E.3
Radioactive Decay
Isotopes, mass defect, binding energy, nuclear stability, alpha, beta and gamma decay, half-life and activity. HL extends to the decay constant and exponential decay equations.
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E.3 Radioactive Decay
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Key Concepts, Radioactive Decay
Isotopes and Nuclear Notation
Isotopes are atoms of the same element (same Z, same number of protons) but with different numbers of neutrons and therefore different mass numbers A. For example, carbon-12 and carbon-14 are both isotopes of carbon (Z = 6), with 6 and 8 neutrons respectively. Most isotopes are stable; unstable ones undergo radioactive decay. Standard notation writes A at the top left and Z at the bottom left of the chemical symbol. Nuclear reactions must conserve both mass number and atomic number on both sides of the equation.
Mass Defect, Binding Energy and E = mc²
The actual mass of a nucleus is always less than the sum of the masses of its constituent protons and neutrons. This difference is the mass defect Δm. By Einstein's mass-energy equivalence E = mc², this mass difference represents the binding energy: the energy released when the nucleus formed, and the energy needed to completely separate it again. Binding energy = Δm × c². In nuclear physics it is convenient to work in atomic mass units: 1 u = 931.5 MeV/c², so a mass defect of 1 u corresponds to a binding energy of 931.5 MeV.
Binding Energy per Nucleon
The binding energy per nucleon is the total binding energy divided by A. It measures how tightly each nucleon is bound. A graph of binding energy per nucleon against mass number peaks near iron (Fe-56) at about 8.8 MeV per nucleon. Elements lighter than iron can release energy by fusion (combining to move towards the peak). Elements heavier than iron can release energy by fission (splitting to move towards the peak). Iron is the most stable nucleus: neither fusion nor fission releases energy from it.
Radioactive Decay: Alpha, Beta and Gamma
Unstable nuclei decay spontaneously to reach a more stable configuration. Alpha decay emits a helium-4 nucleus (2 protons, 2 neutrons), reducing A by 4 and Z by 2. It is strongly ionising but stopped by a few cm of air. Beta-minus decay converts a neutron to a proton, emitting an electron and antineutrino; Z increases by 1. Beta-plus decay converts a proton to a neutron, emitting a positron and neutrino; Z decreases by 1. Gamma decay emits a high-energy photon from an excited nucleus; A and Z are unchanged. Gamma is the most penetrating radiation and the least ionising.
Activity and Half-Life
Activity is the number of decays per second, measured in becquerels (Bq). Radioactive decay is random and spontaneous. The half-life T½ is the time for half the radioactive nuclei in a sample to decay (or for activity to halve). It is constant for a given isotope and ranges from microseconds to billions of years. Background radiation from cosmic rays, radon gas, rocks and medical sources must always be measured and subtracted from experimental count rates.
Decay Constant and Exponential Decay (HL)
The decay constant λ is the probability of a nucleus decaying per unit time (s⁻¹). It is related to half-life by T½ = ln2/λ = 0.693/λ. The number of undecayed nuclei follows N = N₀e^(-λt) and activity follows A = A₀e^(-λt). These equations allow calculation at any time, not just whole-number multiples of the half-life. Activity A = λN: a large sample of a short-lived isotope can have very high activity because λ is large. The continuous energy spectrum of beta decay (rather than discrete energies as seen in alpha and gamma) was evidence for the neutrino, which carries away a variable share of the available energy.
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Frequently Asked Questions, IB Physics Radioactive Decay
What is Radioactive Decay in IB Physics? ↓
Isotopes, mass defect, binding energy, nuclear stability, alpha, beta and gamma decay, half-life and activity. HL extends to the decay constant and exponential decay equations. This topic is part of Theme E (Nuclear & Quantum Physics) in the current IB Physics syllabus.
Is Radioactive Decay SL or HL in IB Physics? ↓
Radioactive Decay is covered by both SL and HL students in the current IB Physics syllabus. HL students study additional depth and extension content beyond the SL core.
What equations do I need for IB Physics Radioactive Decay? ↓
The key equations for Radioactive Decay are covered in the concept tutorial above. For a structured set of notes with all equations, conditions and worked examples, the GradePod Exam Pack includes a revision note template for every topic.
What are common exam mistakes in IB Physics Radioactive Decay? ↓
Common mistakes are covered in detail in the exam technique video above. The GradePod Exam Pack also includes exam-style questions with mark schemes so you can see exactly how marks are awarded and where students typically drop them.
How do I revise Radioactive Decay for the IB Physics exam? ↓
Follow the GradePod three-step method. First, watch the concept tutorial and tick off each learning objective on the checklist above as you go. Second, watch the exam technique video to see how IB-style questions are answered under exam conditions. Third, use the Exam Pack to practise independently with knowledge questions, exam questions and mark schemes. That's it. It works. I promise.