Nuclear Physics · revision map · A-Level 9702, Topic 23
TOPIC 23 · NUCLEAR PHYSICS
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
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NUCLEAR PHYSICS23
Mass Defect & Binding Energy
A nucleus has less mass than its separate nucleons. That missing mass defect Δm is the energy that binds it.
E = Δm c²
mass and energy are
one currency
one currency
- Mass defect Δm = (Z m_p + N m_n) − M_nucleus.
- Binding energy = energy to pull the nucleus fully apart into free nucleons.
- Nuclide equations conserve nucleon number A and proton number Z.
- 1 u = 931 MeV · 1 eV = 1.60 × 10−¹⁹ J.
Binding Energy per Nucleon
Dividing binding energy by nucleon number compares stability across all nuclei.
binding energy per nucleon = E / A- The curve peaks near iron-56: the most stable nuclei.
- Fusion of light nuclei and fission of heavy nuclei both climb toward the peak, releasing energy.
- Higher E/A means a more tightly bound, more stable nucleus.
Random Decay & Activity
Each nucleus decays at random; decay is spontaneous.
- Unaffected by temperature, pressure or chemical state.
- Decay constant λ: probability of decay per unit time.
- Activity A: decays per second, in becquerel (Bq).
- Activity is proportional to N, so it also falls with time.
N = number of undecayed nuclei present
A measured count rate samples this random process, so repeated counts fluctuate about the mean.
Exponential Decay & Half-Life
Loss rate is proportional to N, so the count falls exponentially.
N = N₀ e−λt
A = A₀ e−λt
- Half-life t½: time for N (or A) to halve.
- N, A and the received count all follow the same law.
- A plot of ln A against t is a straight line of gradient −λ.
Each fixed half-life removes the same fraction of nuclei, so the count never quite reaches zero.
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