The GATE Grind

GATE 2025 PH – Question 27

Nuclear and Particle Physics · alpha decay, beta-decay, electromagnetic transitions in nuclei · 1 mark · Multiple select

Which of the following consideration(s) is/are showing that nuclear beta decay, n → p+ e− + ν̅e, has to be a three-body decay?

  1. Continuous distribution of the electron energy
  2. Spin of the final state
  3. Mass of the electron
  4. Mass of the proton

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Show answer and explanation

Correct answer: (A) Continuous distribution of the electron energy; (B) Spin of the final state

Explanation

Neutron beta decay is $n\to p+e^-+\bar\nu_e$. Two experimental facts show that it cannot be a two-body decay $n\to p+e^-$:

**1. The electron energy has a continuous distribution.** In a two-body decay with momentum and energy conservation, the electron would be mono-energetic (a sharp line). The observed **continuous** spectrum shows that a third particle shares the energy. ✓

**2. Angular momentum (spin).** The neutron has spin $\tfrac12$. The proton and the electron each have spin $\tfrac12$, so a two-body final state can have only an integer total angular momentum (spins combined with orbital angular momentum, which is an integer). This cannot equal $\tfrac12$. A third spin-$\tfrac12$ particle (the antineutrino) makes the total half-integer, which agrees with the neutron. ✓

The masses of the electron and proton (C and D) do not give an argument for three bodies. Answer **A and B**.