Radioactive Decay

Most of the atoms around you are perfectly content. The carbon in your pencil, the oxygen in the air, the iron in a nail — their nuclei have sat unchanged since long before the Earth formed, and will sit unchanged long after. But some nuclei are unstable. They have the wrong balance of protons and neutrons — too many neutrons, or simply too many particles crammed together — and sooner or later they do something about it: they fling out a little packet of radiation and settle into a more stable arrangement.

A nucleus that does this is radioactive, and the flinging-out is radioactive decay. It is the nucleus tidying itself up. Each decay changes the nucleus — sometimes turning one element into a completely different one — and sends out an ionising particle or wave that can knock electrons off other atoms as it flies. That is what makes radiation both useful and dangerous, and it is what this page is about.

Three ways a nucleus lets off steam

There are three main kinds of nuclear radiation, named after the first three Greek letters. They are wildly different in what they are made of, how much damage they do as they pass through matter (their ionising power), and how far they get before something stops them (their penetration).

Alpha (α) — a chunky helium nucleus: 2 protons and 2 neutrons stuck together. It is big, heavy and doubly charged, so it barges into everything it meets and rips electrons off like mad — it is by far the most ionising. But that same bulk means it runs out of steam almost at once: a sheet of paper, or the dead outer layer of your skin, stops it dead. It travels only a few centimetres in air.
Beta (β) — a fast-moving electron, thrown out of the nucleus when one of its neutrons turns into a proton. It is tiny and singly charged, so it is moderately ionising and gets much further than alpha: it needs a few millimetres of aluminium to stop it.
Gamma (γ) — not a particle at all, but a burst of high-energy electromagnetic wave, with no mass and no charge. Because it has no charge it barely interacts, so it is the weakest ioniser but the most penetrating: it sails through skin, paper and metal, and is only really cut down by thick lead or concrete.

Notice the pattern: the most ionising radiation is the least penetrating. Alpha does the most damage but travels the shortest way; gamma does the least damage per collision but goes almost anywhere. Play with the diagram below to see it.

What each decay does to the nucleus

A nucleus is labelled by two numbers, written to the left of its symbol:

{}^{A}_{Z}\text{X} \qquad \begin{aligned} A &= \text{mass number (protons} + \text{neutrons)} \\ Z &= \text{atomic number (protons — which element it is)} \end{aligned}

When radiation leaves, it carries some protons, neutrons or energy away with it, so A and Z change in a fixed, predictable way:

Alpha carries off 2 protons and 2 neutrons, so A falls by 4 and Z falls by 2. The atom becomes a different element, two places back in the periodic table.
Beta turns a neutron into a proton (and throws out the new electron). The total particle count is unchanged, so A stays the same, but there is one extra proton, so Z rises by 1 — one place forward.
Gamma is only surplus energy leaving. It carries away no protons and no neutrons, so A and Z both stay the same. (Gamma usually tags along right after an alpha or beta decay.)

Every balanced nuclear equation must keep two running totals equal on both sides of the arrow:

the mass numbers (top numbers) add up to the same value on each side;
the atomic numbers / charges (bottom numbers) add up to the same value on each side.

Those two rules alone let you find an unknown product in a decay — no memorising required.

Worked example 1 — alpha decay of radium

Radium-226 is an alpha emitter. Write the balanced equation and name the new element.

Step 1 — write what you know. Radium has Z = 88, and an alpha particle is a helium nucleus {}^{4}_{2}\text{He}:

{}^{226}_{\ 88}\text{Ra} \;\longrightarrow\; {}^{?}_{?}\text{X} + {}^{4}_{2}\alpha

Step 2 — balance the top numbers. Mass numbers must match: 226 = A + 4, so A = 222.

Step 3 — balance the bottom numbers. Charges must match: 88 = Z + 2, so Z = 86.

Step 4 — identify the element. The element with Z = 86 is radon. So:

{}^{226}_{\ 88}\text{Ra} \;\longrightarrow\; {}^{222}_{\ 86}\text{Rn} + {}^{4}_{2}\alpha

Radium has decayed into a completely different element — the gas radon.

Worked example 2 — beta decay of carbon-14

Carbon-14 (the isotope used in radiocarbon dating) is a beta emitter. A beta particle is written {}^{\ \ 0}_{-1}\beta — mass number 0 (an electron is far too light to count as a nucleon) and charge -1.

{}^{14}_{\ 6}\text{C} \;\longrightarrow\; {}^{?}_{?}\text{X} + {}^{\ \ 0}_{-1}\beta

Mass numbers: 14 = A + 0, so A = 14 — unchanged.

Charges: 6 = Z + (-1), so Z = 7 — up by one. Element 7 is nitrogen:

{}^{14}_{\ 6}\text{C} \;\longrightarrow\; {}^{14}_{\ 7}\text{N} + {}^{\ \ 0}_{-1}\beta

Under the hood a single neutron has turned into a proton, spitting out the electron we see as the beta particle:

{}^{1}_{0}\text{n} \;\longrightarrow\; {}^{1}_{1}\text{p} + {}^{\ \ 0}_{-1}\beta

Sometimes a nucleus is left holding extra energy after an alpha or beta decay — an "excited" state, marked with a little star. It drops to its calm ground state by shedding that energy as a gamma ray, with no change to what it is made of:

{}^{60}_{27}\text{Co}^{*} \;\longrightarrow\; {}^{60}_{27}\text{Co} + \gamma

Same 60 nucleons, same 27 protons, still cobalt — only lighter on energy. This cobalt-60 gamma source is exactly the kind used to sterilise hospital equipment and to treat some cancers.

Decay is random — genuinely random

Here is the strangest and most important fact about radioactivity. If you sit and stare at one single unstable nucleus, you cannot say when it will decay. It might go in the next second; it might sit there for a million years. There is nothing wrong with it, no fuse burning down, no countdown — decay is a random, spontaneous event. Two identical nuclei, side by side, will decay at wildly different times, purely by chance.

And you cannot make a nucleus decay. Heating it, cooling it, crushing it, dissolving it in acid, hitting it with a hammer — none of it changes anything. The nucleus is buried so deep inside the atom that the ordinary chemistry going on outside simply cannot reach it. Radioactive decay is one of the very few processes in nature you can neither predict nor control.

So how can we use something so unpredictable? The trick is numbers. A speck of material holds billions upon billions of nuclei, and while no single one is predictable, the crowd is beautifully regular. We measure the activity of a source — how many nuclei decay each second — in becquerels (Bq), where 1\,\text{Bq} = 1 decay per second. A detector such as a Geiger–Müller tube reports a steady count rate (counts per second), and from that average behaviour we build everything from carbon dating to medical scanners.

You cannot predict or hurry a single decay. "It's been a while, so it's due" is wrong — a nucleus has no memory and no schedule. Each moment is a fresh, independent roll of the dice, and nothing you do to the sample changes the odds.
Most ionising ≠ most dangerous everywhere. Alpha is the most ionising but the least penetrating — outside the body your skin stops it. Don't confuse "does the most damage per hit" with "reaches the furthest": they are opposites here. (Swallow an alpha emitter, though, and there is no skin to protect you — then it is the most dangerous of all.)
Radiation is not "radioactive dust". Radiation is the particles and waves emitted by unstable nuclei. Standing in a beam of gamma rays does not leave radioactive powder on you, and it does not make you radioactive — the energy passes through. (Irradiated food is not radioactive either.) Contamination is a separate thing: actually getting radioactive material on or in you.

Dangerous — and extremely useful

Ionising radiation is risky precisely because it can tear electrons off atoms. Inside living cells it can damage DNA, which is why large doses cause radiation sickness and can trigger cancer, and why radioactive sources are handled with shielding, distance and tongs. Yet the very same ionising power is put to work all around you:

Medicine — gamma sources sterilise surgical instruments; gamma tracers are injected to image organs; focused beams treat tumours (radiotherapy).
Dating the past — the steady decay of carbon-14 tells archaeologists the age of ancient wood, bone and cloth.
Industry — beta sources gauge the thickness of paper or foil as it rolls off a machine, because the amount that gets through depends on the thickness.
Safety — smoke alarms in millions of homes use a tiny alpha source (see below).

Look inside a typical smoke detector and you'll find a speck of americium-241, an alpha emitter. Its alpha particles ionise the air inside a small chamber, letting a tiny electric current flow across the gap. When smoke drifts in, the big smoke particles soak up the alphas and mop up those ions, the current drops — and the alarm screams.

Alpha is the perfect choice: it is easily stopped, so it never escapes the plastic casing to reach you, yet it is intensely ionising, so a minuscule source does the job. It's a lovely example of choosing a radiation to fit the task — the same reasoning a doctor or engineer uses. (And Marie Curie, who coined the word "radioactivity" and discovered radium and polonium, would be amazed that her mysterious "rays" now guard our kitchens.)