Nuclear decay equations: how the mass and atomic numbers change in alpha, beta-minus and beta-plus decay and gamma emission, and balancing nuclear equations.

What this dot point is asking

Edexcel wants you to write balanced nuclear equations for alpha decay, beta-minus decay, beta-plus decay and gamma emission, showing how the mass (nucleon) number and atomic (proton) number change, and to balance the top and bottom numbers across the equation.

Alpha decay

Because the alpha particle carries away 2 protons and 2 neutrons, the parent nucleus becomes a different element with a smaller mass. The equation must balance: the mass numbers (top) and the atomic numbers (bottom) each add up to the same total on both sides. For example, $^{238}_{92}\text{U} \rightarrow\ ^{234}_{90}\text{Th} +\ ^{4}_{2}\alpha$.

Beta-minus decay

The mass number stays the same because the total number of nucleons (protons plus neutrons) is unchanged; a neutron has simply turned into a proton. The new proton raises the atomic number by one. The emitted electron is written $^{0}_{-1}\text{e}$ or $^{0}_{-1}\beta$, with mass number $0$ and "atomic number" $-1$ so the equation balances.

Beta-plus decay and gamma emission

Beta-plus is the mirror image of beta-minus: a proton becomes a neutron, the positron carries away the positive charge, and the atomic number drops by one. Gamma emission usually happens just after another decay, as the nucleus sheds surplus energy; because gamma has no mass and no charge, the nucleus stays the same element with the same mass number.

How Edexcel examines this

This dot point is examined on both tiers as a "write the balanced nuclear equation" question, usually worth two or three marks, for alpha or beta decay. The mark scheme rewards the correct changes to the mass and atomic numbers and a correctly balanced equation, with marks often allocated separately to the new mass number, the new atomic number and the emitted particle. For beta-minus, examiners also reward explaining that a neutron changes into a proton; for beta-plus, that a proton changes into a neutron. The most penalised errors are altering the mass number during beta decay and reversing the direction of the atomic-number change, so fix firmly that beta-minus moves the element one place forward and beta-plus one place back. Always verify that the top numbers balance and the bottom numbers balance across the arrow; this self-check catches most mistakes. Gamma emission may appear as a statement that neither number changes because only energy is lost.

Try this

Q1. State how the mass and atomic numbers change in alpha decay. [2 marks]

• Cue. Mass number decreases by 4; atomic number decreases by 2.

Q2. In beta-minus decay, what happens to the atomic number? [1 mark]

• Cue. It increases by 1 (a neutron becomes a proton).