GATE 2024 PH – Question 26

Nuclear and Particle Physics · conservation laws, isospin symmetry, charge conjugation, parity and time-reversal invariance. · 1 mark · Multiple choice

Let P, Q, R be different nuclei. Which nuclear process is possible?

$\nu_e+{}^A_ZP\to{}^A_{Z+1}Q+e^-$
$\nu_e+{}^A_ZP\to{}^A_{Z-1}R+e^+$
$\nu_e+{}^A_ZP\to{}^A_ZP+e^++e^-$
$\nu_e+{}^A_ZP\to{}^A_ZP+\gamma$

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Correct answer: (A) $\nu_e+{}^A_ZP\to{}^A_{Z+1}Q+e^-$

Explanation

Check each reaction for conservation of charge, baryon number and **lepton number** (the electron lepton number $L_e=+1$ for $e^-$ and $\nu_e$, and $-1$ for $e^+$).

**A. $\nu_e+{}^A_ZP\to{}^A_{Z+1}Q+e^-$:** charge: $Z\to(Z+1)-1=Z$ ✓; $L_e$: $+1\to+1$ ✓; baryon number conserved ✓. This is neutrino capture, $\nu_e+n\to p+e^-$ inside the nucleus. **Possible.** ✓
**B. $\nu_e+{}^A_ZP\to{}^A_{Z-1}R+e^+$:** charge: $Z\to(Z-1)+1=Z$ ✓, but $L_e$: $+1\to-1$ ✗.
**C. $\nu_e+{}^A_ZP\to{}^A_ZP+e^++e^-$:** charge conserved, but $L_e$: $+1\to0$ ✗.
**D. $\nu_e+{}^A_ZP\to{}^A_ZP+\gamma$:** $L_e$: $+1\to0$ ✗.

Answer **A**.