IGCSE Physics Radioactive Decay Questions and Worked Solutions
50 topic-wise practice questions on Radioactive Decay (Unit 5: Nuclear Physics), written to the Cambridge IGCSE Physics 0625 syllabus for 2026–2028, each with a step-by-step worked solution.
Topic guide: Radioactive Decay
Radioactive decay is a change in an unstable nucleus. Alpha and beta decay produce a different element; gamma emission removes energy only. (Extended) Decay equations show the changes in proton and nucleon numbers.
Key formulas
| α decay: A → A − 4, Z → Z − 2 | alpha emission | Extended |
| β decay: A unchanged, Z → Z + 1 | beta emission (n → p + e) | Extended |
| γ emission: A and Z unchanged | gamma emission | Extended |
Prerequisite knowledge
- Nuclide notation (5.1.2)
- Types of emission (5.2.2)
Exam tips & common mistakes
- Check that A and Z balance on both sides
- The product of β decay has the same A
- Gamma does not change the element
Key facts from the syllabus (5.2.3)
- Decay is spontaneous and random
- During α or β decay the nucleus changes to a different element
- Extended isotopes can be radioactive because they have too many neutrons and/or are too heavy
- Extended decay increases stability and reduces the number of excess neutrons
- Extended in β-decay a neutron changes into a proton and an electron
- Extended write decay equations in nuclide notation for α, β and γ
Textbook: §5.2 Radioactivity, pp. 260–274
Define radioactive decay.
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Method: Unstable nucleus change.
State two words describing the nature of radioactive decay.
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Method: Spontaneous and random.
State what happens to the element when a nucleus emits an alpha or beta particle.
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Method: New element.
State whether gamma emission changes the element.
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Method: No change in Z.
Explain what is meant by 'random' in radioactive decay.
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Method: Unpredictable.
State whether temperature or pressure affect the rate of radioactive decay.
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Method: Not affected.
State what is meant by 'spontaneous' in radioactive decay.
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Method: No outside cause.
Explain why it is impossible to predict when a particular nucleus will decay.
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Method: Random.
State which emissions change the proton number of a nucleus.
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Method: α and β.
State the type of decay that produces a nucleus of the same element.
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Method: Gamma.
A sample contains 1000 unstable nuclei. Explain why you cannot say exactly how many will decay in the next minute.
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Method: Random.
State two reasons why isotopes may be radioactive.
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Method: Excess neutrons, too heavy.
Describe the change in the nucleus during beta emission.
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Method: n → p + e.
State the effect of alpha decay on the proton number and nucleon number.
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Method: Z − 2, A − 4.
State the effect of beta decay on the proton number and nucleon number.
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Method: Z + 1, A same.
State the effect of gamma emission on the nucleus.
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Method: Energy only.
Write the decay equation for ²²⁶₈₈Ra emitting an alpha particle (product Rn).
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Method: A − 4, Z − 2.
Write the decay equation for ¹⁴₆C emitting a beta particle (product N).
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Method: Z + 1.
Write the decay equation for ⁹⁰₃₈Sr beta decay (product Y).
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Method: Z + 1.
²³⁸₉₂U decays by alpha emission. State the proton and nucleon numbers of the product.
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Method: Z − 2, A − 4.
A nucleus ²³⁴₉₀Th emits a beta particle. State the product.
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Method: Z + 1.
A nucleus emits two alpha particles and one beta particle starting from ²³⁸₉₂U. State the final Z and A.
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Method: 2α: Z − 4, A − 8; β: Z + 1.
Explain why alpha or beta decay increases the stability of a nucleus.
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Method: Reduces excess.
Write the equation for the gamma emission of an excited ⁶⁰₂₈Ni nucleus.
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Method: Unchanged Z, A.
Explain why beta emission reduces the number of excess neutrons.
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Method: n → p.
State why a nucleus with too many neutrons is likely to undergo beta decay.
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Method: n → p.
State why very heavy nuclei are likely to undergo alpha decay.
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Method: Reduce size.
Write the decay equation for ²¹⁰₈₄Po emitting an alpha particle (product Pb).
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Method: A − 4, Z − 2.
Write the decay equation for ⁴⁰₁₉K emitting a beta particle (product Ca).
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Method: Z + 1.
Write the decay equation for ¹³¹₅₃I beta decay (product Xe).
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Method: Z + 1.
Write the decay equation for ²⁴¹₉₅Am alpha decay (product Np).
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Method: A − 4, Z − 2.
²²²₈₆Rn decays to ²¹⁸₈₄Po. State the type of decay and explain.
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Method: A − 4, Z − 2.
²¹⁴₈₂Pb decays to ²¹⁴₈₃Bi. State the type of decay and explain.
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Method: Z + 1.
A nucleus undergoes alpha decay then two beta decays. State the overall change in Z and A.
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Method: α: −2, −4; 2β: +2.
State what particle is emitted from the nucleus in beta decay and where it comes from.
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Method: Electron from neutron.
Explain why gamma emission often follows alpha or beta decay.
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Method: Excess energy.
²³⁸₉₂U decays to ²⁰⁶₈₂Pb by a series of alpha and beta decays. Calculate the number of alpha decays.
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Method: ΔA = 32.
For the decay series in the previous question, calculate the number of beta decays.
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Method: 8α gives Z − 16; need Z − 10.
State the symbol used for a beta particle in a decay equation.
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Method: ⁰₋₁e.
State the symbol used for an alpha particle in a decay equation.
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Method: ⁴₂He.
Challenge questions
Harder, multi-step questions at the top end of the exam. Attempt these once you are confident with the questions above.
Explain what is meant by radioactive decay being spontaneous and random.
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Method: No trigger; unpredictable.
Write decay equations for ²³⁸₉₂U → Th by alpha decay, then the Th → Pa by beta decay.
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Method: A − 4, Z − 2; Z + 1.
⁶⁰₂₇Co decays by beta emission followed by gamma emission. Write both equations (product Ni).
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Method: Beta then gamma.
²³²₉₀Th decays to ²⁰⁸₈₂Pb by a series of α and β decays. Calculate the number of each.
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Method: ΔA/4 for α; then β from Z.
A nucleus emits an alpha particle then two beta particles. Show that the final nucleus is an isotope of the original.
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Method: Net change.
Explain why carbon-14 (6 protons, 8 neutrons) decays by beta emission, and state the product.
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Method: Neutron excess.
Explain why very heavy nuclei such as radium tend to decay by alpha emission.
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Method: Too heavy.
Explain why gamma emission does not change the element, but often follows alpha or beta decay.
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Method: Excess energy.
An unknown nucleus ᴬ_Z X decays by beta emission to ⁹⁰₃₉Y. Find A and Z and identify X if Z corresponds to strontium (38).
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Method: Reverse beta.
A nucleus ²¹⁸₈₄Po decays to ²¹⁴₈₂Pb then to ²¹⁴₈₃Bi. Identify each decay and write the overall change.
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Method: Compare A and Z.
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