Alpha, beta and gamma decay

Alpha, beta and gamma are the three main types of radiation given out when an unstable nucleus decays. An alpha particle is made of 2 protons and 2 neutrons, identical to a helium nucleus, and is stopped by a sheet of paper. A beta particle is a fast electron made in the nucleus when a neutron turns into a proton, and is stopped by a few millimetres of aluminium. A gamma ray is electromagnetic radiation from the nucleus, and only thick lead or concrete reduces it much.

Alpha, beta and gamma radiation compared

A nucleus decays when it has the wrong balance of protons and neutrons, or simply too much energy. Which radiation it gives out depends on what is wrong with it.

The pattern runs both ways: the more strongly a radiation ionises, the faster it loses energy and the shorter its range. Alpha particles are big and highly charged, so they knock electrons off almost every atom they pass and stop quickly. Gamma rays have no charge and rarely interact, so they travel a long way.

That is why the danger depends on where the source is. Outside the body, alpha is the least dangerous, because it cannot get through the outer layer of skin. Inside the body, swallowed or breathed in, alpha is the most dangerous, because all its ionisation is concentrated in a small volume of living cells.

Nuclear decay equations: the rules

Each nucleus is written with its mass number (protons + neutrons) on top and its atomic number (protons) underneath, before the symbol. For example, ²³⁸₉₂U is uranium with 92 protons and 238 nucleons.

In every nuclear equation, two totals must balance:

• The mass numbers (top numbers) add up to the same on both sides.
• The atomic numbers (bottom numbers, the charge) add up to the same on both sides.

If the atomic number changes, the element changes, so use the periodic table to name the new nucleus.

Alpha decay equation

In alpha decay the nucleus loses 2 protons and 2 neutrons, so the mass number falls by 4 and the atomic number falls by 2.

For example, uranium-238 decays by alpha emission into thorium-234:

Check: 238 = 234 + 4 and 92 = 90 + 2. Alpha decay is most common in very heavy nuclei, which are too big for the strong nuclear force to hold together comfortably.

Beta minus decay

Beta minus decay happens in nuclei with too many neutrons. A neutron turns into a proton, and the nucleus throws out an electron and an electron antineutrino:

The mass number stays the same, because a neutron has become a proton, and the atomic number goes up by 1.

Carbon-14, used in radiocarbon dating, decays this way into nitrogen-14:

At GCSE you can leave out the antineutrino. At A-level, include it: it was proposed because the beta electrons come out with a spread of energies, so another particle had to be carrying the rest.

At the quark level, one down quark in the neutron changes into an up quark. The neutron (udd) becomes a proton (uud) through the weak interaction, by giving off a W⁻ boson that then decays into the electron and the antineutrino.

Beta plus decay

Beta plus decay, also called positron emission, happens in nuclei with too many protons. A proton turns into a neutron and the nucleus gives out a positron (an anti-electron) and an electron neutrino:

The mass number stays the same and the atomic number goes down by 1.

Sodium-22 is a positron emitter, decaying into neon-22:

At the quark level, an up quark becomes a down quark and a W⁺ boson, which decays into the positron and the neutrino. Positron emitters are used in PET scans in hospitals.

Electron capture

Electron capture is the other way for a nucleus with too many protons to become more stable. Instead of emitting a positron, the nucleus pulls in one of its own inner electrons. That electron combines with a proton to make a neutron, and an electron neutrino is given out:

The result for the nucleus is the same as beta plus decay: the mass number stays the same and the atomic number falls by 1. Beryllium-7 decays this way into lithium-7:

The gap left by the captured electron is filled by an electron from a higher shell, so electron capture is usually followed by an X-ray.

Feynman diagrams for beta decay and electron capture

A-level Physics represents these weak interactions with simple Feynman diagrams. Time runs up the page, particles are straight lines with arrows, and the exchange particle is a wavy line between two meeting points, called vertices.

For the electron capture Feynman diagram, draw the proton coming in on the left and leaving as a neutron. Draw the electron coming in on the right and leaving as an electron neutrino. Join the two vertices with a wavy line labelled W⁺, going from the proton side to the electron side. Charge balances at each vertex: the proton (+1) becomes a neutron (0) and a W⁺ (+1), and the W⁺ (+1) plus the electron (−1) gives a neutrino (0).

Gamma decay

After alpha or beta decay, the new nucleus is often left with extra energy, in an excited state. It gets rid of that energy by emitting a gamma ray. Nothing else changes: the mass number and atomic number stay the same.

The m in technetium-99m means metastable, an excited state that lasts for hours. That makes it useful as a medical tracer: it gives out gamma rays, which escape the body to be detected, and no alpha or beta particles.

Balancing nuclear equations: worked examples

Example 1: name the product

Bismuth-212, ²¹²₈₃Bi, decays by alpha emission. What does it become?

Mass number: 212 − 4 = 208. Atomic number: 83 − 2 = 81. Element 81 is thallium.

Example 2: find the missing particle

Complete this equation: ²³⁴₉₀Th → ²³⁴₉₁Pa + X.

The mass number is unchanged at 234, so X has mass number 0. The atomic number goes from 90 to 91, so X must have atomic number 90 − 91 = −1. A particle with mass number 0 and charge −1 is an electron: X is a beta particle, ⁰₋₁e.

Example 3: a short decay chain

Uranium-238 decays by alpha emission, then the product decays by beta minus emission twice. What is the final nucleus?

• Alpha: ²³⁸₉₂U → ²³⁴₉₀Th
• Beta minus: ²³⁴₉₀Th → ²³⁴₉₁Pa
• Beta minus: ²³⁴₉₁Pa → ²³⁴₉₂U

The final nucleus is uranium-234. One alpha and two beta minus decays bring the atomic number back to 92, so the element is uranium again, but a different isotope.

Example 4: counting decays in a series (A-level)

The uranium-238 series ends at lead-206, ²⁰⁶₈₂Pb. How many alpha and beta minus decays happen along the way?

Only alpha decay changes the mass number, by 4 each time. The mass number falls by 238 − 206 = 32, so there are 32 ÷ 4 = 8 alpha decays.

Eight alpha decays lower the atomic number by 16, to 92 − 16 = 76. Lead's is 82, which is 6 higher, and each beta minus decay raises it by 1. So there are 6 beta minus decays.

Now try one from the Nuclear Energy course. Work out the nucleus that each decay produces, then press Mark to check your answer in the course.

Summary of decay types

Common mistakes

• Mixing up the two numbers. Mass number goes on top, atomic number underneath. Alpha decay takes 4 off the top and 2 off the bottom.
• Keeping the old element symbol. If the atomic number changes, the element changes. Look up the new atomic number.
• Thinking a beta particle comes from the electron shells. It is made in the nucleus when a neutron turns into a proton.
• Saying gamma rays change the nucleus into a new element. Gamma emission only removes energy.
• Saying alpha is always the most dangerous. Outside the body it is the least dangerous; inside, it is the most.
• Mixing up neutrinos and antineutrinos at A-level. Beta minus gives an antineutrino; beta plus and electron capture give a neutrino.

What your course needs

This was checked against AQA's specifications in November 2026.

• GCSE Physics and Combined Science: alpha, beta (a high speed electron from the nucleus as a neutron turns into a proton), gamma and neutron emission. You need their penetration, range in air and ionising power, and nuclear equations for alpha and beta decay.
• A-level Physics: adds beta plus decay and electron capture as decay modes, nuclear excited states and gamma emission, the uses of technetium-99m, and Feynman diagrams for beta minus, beta plus and electron capture with W⁺ and W⁻ as the exchange particles.

Practise nuclear physics in a short timed paper

Radioactivity is a regular topic in GCSE Physics, and nuclear and particle physics return at A-level. GCSE Physics Higher and A-level Physics: Year 2 each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course. To learn the topic from the start, the Nuclear Energy course covers decay, half-life, fission and fusion, and the Half Life Calculator works out how much of a sample is left after any time.

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