Beta decay

Beta decay is a form of radioactive decay in which an unstable atomic nucleus transforms into a more stable one by emitting a beta particle. A beta particle may be either an energetic electron or a positron, created at the moment of decay rather than existing beforehand within the nucleus. The process changes one nucleon species into another and alters the atomic number while keeping the mass number unchanged. Beta decay plays an essential role in nuclear stability, radioactive dating, stellar processes and fundamental particle physics.

Nature of Beta Decay and Nuclear Stability

Nuclei achieve stability through a balance between protons and neutrons. When a nuclide has an excess of either type of nucleon, it may undergo beta decay to move closer to the valley of stability. The likelihood of this transition is governed by the nuclear binding energy, which determines whether the total energy release—known as the Q value—is positive. Only decays with positive Q values are energetically possible.
Beta decay operates through the weak interaction, one of the four fundamental forces of nature. At the quark level, neutrons and protons consist of down and up quarks. Beta processes occur when a quark inside a nucleon changes flavour, mediated by the weak force. A down quark converting to an up quark produces beta minus emission, while an up quark converting to a down quark produces beta plus emission. Electron capture, in which a proton absorbs an inner-shell electron to transform into a neutron and emit a neutrino, is sometimes considered a related weak-interaction process.

Types of Beta Decay

Two principal types of beta decay are recognised:
Beta minus decay (β⁻ decay)In β⁻ decay a neutron converts into a proton. The reaction produces an electron and an electron antineutrino. This process increases the atomic number by one while leaving the mass number unchanged. An example is the decay of carbon-14 into nitrogen-14, widely used in radiocarbon dating, with a half-life of about 5,700 years. Tritium, or hydrogen-3, decays similarly to form helium-3.
Beta plus decay (β⁺ decay)In β⁺ decay a proton converts into a neutron. The process emits a positron and an electron neutrino. The daughter nuclide has the same mass number but an atomic number one unit lower. An example is the decay of magnesium-23 into sodium-23 with a half-life of about 11.3 seconds. Beta plus emission is energetically possible only when the mass of the parent exceeds that of the daughter by more than the combined mass of the emitted particles.
In both β⁻ and β⁺ processes, the principle of lepton number conservation applies. Electrons, positrons and their associated neutrinos and antineutrinos are leptons with designated quantum numbers: particles carry a lepton number of +1, while antiparticles carry −1. Since protons and neutrons have zero lepton number, β⁻ emission must produce an electron and an antineutrino, while β⁺ emission must produce a positron and a neutrino to preserve this conservation law.

Energy Distribution and the Beta Spectrum

A distinctive feature of beta decay is its continuous energy spectrum. Unlike alpha or gamma emissions, where the emitted particle carries a fixed amount of energy determined by the difference between nuclear energy levels, the beta particle in beta decay can take a range of energies from zero up to a specific maximum. This maximum corresponds to the Q value of the decay.
Because energy and momentum must be conserved, the total decay energy is shared among three participants—the beta particle, the neutrino or antineutrino, and the recoiling daughter nucleus. The neutrino, which interacts only weakly with matter, may carry away a substantial fraction of the total energy, leaving the electron or positron with a continuously variable kinetic energy. For example, in the decay of bismuth-210 the total energy is 1.16 MeV, but an electron observed at 0.40 MeV implies that the remaining energy belongs to the antineutrino and the recoil of the nucleus.

Early Observations and the Emergence of Beta Radiation

Radioactivity was first identified in 1896 by Henri Becquerel while studying uranium salts. Marie and Pierre Curie soon discovered additional radioactive substances and characterised their emissions. In 1899 Ernest Rutherford distinguished alpha and beta radiation based on their differing penetrating abilities. Alpha particles could be stopped by paper or thin metal foil, whereas beta particles could penetrate more deeply through several millimetres of aluminium.
Investigations at the turn of the century rapidly improved understanding. In 1900 Paul Villard discovered an even more penetrating radiation, later termed gamma rays. In the same year Becquerel demonstrated that beta particles had the same mass-to-charge ratio as electrons, reinforcing the view that beta radiation consisted of electrons emitted during nuclear transformations. By 1901 Rutherford and Frederick Soddy established that radioactive decay alters one element into another, initiating the study of nuclear transmutation.

Development of the Theory of Nuclear Transmutation

By 1913 researchers such as Soddy and Kazimierz Fajans formulated the displacement laws describing how alpha and beta emissions shift elements along the periodic table. Beta emission moves an element one place to the right by increasing its atomic number, while alpha emission moves it two places to the left.
However, as experimental techniques improved, inconsistencies emerged. The energy spectrum of beta particles appeared continuous rather than discrete, contradicting the expectation that a single nuclear transition should produce a particle with a well-defined energy. Measurements by Lise Meitner, Otto Hahn and later by James Chadwick indicated that the emitted electrons displayed a broad spread of energies. This posed a severe challenge to the conservation of energy, which would be violated if only a single electron emerged from the decay.
A related puzzle involved the conservation of angular momentum. Nuclear spin values, inferred from spectral studies, did not align with the spin carried by electrons alone in beta decay. A missing component seemed necessary to conserve both momentum and angular momentum.

Discovery of the Neutrino Concept

Wolfgang Pauli proposed a groundbreaking solution in 1930. He suggested the existence of a light, neutral particle emitted alongside the beta particle. This particle would carry away the missing energy, momentum and angular momentum. Pauli initially referred to it as the “neutron”, though this name was later given to James Chadwick’s massive neutral particle discovered in 1932.
Enrico Fermi renamed Pauli’s hypothetical particle the neutrino, meaning “little neutral one”, and in 1933 introduced a comprehensive theoretical framework describing beta decay. Fermi’s formulation established beta decay as a weak-interaction process in which particles could be created and annihilated, analogous to photon emission in atomic transitions.
Although neutrinos interact very weakly with matter, further indirect evidence for their existence accumulated. Observations of nuclear recoil during electron capture supported the theory. Direct detection eventually came in 1956 when Clyde Cowan and Frederick Reines observed antineutrinos from a nuclear reactor, confirming a key component of weak-interaction physics.

Significance in Modern Nuclear and Particle Physics

Beta decay remains central to the understanding of radioactive processes, nuclear structure and particle physics. It underpins methods such as radiocarbon dating, plays a role in the synthesis of elements in stars and contributes to the study of lepton conservation laws. Observations of beta decay and its associated neutrinos have provided essential insights into the weak force, one of the fundamental interactions governing the structure of matter.