-226 (Z = 88) emits an alpha particle and becomes radon (Z = 86). Determine the mass number of the radon nuclide and write the nuclear equation in words.

Problem 3 Cobalt-60 beta decay ★★★

Cobalt-60 (Z = 27) decays by beta-minus emission to an isotope of nickel. Find the mass number and proton number of the nickel nuclide.

Problem 4 Three half-lives of cobalt-60 ★★★

A source for sterilising spices in Pune has an activity of 8.0 × 10⁶ Bq. Cobalt-60 has a half-life of 5.27 years. Calculate the activity after 15.8 years.

Problem 5 Mass and energy units ★★★

Convert the following.
1. A mass defect of 0.0305 u into MeV (1 u = 931.5 MeV/c²).
2. An energy of 4.0 MeV into joules (1 MeV = 1.60 × 10⁻¹³ J).

Problem 6 Decay constant of caesium-137 ★★★

Chiamaka in Lagos reads that caesium-137 has a half-life of 30.1 years. Calculate its decay constant in s⁻¹. Use 1 year = 3.156 × 10⁷ s.

Problem 7 Activity of a radon sample ★★★

A sealed chamber in Leeds holds 2.0 × 10¹⁵ nuclei of radon-222, of half-life 3.82 days.
1. Calculate the decay constant in s⁻¹.
2. Then calculate the activity.

Problem 8 Phosphorus-32 tracer ★★★

Wanjiru in Nairobi uses phosphorus-32 (half-life 14.3 days) as a tracer for fertiliser uptake in maize. Calculate the percentage of the phosphorus-32 left after 30 days.

Problem 9 Reading a decay graph ★★★

The graph shows the activity of a sodium-24 sample.

1. Use the graph to find the half-life.
2. Then find the activity at 45 hours.
3. Finally, find the time at which the activity falls to 240 Bq.

Problem 10 A PET tracer ★★★

Kofi in Accra learns that fluorine-18, used in PET scans, has a half-life of 110 minutes. A dose is delivered at 2000 MBq. Calculate how long it takes for the activity to fall to 300 MBq.

Problem 11 Binding energy of the deuteron ★★★

Use atomic masses: hydrogen atom 1.007825 u, neutron 1.008665 u, deuterium atom 2.014102 u. Calculate the mass defect, the binding energy in MeV and the binding energy per nucleon.

Problem 12 A milligram of mass ★★★

Aarav in Pune imagines that 1.0 mg of matter is converted completely to energy. Use c = 3.00 × 10⁸ m/s.
1. Calculate the energy released in J.
2. Then convert it to kWh (1 kWh = 3.6 × 10⁶ J).
3. A home uses 5.0 kWh per day. Calculate how many years this energy would supply it.

Problem 13 Energy of an alpha decay ★★★

Use atomic masses: radium-226 226.02541 u, radon-222 222.01758 u, helium-4 4.00260 u. Calculate the energy released in the decay radium-226 → radon-222 + helium-4, in MeV.

Problem 14 Reading a decay series ★★★

The grid shows the start of a radioactive series, with mass number A against proton number Z.

1. Name the type of decay at each step 1 to 4.
2. Then calculate how many neutrons the nuclide uranium-238 has (Z = 92).
3. Finally, state the relation between uranium-238 and uranium-234.

Problem 15 Spot the errors ★★★

Diego in Texas wrote three statements. Explain why each is wrong and correct it.
1. “After two half-lives all the nuclei have decayed.”
2. “In beta-minus decay the mass number falls by one.”
3. “Binding energy is the energy given out when a nucleus is pulled apart.”

Problem 16 Reading a binding energy chart ★★★

The bar chart shows binding energy per nucleon for some nuclides.

1. State which nuclide in the chart is the most stable and explain why.
2. Then calculate the total binding energy of iron-56 in MeV and the mass defect in u.
3. Finally, use the chart to calculate the energy released when two hydrogen-2 nuclei fuse into one helium-4 nucleus.

Problem 17 Fission of uranium-235 ★★★

A neutron strikes uranium-235 (Z = 92) and the nucleus splits into xenon-140 (Z = 54), strontium-94 (Z = 38) and neutrons. The binding energies per nucleon are: uranium-235 7.59 MeV, xenon-140 8.29 MeV, strontium-94 8.59 MeV. Use N_A = 6.02 × 10²³ mol⁻¹.
1. Find the number of neutrons released, by balancing A and Z.
2. Then calculate the energy released in one fission in MeV.
3. Finally, calculate the energy released when 1.00 kg of uranium-235 undergoes fission, in joules (1 MeV = 1.60 × 10⁻¹³ J).

Problem 18 Fusion fuel per kilogram ★★★

A deuterium nucleus (H-2, 1.11 MeV per nucleon) and a tritium nucleus (H-3, 2.83 MeV per nucleon) fuse to form helium-4 (7.07 MeV per nucleon) and a neutron. Use 1 u = 1.661 × 10⁻²⁷ kg and 1 MeV = 1.60 × 10⁻¹³ J.
1. Calculate the energy released by one reaction in MeV.
2. Then calculate the energy released per kilogram of deuterium–tritium fuel, taking the mass of one reacting pair as 5.00 u.
3. Fission of uranium-235 gives about 8 × 10¹³ J per kg. Compare the two.

Problem 19 A straight line from a decay ★★★

Imani in Mombasa records the activity of a short-lived sample at two-hour intervals.

Time t (h)	0	2	4	6	8
Activity A (kBq)	80.0	63.5	50.4	40.0	31.8

1. Explain why a graph of ln A against t is a straight line.
2. Then calculate ln A for t = 0 and for t = 8 h, and find the gradient between these points.
3. Finally, determine the decay constant and the half-life.

Problem 20 A gram of radium ★★★

Radium-226 has a half-life of 1600 years. Use N_A = 6.02 × 10²³ mol⁻¹, molar mass 226 g/mol and 1 year = 3.156 × 10⁷ s.
1. Calculate the number of nuclei in 1.00 g.
2. Then calculate the decay constant in s⁻¹ and the activity of 1.00 g.
3. Finally, calculate the activity of this sample after 400 years.