QB_PH_SEC9_024: Particle Physics & Fundamental Interactions

The Gell-Mann-Nishijima relation connecting electric charge $Q$, third component of isospin $I_3$, baryon number $B$, and strangeness $S$ for hadrons is

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Isospin Multiplet Center of Charge**: For an isospin multiplet of total isospin $I$, the charges are symmetrically distributed around an average value $\bar{Q}$: $Q = I_3 + \bar{Q}$ 2. **Hypercharge Definition ($Y$)**: Gell-Mann and Nishijima introduced hypercharge $Y = B + S$ such that $\bar{Q} = Y/2$: $Q = I_3 + \frac{Y}{2} = I_3 + \frac{B + S}{2}$ 3. **Validation on Protons and Neutrons**: - Proton ($p$): $I_3 = +1/2, B = 1, S = 0 \implies Q = +1/2 + 1/2 = +1$ (Matches) - Neutron ($n$): $I_3 = -1/2, B = 1, S = 0 \implies Q = -1/2 + 1/2 = 0$ (Matches) - $\Lambda^0$: $I_3 = 0, B = 1, S = -1 \implies Q = 0 + (1 - 1)/2 = 0$ (Matches) 4. **Conclusion**: Option (A) is correct.