GATE 2021 PH – Question 55
The Gell-Mann–Okubo baryon mass formula is $$M=M_0+aY+b\left[I(I+1)-\frac14Y^2\right],$$ where $M_0,a,b$ are constants, $I$ is isospin and $Y$ is hypercharge. If the mass of $\Sigma$ hyperons equals that of $\Lambda$ hyperons, which options are correct?
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Show answer and explanation
Correct answer: (B) $M\propto Y$; (C) $M$ does not depend on $I$.
Explanation
For $\Sigma$, $I=1,Y=0$ and $M_\Sigma=M_0+2b$; for $\Lambda$, $I=0,Y=0$ and $M_\Lambda=M_0$. Equality forces $b=0$. The remaining relation is $M=M_0+aY$, independent of $I$ and linear in $Y$. The official key selects B and C. Strictly B’s proportionality notation applies to $M-M_0$, since the printed formula retains an additive constant; its intended meaning is linear dependence on hypercharge.