Published by Patrick Mutisya · 14 days ago
Understand that α‑particles have discrete energies whereas β‑particles exhibit a continuous range of energies because (anti)neutrinos are emitted in β‑decay.
In α‑decay a nucleus emits a helium‑4 nucleus (α‑particle). The reaction can be written as
\$^{A}{Z}\!X \;\rightarrow\; ^{A-4}{Z-2}\!Y \;+\; \alpha\$
The energy released (Q‑value) is fixed by the difference in binding energies of the parent and daughter nuclei:
\$Q = \bigl[M(^{A}{Z}X) - M(^{A-4}{Z-2}Y) - M_{\alpha}\bigr]c^{2}\$
Because the α‑particle and the recoiling daughter nucleus share this fixed Q‑value, the kinetic energy of the α‑particle appears at a single, well‑defined value (apart from a small recoil correction). This leads to a line spectrum of α‑particle energies.
In β‑decay a neutron transforms into a proton, an electron (β‑particle) and an (anti)neutrino:
\$^{A}{Z}\!X \;\rightarrow\; ^{A}{Z+1}\!Y \;+\; e^{-} \;+\; \bar{\nu}_{e}\$
Energy conservation requires
\$Q = T{e} + T{\nu} + T_{\text{recoil}}\$
where \$T{e}\$ is the kinetic energy of the electron, \$T{\nu}\$ the kinetic energy of the (anti)neutrino, and \$T{\text{recoil}}\$ the recoil energy of the daughter nucleus. Since the neutrino can carry away any amount of energy between 0 and \$Q\$, the electron’s kinetic energy \$T{e}\$ can vary continuously from 0 up to \$Q\$ (minus a tiny recoil term). This produces the observed continuous β‑spectrum.
| Feature | α‑decay | β‑decay |
|---|---|---|
| Emitted particle | Helium‑4 nucleus (massive, charge +2e) | Electron (or positron) + (anti)neutrino (nearly massless) |
| Energy of emitted particle | Discrete (single value for a given transition) | Continuous range from 0 to \$Q\$ |
| Reason for energy distribution | Two‑body kinematics – only the α‑particle and recoil nucleus share fixed \$Q\$ | Three‑body kinematics – energy shared among electron, neutrino and recoil nucleus |
| Typical kinetic energy | 4–9 MeV (depends on nucleus) | Up to a few MeV, but spread continuously |
| Detection signature | Sharp peak in energy spectrum | Broad, smooth spectrum |
The continuous β‑spectrum was a major puzzle until the neutrino was postulated (by Pauli, 1930) to carry away the missing energy and momentum. Without the neutrino, energy conservation would force the electron to have a single energy, contradicting experimental observations.