Radioactivity

Inside a nucleus two forces compete. The strong nuclear force pulls all the nucleons together but only reaches its immediate neighbours. Electrostatic repulsion pushes the protons apart and reaches right across the nucleus. In a small nucleus the strong force wins easily; as nuclei get larger the repulsion catches up, and beyond about 83 protons no arrangement is stable at all.

An unstable nucleus sheds the imbalance by emitting radiation. Two words matter here and both are worth marks. The process is spontaneous: nothing triggers it, and heating, cooling or chemical reaction make no difference. It is also random: you cannot predict which nucleus will go next, or when.

Randomness at the level of one nucleus becomes near-perfect predictability across a sample, because a gram of material contains something like 10²² nuclei. This is exactly why half-life is a reliable quantity even though each individual decay is not.

Three types of emission are met at this level, and they differ in almost every respect: what they are made of, what charge they carry, how far they travel and what stops them.

An alpha particle is a helium nucleus — two protons and two neutrons — so it is relatively massive and carries a charge of +2. That large charge makes it strongly ionising: it rips electrons off the atoms it passes and loses its energy quickly. It travels only a few centimetres in air and is stopped by a sheet of paper.

A beta particle is a fast-moving electron, created when a neutron in the nucleus turns into a proton. It is far lighter, carries a charge of −1, and is much less ionising, so it penetrates further — a few millimetres of aluminium will stop it.

A gamma ray is not a particle at all but a high-frequency electromagnetic wave. It has no charge and no mass, ionises only weakly, and is the most penetrating: several centimetres of lead reduce it, but nothing absorbs it completely.

A decay equation must balance twice over: the nucleon numbers on each side must be equal, and so must the proton numbers. Get both right and the identity of the new element follows automatically from the periodic table.

In alpha decay the nucleus loses two protons and two neutrons, so A falls by 4 and Z falls by 2. The element moves two places back in the periodic table.

In beta decay a neutron becomes a proton and an electron, and the electron is ejected. The nucleon number does not change at all, because a neutron has simply been swapped for a proton. The proton number rises by 1, so the element moves one place forward.

In gamma emission the nucleus loses energy but no particles, so neither number changes. Gamma emission usually accompanies alpha or beta decay rather than happening alone — the nucleus is left in an excited state and sheds the surplus energy as a gamma ray.

Radioactive decay does not proceed at a steady rate. Each nucleus has the same chance of decaying in the next second, so the more undecayed nuclei remain, the more decays happen — and as the sample is used up, the activity falls away. The result is that equal fractions decay in equal times, not equal amounts.

That is why half-life works. Whatever you start with, half of it is gone after one half-life, a quarter remains after two, an eighth after three. Half-lives range from fractions of a second to billions of years depending on the isotope, but the pattern is always the same shape.

The curve never reaches zero. Each halving takes the same time and removes half of what is left, so the graph flattens out towards the axis without ever touching it.

Each marked step is one half-life, and each one halves what is left rather than what you started with. Change the half-life slider and the shape of the curve is identical — only the timescale stretches.

Before any measurement can be used, the background count must be dealt with. Ionising radiation is present everywhere — from radon gas seeping out of rocks, from cosmic rays, from the potassium in our own bodies, from food and building materials. A detector registers all of it whether or not your source is there.

The procedure is always: measure the background with the source removed, then subtract that from every reading. A reading that has had the background taken off is called the corrected count rate, and half-life questions are answered using corrected values only.

The calculation itself is short. Work out how many half-lives have passed, then halve that many times — which means dividing by 2ⁿ, not by 2n. Dividing by 8 instead of by 2³ is the most common single error in this topic.