Question

Which of the following consideration(s) is/are showing that nuclear beta decay, \( n \to p + e^{-} + \bar{\nu}_e \), has to be a three-body decay?

• A. Continuous distribution of the electron energy
• B. Spin of the final state
• C. Mass of the electron
• D. Mass of the proton

Hint:

The continuous electron energy distribution in beta decay and the involvement of three particles (proton, electron, and antineutrino) confirm that it is a three-body decay process.

Answer 1

The Correct Option is A, B

1. Continuous distribution of the electron energy:

   In beta decay, the energy of the emitted electron is not fixed, but follows a continuous distribution. This is because the decay involves three particles: the neutron, proton, electron, and antineutrino. The energy of the electron is shared between these three particles, resulting in a continuous energy spectrum. This feature indicates that beta decay is a three-body decay process.

   Therefore, (A) is correct.

2. Spin of the final state:

   The spin of the final state is crucial for the decay process. In beta decay, the final state consists of a proton, an electron, and an antineutrino, and their spins are arranged in such a way that the angular momentum is conserved. This is possible only if there are three particles involved in the decay, confirming that it is a three-body decay.

   Therefore, (B) is correct.

3. Mass of the electron:

   The mass of the electron does not directly determine whether the decay is a three-body decay. While the electron mass affects the energy distribution in the decay, it is the presence of three particles in the final state that creates the continuous energy spectrum.

   Therefore, (C) is incorrect.

4. Mass of the proton:

   The mass of the proton does not directly imply that the decay must be a three-body decay. The number of particles involved in the decay process is what matters in determining whether it is a three-body decay.

   Therefore, (D) is incorrect.