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AS & A-Level Physics 23 — Nuclear Energy and Radioactive Decay

AS & A-Level Physics 23 — Nuclear Energy and Radioactive Decay

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 23 of 26: Nuclear energy and radioactive decay. Concepts, worked applications and misconception checks.

Physics EN A-Level
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Representing Nuclear Reactions with Equations

Nuclear reactions involve changes within the nucleus of an atom. We represent these changes using nuclear equations, which must adhere to two fundamental conservation laws: conservation of nucleon number (mass number, AA) and conservation of proton number (atomic number, ZZ). The notation for a nuclide is ZAX^A_Z X, where XX is the chemical symbol. In a nuclear equation, the sum of the nucleon numbers on the reactant side must equal the sum on the product side. Similarly, the sum of the proton numbers on the reactant side must equal the sum on the product side. This ensures that the total number of protons and neutrons, and the total charge, remain constant throughout the reaction.

Key points

  • Nuclear equations use the nuclide notation ZAX^A_Z X.
  • The total nucleon number (AA) must be conserved across the reaction.
  • The total proton number (ZZ) must be conserved across the reaction.
  • Common particles include alpha (24α^4_2\alpha or 24He^4_2\text{He}), beta-minus (−10β^0_{-1}\beta or −10e^0_{-1}\text{e}), beta-plus (+10β^0_{+1}\beta or +10e^0_{+1}\text{e}), neutron (01n^1_0\text{n}), and proton (11p^1_1\text{p} or 11H^1_1\text{H}).

Worked example

Question

A nucleus of Carbon-14 (614C^{14}_6\text{C}) undergoes beta-minus decay. Write the nuclear equation for this reaction and identify the daughter nucleus.

Solution

1. Start with the parent nucleus and the emitted particle: 614C→Daughter Nucleus+−10e+νˉe^{14}_6\text{C} \rightarrow \text{Daughter Nucleus} + ^0_{-1}\text{e} + \bar{ν}_e.
2. Apply conservation of nucleon number (AA): 14=Adaughter+0⇒Adaughter=1414 = A_{\text{daughter}} + 0 \Rightarrow A_{\text{daughter}} = 14.
3. Apply conservation of proton number (ZZ): 6=Zdaughter+(−1)⇒Zdaughter=76 = Z_{\text{daughter}} + (-1) \Rightarrow Z_{\text{daughter}} = 7.
4. Identify the element with atomic number 7, which is Nitrogen (N).
5. The complete nuclear equation is: 614C→714N+−10e+νˉe^{14}_6\text{C} \rightarrow ^{14}_7\text{N} + ^0_{-1}\text{e} + \bar{ν}_e.

614C→714N+−10e+νˉe^{14}_6\text{C} \rightarrow ^{14}_7\text{N} + ^0_{-1}\text{e} + \bar{ν}_e. The daughter nucleus is Nitrogen-14.

Common pitfalls

  • Incorrectly identifying the nucleon and proton numbers for common particles (e.g., alpha, beta, neutron, proton).
  • Failing to balance both the nucleon numbers and the proton numbers across the reaction arrow, leading to an incorrect product nuclide.

Prerequisites

  • Understanding of nuclide notation ZAX^A_Z X.
  • Knowledge of conservation of nucleon number and charge in nuclear processes.
  • Familiarity with the composition and notation of alpha, beta, and gamma radiations.
  • Ability to represent alpha and beta decay by radioactive decay equations.
Further resources