Alpha, Beta & Gamma Decay
How unstable nuclei change.
Lesson at a glanceShow the key points
- α: Z − 2, A − 4; Q = [m(X) − m(Y) − m(He)]c².
- β⁻: Q = [m(X) − m(Y)]c²; β⁺: subtract 2mₑc².
- β energies are spread because the neutrino shares Q.
- γ: excited nucleus emits a photon; Z, N unchanged.
A nucleus off the valley of stability will not stay as it is. It throws out an alpha particle, turns a neutron into a proton (or the reverse), or sheds extra energy as a gamma photon, moving step by step towards stability.
Alpha decay
The nucleus emits an alpha particle, a helium-4 nucleus (2 protons, 2 neutrons):
Z changes, so the element changes: the parent becomes a different daughter. For example ²¹²Bi (83 protons) → ²⁰⁸Tl (81 protons) + α. Alpha decay is typical of nuclei with A > 210, which are too large for the nuclear force to hold against Coulomb repulsion.
Find the kinetic energy of the α particle in ²²⁶Ra → ²²²Rn + α, ignoring the recoil of the radon. Atomic masses: ²²⁶Ra 226.025410 u, ²²²Rn 222.017578 u, ⁴He 4.002603 u.
Beta decay
Beta decay changes N/Z by converting one kind of nucleon into the other, through the weak force.
β⁻: a neutron becomes a proton
A nucleus with too many neutrons converts one, creating an electron and an antineutrino (uncharged, almost massless, spin ½):
The heavy daughter barely moves, so Q is shared between the electron and the antineutrino in any proportion. The electron’s kinetic energy can be anything from zero up to Q.
β⁺: a proton becomes a neutron
A nucleus with too many protons converts one, creating a positron (the electron’s antiparticle: same mass, charge +e) and a neutrino. An electron and a positron that meet annihilate into energy; the neutrino and antineutrino are also antiparticles of each other.
A free proton cannot do this: the neutron is heavier, so Q would be negative. A free neutron, however, does decay (half-life about 10 minutes).
Electron capture
Instead of emitting a positron, the nucleus may swallow one of its own atomic electrons, usually from the K shell: p + e⁻ → n + ν, so AZX + e⁻ → AZ−1Y + ν, with Q = [m(X) − m(Y)]c² (46.15). The hole left in the K shell is filled from above, so X-rays follow.
Find Q for (a) ¹⁴C → ¹⁴N + e⁻ + ν̄ and (b) ²²Na → ²²Ne + e⁺ + ν. Atomic masses: ¹⁴C 14.003242 u, ¹⁴N 14.003074 u, ²²Na 21.994437 u, ²²Ne 21.991385 u.
⁶⁰Co (59.933817 u) β⁻-decays to a ⁶⁰Ni nucleus in an excited state 2.506 MeV above its ground state (ground-state atomic mass 59.930786 u). What is the maximum kinetic energy of the electron?
Decay series
The daughter may itself be unstable and decay again, and so on until a stable nucleus is reached. Uranium-238 passes through fourteen decays before ending as lead-206.
Gamma decay
Nucleons occupy discrete energy levels, typically MeV apart, far too far to excite by heating. But an α or β decay often leaves the daughter in an excited state. It then drops to its ground state by emitting one or more photons, just as an excited atom emits light, only with far more energy. This electromagnetic radiation is a gamma ray, with λ = hc/E. Neither Z nor N changes.
The excited ⁶⁰Ni nucleus from the example above reaches its ground state by emitting two photons in turn, of 1.173 MeV and 1.333 MeV. Check the energy, and find the wavelength of the second photon.
α, β and γ emission are together called radioactive decay, and the rays nuclear radiation.
Properties of the radiations
| α rays | β rays | γ rays | |
|---|---|---|---|
| What | Helium nuclei (+2e) | Electrons (β⁻) or positrons (β⁺) from nuclei | Short-wavelength photons |
| Deflected by E, B fields? | Yes | Yes | No |
| Penetration | Low: a few cm of air | Medium: several m of air | Highest |
| Ionizing power | Highest | Medium | Lowest |
| Energies from one decay | All equal | Spread from 0 to Q | All equal (each line) |
| Speed | ~10⁶–10⁷ m/s | Up to near c | c |
α and (weakly) β particles make some fluorescent materials flash (scintillation), and all three ionize gases.
- 1α decay: Z − 2, A − 4; Q = [m(X) − m(Y) − m(He)]c².
- 2β⁻: n → p + e⁻ + ν̄, Q = [m(X) − m(Y)]c²; β⁺: p → n + e⁺ + ν, Q = [m(X) − m(Y) − 2mₑ]c².
- 3Electron capture: p + e⁻ → n + ν, followed by X-rays.
- 4β energies are spread (neutrino shares Q); α and γ energies are sharp.
- 5γ decay: excited nucleus emits a photon; Z and N unchanged.
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