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Radioactivity was discovered by Henri Becquerel in 1896, when he noticed that uranium salts left in a drawer had fogged a photographic plate in the absence of any light. Within a few years, Marie and Pierre Curie had isolated two new radioactive elements (polonium and radium), and Ernest Rutherford had classified the emissions into three distinct types based on how they were deflected by electric and magnetic fields. He labelled them with the first three letters of the Greek alphabet: alpha (α), beta (β) and gamma (γ). Over a century later, those names are still in use — and the underlying physics is part of Module 6.4 — Nuclear and Particle Physics of the OCR A-Level Physics A specification (H556).
This lesson introduces the three main modes of radioactive decay (together with the β^+ variant that becomes important in medical imaging later in the course), shows you how to write and balance nuclear equations, and sets out the typical properties and hazards of each type of radiation.
A radioactive nucleus is one that is unstable: it contains too many or too few neutrons for its proton number, or too much total mass, and it spontaneously transforms itself into a more stable configuration by emitting particles or photons. The transformation is governed by the laws of quantum mechanics and cannot be predicted for any individual nucleus — all we can say is the probability that a given nucleus will decay in a given time interval. This is the subject of Lesson 2 on the decay constant and half-life.
Decay is a spontaneous and random process. It is spontaneous in the sense that no external trigger is required: the nucleus rearranges itself from within. It is random in the sense that we cannot predict when a particular nucleus will decay — only the probability per unit time. Despite this randomness at the level of single nuclei, the behaviour of a large collection of nuclei is beautifully predictable, following a simple exponential law.
The OCR specification asks you to recognise and write equations for four kinds of decay:
α): emission of a helium-4 nucleus.β^-): emission of an electron and an antineutrino.β^+): emission of a positron and a neutrino.γ): emission of a high-energy photon from an excited nucleus.All four are examples of conservation laws in action. In every decay, charge is conserved, nucleon number is conserved, and (with neutrinos and antineutrinos included) lepton number is conserved. We shall see these rules in play shortly.
In alpha decay, the nucleus emits an alpha particle, which is a helium-4 nucleus consisting of two protons and two neutrons. The alpha particle carries away 4 nucleons and 2 units of positive charge. The parent nucleus therefore loses 4 from its nucleon (mass) number A and 2 from its proton (atomic) number Z:
(A,Z)X → (A-4, Z-2)Y + (4,2)He
A standard example is the alpha decay of uranium-238 to thorium-234:
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Check the arithmetic: 238 = 234 + 4 (nucleon number conserved), 92 = 90 + 2 (charge conserved). Every balanced nuclear equation must pass these two simple checks.
Alpha particles are heavy (about 7300 times the mass of an electron) and doubly charged, so they interact strongly with matter and lose energy rapidly. A typical alpha particle travels only a few centimetres in air and is stopped by a sheet of paper or the outermost dead layer of skin. Alpha emitters are therefore harmless outside the body — but extremely dangerous if ingested or inhaled, because their short range concentrates all the ionising energy into a tiny volume of living tissue.
Alpha decay tends to occur in very heavy nuclei (Z > 82), where the Coulomb repulsion between protons becomes comparable to the strong nuclear force holding the nucleus together. The alpha particle itself is an exceptionally tightly bound cluster, which is why it is emitted intact rather than as two separate nucleons.
In beta-minus decay, a neutron inside the nucleus transforms itself into a proton, emitting an electron (the β^- particle) and an electron antineutrino:
n → p + e^- + ν̄_e
At the nuclear level, the nucleon number is unchanged (a neutron has become a proton, both being nucleons), while the atomic number increases by 1 (one more proton):
(A,Z)X → (A, Z+1)Y + (0,-1)e + ν̄_e
A classic example is the beta-minus decay of carbon-14:
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄_e
Carbon-14 beta-decays to nitrogen-14 with a half-life of about 5730 years. This is the decay on which radiocarbon dating is based.
Beta-minus particles are fast-moving electrons, typically with kinetic energies of the order of 1 MeV. Because electrons are light, they have much longer ranges in matter than alpha particles — several metres in air and up to a few millimetres in aluminium. They ionise less densely and are less immediately dangerous externally, but they can still burn skin and damage tissue.
The antineutrino (ν̄_e) was proposed by Pauli in 1930 to rescue conservation of energy. Without it, the emitted electron would have a fixed energy (as in alpha decay), but experiments showed that beta particles emerge with a continuous spectrum of energies up to some maximum. Pauli's neutrino carries the "missing" energy away invisibly. It was finally detected in 1956 by Reines and Cowan, confirming the picture.
In beta-plus decay, a proton transforms into a neutron, emitting a positron (the antiparticle of the electron) and an electron neutrino:
p → n + e^+ + ν_e
The atomic number decreases by 1 (one fewer proton), while the nucleon number is unchanged:
(A,Z)X → (A, Z-1)Y + (0,+1)e + ν_e
A standard example is the beta-plus decay of fluorine-18, the radiotracer used in PET scans (which we meet in Lesson 14):
¹⁸₉F → ¹⁸₈O + ⁰₊₁e + ν_e
Fluorine-18 beta-plus-decays to oxygen-18 with a half-life of about 110 minutes — conveniently short for medical use, long enough to prepare a dose and inject it before it all decays away.
Beta-plus decay is less common than beta-minus decay overall but is vital in nuclear medicine. It only occurs in nuclei where the mass difference between parent and daughter exceeds 2m_ec^2 (the rest energy of the emitted positron plus an electron that must be "created" from vacuum to conserve lepton number, though this is a subtlety you need not worry about at A-Level).
The emitted positron does not travel far. Within a millimetre or so it encounters an electron and annihilates (Lesson 8), producing two 511 keV gamma photons travelling in opposite directions. It is these photons, not the positron itself, that PET scanners detect.
In gamma decay, a nucleus in an excited state drops to a lower energy state, emitting the excess energy as a single high-energy photon (a gamma ray, γ):
(A,Z)X* → (A,Z)X + γ
The star * denotes an excited nuclear state. Note that neither A nor Z changes: the nucleus is the same species, just in a lower-energy configuration. Gamma emission is the nuclear analogue of the photon emission you met in quantum physics, but with photon energies in the MeV range rather than the eV range.
A typical example is the decay of technetium-99m, the most widely used medical imaging radioisotope:
⁹⁹ᵐ₄₃Tc → ⁹⁹₄₃Tc + γ (E_γ = 140 keV)
The "m" stands for metastable: it is an excited state of Tc-99 that has an unusually long half-life of about 6 hours, long enough for it to be delivered to a hospital and injected into a patient. When it decays it emits a 140 keV gamma photon, which is ideal for imaging — energetic enough to pass through the body, but not so energetic that it cannot be detected efficiently.
Gamma rays are the most penetrating form of radiation. They can pass through several centimetres of lead and many metres of concrete; they are only attenuated, never fully stopped, by ordinary shielding. They are usually emitted alongside alpha or beta decay, as the daughter nucleus rearranges itself into its ground state.
| Decay | Particle emitted | ΔA | ΔZ | Charge | Mass (u) | Range in air | Stopped by |
|---|---|---|---|---|---|---|---|
Alpha (α) | ⁴₂He nucleus | −4 | −2 | +2e | 4.00 | few cm | paper / skin |
Beta-minus (β^-) | electron + antineutrino | 0 | +1 | −e | ≈0.00055 | few m | few mm aluminium |
Beta-plus (β^+) | positron + neutrino | 0 | −1 | +e | ≈0.00055 | few mm | annihilates quickly |
Gamma (γ) | photon | 0 | 0 | 0 | 0 | many m | cm of lead |
The values of ΔA and ΔZ are the changes in nucleon number and proton number of the parent nucleus. A single nuclear event rarely involves more than one of these processes happening at the same time — but a given radioisotope may undergo several decays in succession, forming a decay chain.
Every balanced nuclear equation must satisfy two rules:
A) on the left equals the sum on the right.Z) on the left equals the sum on the right.Leptons (electrons, positrons, neutrinos, antineutrinos) have A = 0, so they contribute nothing to the nucleon count. Electrons have Z = -1 (for counting purposes, reflecting their negative charge); positrons have Z = +1. Neutrinos and antineutrinos have zero charge and zero nucleon number, so they do not appear in the A/Z balancing, but you must still write them in to make the equation physically complete.
Radium-226 alpha-decays. Write the full nuclear equation and identify the daughter nucleus.
Solution. The parent is ²²⁶₈₈Ra. An alpha particle carries away 4 nucleons and 2 protons, so the daughter has A = 226 - 4 = 222 and Z = 88 - 2 = 86. Element 86 is radon (Rn). Hence:
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
The daughter is radon-222, itself radioactive, and part of the natural uranium decay chain.
Strontium-90 beta-minus-decays. Write the nuclear equation.
Solution. The parent is ⁹⁰₃₈Sr. In beta-minus decay A is unchanged and Z increases by 1, giving ⁹⁰₃₉Y (yttrium-90).
⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e + ν̄_e
Check: A: 90 = 90 + 0 + 0 ✓; Z: 38 = 39 + (-1) + 0 ✓.
Sodium-22 beta-plus-decays. Write the nuclear equation.
Solution. The parent is ²²₁₁Na. Beta-plus decay leaves A unchanged and decreases Z by 1, giving ²²₁₀Ne (neon-22).
²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + ν_e
Check: A: 22 = 22 + 0 + 0 ✓; Z: 11 = 10 + 1 + 0 ✓.
Uranium-238 decays via a long chain of alphas and betas, eventually reaching stable lead-206. How many alpha and beta-minus decays are involved in total?
Solution. The total changes are ΔA = 206 - 238 = -32 and ΔZ = 82 - 92 = -10.
Each alpha decay gives ΔA = -4, ΔZ = -2. Each beta-minus decay gives ΔA = 0, ΔZ = +1.
Let n_α be the number of alphas and n_β the number of betas. Then:
-4 n_α = -32 → n_α = 8
-2 n_α + n_β = -10
-16 + n_β = -10 → n_β = 6
So the uranium-238 chain involves 8 alpha decays and 6 beta-minus decays. This is the standard "4n+2" actinium series, and it is the main source of radon gas in buildings built over granite.
flowchart TB
P["Parent nucleus<br/>(A, Z)"]
A["Alpha decay<br/>Emits ⁴₂He<br/>(A−4, Z−2)"]
Bm["Beta-minus decay<br/>n → p + e⁻ + ν̄<br/>(A, Z+1)"]
Bp["Beta-plus decay<br/>p → n + e⁺ + ν<br/>(A, Z−1)"]
G["Gamma decay<br/>Excited → ground<br/>(A, Z) unchanged"]
P --> A
P --> Bm
P --> Bp
P --> G
flowchart LR
S["Source"] --> P1["Paper"] --> Al["Aluminium<br/>(few mm)"] --> Pb["Lead<br/>(several cm)"] --> X["Beyond"]
S -.alpha.-> P1
S -.beta.-> Al
S -.gamma.-> Pb
Alpha is stopped by paper. Beta is stopped by a few millimetres of aluminium. Gamma is only attenuated, never completely stopped, by lead shielding — the question is one of intensity, which we quantify in Lesson 10 on X-ray attenuation.
An inverse relationship holds between penetrating power and ionising ability. Alpha particles, with their high charge and low speed, ionise air very densely — producing of order 10^5 ion pairs per centimetre of track. Beta particles ionise perhaps 100 times less densely. Gamma rays barely ionise at all directly; they transfer their energy mainly by Compton scattering or photoelectric absorption, in discrete events separated by centimetres of travel.
Biologically, this has important consequences. Alpha radiation is the most dangerous if the source is internal — inside the lungs or the gut — because it dumps its energy in a tiny volume of tissue. Gamma radiation is more dangerous externally because it penetrates deep into the body. Beta radiation is intermediate.
When writing a nuclear equation, always check that the top (nucleon) and bottom (charge) numbers balance. In OCR papers, failure to include the antineutrino in a beta-minus decay or to balance
Zcorrectly is the single commonest source of lost marks on this topic.
Remember: in
β^-decay the emitted particle is an antineutrino (ν̄_e), but inβ^+decay it is a neutrino (ν_e). This is required by lepton number conservation, which the OCR specification mentions explicitly.
A or Z balancing, OCR mark schemes explicitly require it to be written in.β^- and β^+. β^- is a fast electron emitted when a neutron turns into a proton (Z increases); β^+ is a positron emitted when a proton turns into a neutron (Z decreases).⁴₂He for an alpha particle. You must include the nucleon and charge numbers so the equation can be balanced.A and Z unchanged. Students sometimes alter the daughter nucleus unnecessarily.1 \text{ MeV} = 1.60 \times 10^{-13} J.⁴₂He nucleus; ΔA = -4, ΔZ = -2.ΔA = 0, ΔZ = +1; the underlying process is n → p + e^- + ν̄_e.ΔA = 0, ΔZ = -1; the underlying process is p → n + e^+ + ν_e.ΔA = 0, ΔZ = 0.In the next lesson we put numbers on how fast a sample of radioactive nuclei decays, by introducing the decay constant and the half-life.