Atoms, Nuclei and Radiation

The α-scattering experiment showed that an atom's mass and positive charge are concentrated in a tiny nucleus. A nuclide is written $^A_Z\text{X}$ ( $A$ nucleons, $Z$ protons). Unstable nuclei emit α (a helium nucleus), β⁻ (an electron plus an antineutrino), β⁺ (a positron plus a neutrino) or γ (a photon). Nucleon number and charge are conserved in every decay.

Cambridge 9702 Paper 1Cambridge 9702 Paper 2Edexcel YPH11 WPH14AQA 7408 Paper 1AQA 7408 Paper 2≈ 35 minRevision 5 · updated 2026-10-27

Section 1 of 14

Learning objectives

Explain what α-scattering reveals about the nucleus.
Use nuclide notation and describe isotopes.
Describe α, β⁻, β⁺ and γ radiation and write balanced decay equations.
Explain why β energies are continuous, using the (anti)neutrino.

Pause and think

Geiger and Marsden fired α-particles at gold foil. About $1$ in $8000$ bounced back. Rutherford said it was "as if you fired a $15$ -inch shell at tissue paper and it came back". Why was it so surprising?

Section 2 of 14

Core idea

Start hereBullets bouncing off tissue paper

Rutherford said firing alpha particles at gold foil and seeing some bounce back was "as if you fired a 15-inch shell at tissue paper and it came back". Only a tiny, dense, charged nucleus could do that.

The big idea

Tiny dense positive nucleus. $^A_ZX$ . Decays conserve $A$ and charge. β decay emits an (anti)neutrino: shown by the continuous β energy spectrum.

1. Alpha scattering

Alpha scattering: number deflected falls steeply with angle

Very few alpha particles bounce back, but some do: only a tiny concentrated positive charge could repel them so strongly.

Most pass straight through: mostly empty space.
Few deflected > 90°: small, massive, positive nucleus (~ $10^{-15}$ m vs ~ $10^{-10}$ m).

2. Decay equations

Worked exampleThree decays

α from Ra-226; β⁻ of a neutron; β⁺ of a proton.

Goal: Balanced equations.
Strategy: Conserve $A$ and $Z$ ; add neutrinos.

$^{226}_{\ 88}\text{Ra}\to{}^{222}_{\ 86}\text{Rn}+{}^4_2\alpha$
α.
$^1_0n\to{}^1_1p+{}^{\ 0}_{-1}e+\bar\nu$
β⁻ with antineutrino.
$^1_1p\to{}^1_0n+{}^{\ 0}_{+1}e+\nu$
β⁺ with neutrino.

AnswerAs shown.

✓ CheckTop and bottom numbers balance in each ✓.

β⁻ energy spectrum: a continuous range

If only the electron were emitted, all would have the same energy. The spread shows a third particle shares it.

Why the neutrino was predicted

$\text{two-body decay}\Rightarrow\text{fixed energy}$
Momentum and energy conservation fix how it is shared.
$\beta\text{ energies are continuous}$
Observed: a spread of energies.

A third, unseen particle (the neutrino) must share the energy.

Pause and think

$^{238}_{\ 92}$ U after 2 α and 1 β⁻?

Summary

Rutherford model.
Conserve $A$ and $Z$ ; neutrinos in β.

Nuclide: Nucleus with given A and Z.

HistoryPauli's desperate remedy. In the

1920

s, β-particles came out with a spread of energies, apparently breaking energy conservation. In

1930

Wolfgang Pauli proposed an invisible neutral particle to carry the missing energy, calling it a "desperate remedy". The neutrino was finally detected in

1956

, at a nuclear reactor.

Fun factA neutrino flood. About

65

billion solar neutrinos pass through every square centimetre of your body every second, day and night (they go straight through the Earth). In your whole lifetime, perhaps one will interact with an atom in you.

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