Nuclear Physics: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 20 · 9478 Topic 20 · Read time: ~12 minutes
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Key Formulas
The nuclear atom
In Rutherford's α-particle scattering experiment, most α-particles passed straight through gold foil, a few were deflected, and very few bounced back. So the atom is mostly empty space, with its mass and positive charge in a tiny nucleus.
Proton number Z = number of protons. Nucleon number A = protons + neutrons. A nuclide is written ᴬ_Z X.
Isotopes have the same Z but different numbers of neutrons.
Radioactive decay
Decay is spontaneous (unaffected by external conditions) and random (you cannot predict which nucleus decays next). The random nature shows up as fluctuations in count rate.
Background radiation comes from rocks, building materials, cosmic rays and medical sources. Subtract it from readings before analysing a sample.
α: helium nucleus, highly ionising, stopped by paper. β: fast electron, moderately ionising, stopped by a few mm of aluminium. γ: electromagnetic radiation, weakly ionising, reduced by thick lead.
Activity A = λN. Activity, N and count rate all decay as x = x₀e^(−λt). Half-life t½ is the time for x to halve: λ = ln 2/t½.
Trick: If the time is a whole number of half-lives, skip the exponential: after n half-lives, x = x₀/2ⁿ.
Trap: The decay constant λ has nothing to do with wavelength. It is a probability of decay per unit time, in s⁻¹.
Nuclear equations and conservation laws
In any nuclear process, nucleon number, charge and mass-energy are conserved. Balance the top and bottom numbers on each side of a nuclear equation.
Beta electrons are emitted with a range of energies. To conserve energy and momentum, another particle must carry the rest: this predicted the (anti)neutrino.
Applications and hazards depend on half-life (a medical tracer needs a short one; a smoke detector source a long one) and on penetration and ionisation (α is dangerous inside the body; γ is used for sterilisation and imaging).
Mass defect and binding energy
A nucleus has less mass than its separate nucleons. This mass defect Δm corresponds to the binding energy, BE = Δmc²: the energy needed to separate the nucleus completely into its nucleons.
Binding energy per nucleon measures stability. It peaks near iron-56.
Fusion of light nuclei and fission of heavy nuclei both move towards that peak, increasing binding energy per nucleon and releasing energy.
Trap: Compare binding energy per nucleon, not total binding energy, to decide whether a reaction releases energy.
Worked Example
A sample of iodine-131 has a half-life of 8.0 days and an initial activity of 4.0 × 10⁶ Bq.
(a) Calculate the decay constant in s⁻¹. [2]
t½ = 8.0 × 24 × 3600 = 6.91 × 10⁵ s
λ = ln 2 / t½ = 1.00 × 10⁻⁶ s⁻¹
(b) Calculate the number of undecayed nuclei initially. [1]
N = A / λ = 4.0 × 10⁶ ÷ 1.00 × 10⁻⁶ = 4.0 × 10¹²
(c) Calculate the activity after 24 days. [1]
24 days = 3 half-lives, so A = 4.0 × 10⁶ ÷ 2³ = 5.0 × 10⁵ Bq
(d) Explain why iodine-131 is suitable as a medical tracer, in terms of its half-life. [1]
Its half-life is long enough to be measured during the procedure but short enough that it doesn't stay active in the body for long.
Why this question is a good test of the topic: it requires converting days to seconds for λ, links activity to N, and rewards spotting the whole-number half-lives shortcut.
Frequently Asked Questions
What did Rutherford scattering show?
That the atom is mostly empty space with a tiny, dense, positively charged nucleus.
What does random and spontaneous decay mean?
Random: you can't predict which nucleus decays next. Spontaneous: decay is unaffected by external conditions like temperature or pressure.
What is the relationship between activity and decay constant?
A = λN. Activity equals the decay constant times the number of undecayed nuclei.
Why was the neutrino predicted?
Beta particles have a range of energies, so another particle must carry away the missing energy and momentum to conserve them.
Why do both fission and fusion release energy?
Both produce nuclei with higher binding energy per nucleon, closer to the peak near iron.
Half-life and binding energy questions costing marks?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.