Alpha, Beta, and Gamma Radioactive Decay

Radioactive decay is the spontaneous transformation of an unstable nucleus with the emission of radiation: alpha decay emits a helium-4 nucleus (⁴₂He), beta decay converts a neutron into a proton (β⁻, emitting an electron and an antineutrino) or a proton into a neutron (β⁺, emitting a positron and a neutrino), and gamma decay emits a high-energy photon as the nucleus drops to a lower energy state. In brief: in nuclear equations, the sum of the nucleon numbers (A) and the sum of the charges (Z) are conserved. Alpha particles are stopped by paper, beta particles by a few millimeters of aluminum, and gamma rays need thick lead or concrete. Alpha is the most strongly ionizing and gamma the least. The energy released in a decay is the Q-value, from the mass difference.

Smoke detectors, carbon dating, nuclear medicine and the natural radioactivity of rocks involve decay. This guide describes the three main types of radioactive emission, the nuclear equations, the properties of the radiations, compares them in a table, works through numerical examples of decay energies and corrects common mistakes.

Why do nuclei decay?

A nucleus is unstable if it can reach a state of lower energy (a more tightly bound state) by emitting radiation. Heavy nuclei (Z > 83) have too many protons and too large a size for the short-range strong force to balance electric repulsion; nuclei with too many neutrons or too few neutrons compared with the stable ratio convert one type of nucleon into the other. Decay is a random process: the probability that a given nucleus decays in a short time is constant and does not depend on temperature, pressure or chemical state, but the time at which a particular nucleus decays cannot be predicted. For a large number of nuclei the behavior follows the exponential law with a half-life, discussed in the next article. The radiation is called ionizing since it removes electrons from atoms along its path.

What is alpha decay?

An alpha particle is a helium-4 nucleus (2 protons and 2 neutrons, charge +2e). It is emitted by heavy nuclei, with a typical energy of 4 to 9 MeV. The nucleus loses 4 nucleon numbers and 2 protons: ^A_ZX → ^A−4_Z−2Y + ⁴₂He. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Alpha particles are massive and charged, so they interact strongly with matter and lose energy rapidly: the range in air is a few centimeters, and they are stopped by a sheet of paper or the outer layer of skin. They are the most ionizing radiation (and are very dangerous if the source is swallowed or inhaled, for example radon gas). Alpha particles from a given nuclide have discrete energies. The tunneling of the alpha particle through the nuclear barrier determines the half-life.

What is beta decay?

• Beta-minus (β⁻): a neutron in the nucleus changes into a proton, an electron and an electron antineutrino: n → p + e⁻ + ν̄_e. The nucleus: ^A_ZX → ^A_Z+1Y + e⁻ + ν̄_e. Example: ¹⁴₆C → ¹⁴₇N + e⁻ + ν̄_e. It occurs in neutron-rich nuclei.
• Beta-plus (β⁺, positron emission): p → n + e⁺ + ν_e. The nucleus: ^A_ZX → ^A_Z−1Y + e⁺ + ν_e. Example: ¹⁸₉F → ¹⁸₈O + e⁺ + ν_e (used in PET scans). Electron capture is a competing process.

The energy released is shared between the electron (or positron) and the neutrino, so beta particles have a continuous range of energies from zero to a maximum; this led Wolfgang Pauli to postulate the neutrino in 1930. Beta particles are lighter than alpha particles, are less ionizing and more penetrating (several meters in air, stopped by a few millimeters of aluminum). The weak interaction is responsible for beta decay.

What is gamma decay?

After alpha or beta decay, the daughter nucleus is often left in an excited state. It reaches the ground state by emitting a gamma-ray photon of energy typically 0.1 to a few MeV: ^A_ZX* → ^A_ZX + γ. The nucleus keeps the same A and Z. The photon energies are discrete and characteristic of the nuclide: cobalt-60 emits 1.17 and 1.33 MeV. Gamma rays are not charged, and are the least ionizing and most penetrating radiation: their intensity decreases exponentially in matter, requiring thick lead or concrete. Some excited states are long-lived (isomers), such as technetium-99m (6 hours), widely used in medical imaging.

The three radiations compared

Worked example: decay equations and energies

1. Alpha decay of radium-226: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Check: A: 226 = 222 + 4; Z: 88 = 86 + 2.

2. Energy of the decay of uranium-238. Atomic masses: ²³⁸U 238.050788 u, ²³⁴Th 234.043601 u, ⁴He 4.002603 u. Δm = 238.050788 − 234.043601 − 4.002603 = 0.004584 u. Q = 0.004584 × 931.5 = 4.27 MeV. Because of the conservation of momentum, the alpha particle carries Q × 234 ÷ 238 = 4.20 MeV, and the thorium nucleus recoils with the rest, 0.07 MeV.
3. Beta-minus decay of carbon-14. ¹⁴₆C → ¹⁴₇N + e⁻ + ν̄_e. With atomic masses 14.003242 u and 14.003074 u, Δm = 0.000168 u, Q = 0.156 MeV. The electron has a maximum energy of 0.156 MeV (the average is lower, about 0.05 MeV).
4. Unknown product. Thorium-234 (Z = 90) emits a beta-minus particle: the daughter has A = 234 and Z = 91, which is protactinium-234 (²³⁴₉₁Pa).

5. Decay series. Uranium-238 decays by 8 alpha and 6 beta-minus emissions to stable lead-206: A: 238 − 8 × 4 = 206 ✓; Z: 92 − 8 × 2 + 6 = 82 ✓.
6. Gamma decay. ⁶⁰Co → ⁶⁰Ni* + e⁻ + ν̄_e (beta), followed by ⁶⁰Ni* → ⁶⁰Ni + γ (1.17 MeV) and the second photon (1.33 MeV). The wavelength of a 1.17 MeV photon is 1,240 ÷ 1.17 × 10⁶ = 1.06 × 10⁻³ nm.

How was radioactivity discovered?

Henri Becquerel discovered radioactivity in 1896, when uranium salts fogged photographic plates in the dark. Marie and Pierre Curie isolated polonium and radium in 1898, and shared the 1903 Nobel Prize in Physics with Becquerel. Ernest Rutherford named alpha and beta rays in 1899 (from their penetration), and Paul Villard discovered gamma rays in 1900. Rutherford and Frederick Soddy proposed in 1902 that radioactivity is the transmutation of one element into another. The neutrino was proposed by Pauli in 1930 and detected by Cowan and Reines in 1956.

Which mistakes are common?

Mistake 1: Thinking that gamma rays change the element

Gamma emission does not change A or Z. Alpha and beta decays do.

Mistake 2: Saying that beta particles are orbital electrons

They are created in the decay of a neutron in the nucleus.

Mistake 3: Forgetting the antineutrino or neutrino

Lepton number and energy balance require it in beta decay.

Mistake 4: Believing that the most penetrating radiation is the most harmful outside the body

Alpha emitters are the most hazardous when inside the body, since all their energy is deposited in a small volume of tissue.