Radioactive Decay and Nuclear Equations

When an unstable nucleus decays, it throws out nuclear radiation and changes into a different nucleus. There are three kinds of radiation you must know — alpha, beta and gamma, named after the first three letters of the Greek alphabet ( $\alpha$ , $\beta$ , $\gamma$ ) — and they differ hugely in what they are made of, how far they travel and how strongly they ionise the materials they pass through. We can record exactly what happens in a decay using a nuclear equation, a kind of balance sheet for the nucleus that must always balance. This lesson, part of Topic P4 (Waves and radioactivity) of OCR Gateway Combined Science A, describes the three radiations, explains what "ionising" means, and shows how to write and balance nuclear equations for alpha, beta and gamma decay.

By the end of this lesson you should be able to describe the nature, charge and mass of alpha, beta and gamma radiation, compare their penetrating ability and ionising power, explain what ionisation is, and write and balance nuclear equations (conserving both mass number and atomic number).

This lesson combines AO1 recall of the three radiations with strong AO2 application when you write and balance nuclear equations, conserving both mass number and atomic number, and AO3 reasoning when you compare penetrating ability with ionising power.

Alpha, Beta and Gamma Radiation

Alpha radiation ( $\alpha$ ) is a stream of alpha particles. An alpha particle is a helium nucleus — two protons and two neutrons bound together — emitted at high speed. It is written $^{4}_{2}\text{He}$ or $^{4}_{2}\alpha$ . It has a relative charge of $+2$ and a relative mass of $4$ (the heaviest of the three). Because it is large, slow and highly charged, it interacts strongly with atoms and is very strongly ionising, but it is weakly penetrating — it is stopped by a sheet of paper, by the skin, or by a few centimetres of air.

Beta radiation ( $\beta$ ) is a stream of beta particles. A beta particle is a fast-moving electron emitted from the nucleus, written $^{\ \ 0}_{-1}\text{e}$ or $^{\ \ 0}_{-1}\beta$ . It seems strange that an electron comes out of the nucleus, but it is created at the moment of decay when a neutron turns into a proton. It has a relative charge of $-1$ and a negligible mass ( $\tfrac{1}{1836}$ ). It is moderately ionising and moderately penetrating — stopped by a few millimetres of aluminium, and it travels about a metre in air.

Gamma radiation ( $\gamma$ ) is not a particle at all but a high-frequency electromagnetic wave released from the nucleus, often straight after an alpha or beta decay leaves the nucleus with surplus energy. It is written $^{0}_{0}\gamma$ . It has no charge and no mass. Because it has neither charge nor mass, it interacts only weakly with matter, so it is weakly ionising but highly penetrating — it is only ever reduced (never fully stopped) by thick lead or thick concrete.

Exam Tip: Learn the "stopped by" sequence: alpha → paper/skin, beta → a few mm of aluminium, gamma → reduced by thick lead/concrete. Say gamma is "reduced" by lead, not "stopped" — a common misconception is that lead absorbs gamma completely, but it can only cut it down, never remove it entirely.

Comparing Penetration and Ionising Power

The defining feature of the three radiations is the trade-off between penetration and ionising power: the more strongly a radiation ionises, the less far it penetrates, and vice versa.

Radiation	What it is	Charge	Mass	Stopped / reduced by	Range in air	Ionising power
Alpha ( $\alpha$ )	Helium nucleus (2p + 2n)	$+2$	$4$	Paper, skin, few cm of air	A few cm	Very strong
Beta ( $\beta$ )	Fast electron	$-1$	≈ 0	A few mm of aluminium	~1 m or more	Moderate
Gamma ( $\gamma$ )	High-frequency EM wave	$0$	$0$	Reduced by thick lead/concrete	Very long	Weak

The pattern to remember: alpha = strongly ionising, weakly penetrating; gamma = weakly ionising, strongly penetrating; beta = in between on both counts.

Exam Tip: Remember the inverse link: the more ionising a radiation is, the less penetrating it is. This is why alpha (most ionising) is stopped most easily and gamma (least ionising) penetrates furthest.

What "Ionising" Means and Why It Matters

The single most important property of nuclear radiation is its ionising power — its ability to knock electrons off atoms, turning neutral atoms into charged ions. When a fast alpha or beta particle, or a gamma ray, passes through a material, it transfers energy to the atoms it meets and can pull electrons away from them. Each "knock" creates an ion and uses up a little of the radiation's energy.

This explains the inverse link between ionising power and penetration:

A strongly ionising radiation (like alpha) creates a great many ions in a short distance, so it loses its energy quickly and is stopped after only a short distance — it penetrates poorly.
A weakly ionising radiation (like gamma) creates very few ions as it passes, so it loses its energy slowly and can travel a long way before being absorbed — it penetrates deeply.

Ionising power also explains why radiation is hazardous to living things: ionising the atoms in living cells can damage or kill them, or alter the DNA — which is the basis of both the dangers and several of the medical uses of radiation you will meet in the next lesson.

Exam Tip: "Ionising" means knocking electrons off atoms to form ions. The more ionising a radiation, the more energy it loses per centimetre, so the less it penetrates — which is exactly why alpha (most ionising) is stopped most easily and gamma (least ionising) penetrates furthest.

Writing Nuclear Equations: The Two Golden Rules

A nuclear equation uses the standard nuclide notation $^{A}_{Z}\text{X}$ , where $A$ is the mass number (top) and $Z$ is the atomic number (bottom). The particles you will meet are:

Particle	Symbol	Mass number ( $A$ )	Atomic number ( $Z$ )
Alpha particle	$^{4}_{2}\text{He}$	$4$	$2$
Beta particle	$^{\ \ 0}_{-1}\text{e}$	$0$	$-1$
Gamma ray	$^{0}_{0}\gamma$	$0$	$0$

Notice that the beta particle is written with an atomic number of $-1$ . This is not because it contains a negative proton, but because giving it a "charge number" of $-1$ makes the equation balance correctly — its single negative charge has to be accounted for. The two golden rules for any nuclear equation are:

the sum of the mass numbers (top numbers) is the same on both sides (nucleons are conserved), and
the sum of the atomic numbers (bottom numbers) is the same on both sides (charge is conserved).

Exam Tip: The two rules to apply every time are: top numbers balance (mass number conserved) and bottom numbers balance (charge conserved). Check both before you finish.

Alpha Decay

In alpha decay, the nucleus emits an alpha particle ( $^{4}_{2}\text{He}$ ). Since the alpha particle carries away 2 protons and 2 neutrons, the original nucleus loses 4 from its mass number and loses 2 from its atomic number:

mass number: $A \to A - 4$
atomic number: $Z \to Z - 2$

Losing 2 protons means the atom becomes a different element, two places back in the periodic table. A classic example is the alpha decay of uranium-238 into thorium-234:

$^{238}_{\ 92}\text{U} \rightarrow\ ^{234}_{\ 90}\text{Th} + {}^{4}_{2}\text{He}$

Check it balances. Mass numbers: $238 = 234 + 4$ . ✓ Atomic numbers: $92 = 90 + 2$ . ✓ Both sides balance, so the equation is correct.

Worked Example 1 — Alpha decay of radium-226

Radium-226, $^{226}_{\ 88}\text{Ra}$ , decays by emitting an alpha particle. Write the nuclear equation and identify the daughter nucleus. (Radon has atomic number 86.)

Step 1 — alpha decay reduces the mass number by 4: $226 - 4 = 222$ .

Step 2 — alpha decay reduces the atomic number by 2: $88 - 2 = 86$ .

Step 3 — atomic number 86 is radon (Rn), so the daughter is $^{222}_{\ 86}\text{Rn}$ .

Step 4 — write the equation:

$^{226}_{\ 88}\text{Ra} \rightarrow\ ^{222}_{\ 86}\text{Rn} + {}^{4}_{2}\text{He}$

Step 5 — check: mass numbers $226 = 222 + 4$ ✓; atomic numbers $88 = 86 + 2$ ✓.

Answer: $^{226}_{\ 88}\text{Ra} \rightarrow\ ^{222}_{\ 86}\text{Rn} + {}^{4}_{2}\text{He}$ — radium-226 decays to radon-222.

Exam Tip: For alpha decay, do $A - 4$ and $Z - 2$ , then use the new atomic number to name the daughter element. Always finish by checking both totals balance.

Radioactive Decay and Nuclear Equations

Radioactive Decay and Nuclear Equations

Alpha, Beta and Gamma Radiation

Comparing Penetration and Ionising Power

What "Ionising" Means and Why It Matters

Writing Nuclear Equations: The Two Golden Rules

Alpha Decay

Worked Example 1 — Alpha decay of radium-226

Beta Decay

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