How Does the Continuous Spectrum of Beta Decay Provide Evidence for the Neutrino? (HL)

The continuous spectrum shows that the decay energy is shared in varying proportions among three products, including an unseen neutrino. Without the neutrino, beta particles from a particular nuclear transition would have approximately one fixed energy.

Level: Additional higher level (AHL): E.3 Radioactive decay.

The Reasoning

In beta-minus decay, a neutron changes into a proton, producing an electron and an electron antineutrino:

$$n \rightarrow p + e^- + \bar{\nu}_e$$

The energy released by a particular nuclear transition has a fixed value. If the only products were the daughter nucleus and the electron, conservation of energy and momentum would determine one specific electron kinetic energy, allowing for the daughter nucleus's recoil. The beta spectrum would therefore be discrete rather than continuous.

Experiments instead show beta particles with kinetic energies ranging continuously from nearly zero to a maximum endpoint energy.

The neutrino resolves this result. In each decay, the electron and neutrino carry different fractions of the available energy, while the daughter nucleus also recoils. When the electron has relatively little kinetic energy, the neutrino carries more; near the endpoint, the neutrino carries very little energy. The neutrino also carries momentum, preserving conservation of momentum in each individual decay.

A common misconception is that energy is temporarily “lost” during beta decay. It is not lost: the apparently missing energy and momentum are carried away by the weakly interacting neutrino, which is difficult to detect.

Exam Technique

For an IB Explain question, link three points clearly: fixed decay energy, the observed continuous beta spectrum, and variable sharing of energy and momentum with a neutrino. Do not merely state that the neutrino exists; explain why a third particle is required by conservation laws.