The relative population in two states with energies $E_{1}$ and $E_{2}$ satisfying Boltzmann distribution is given by $n_{1} / n_{2}=(3 / 2) \exp \left[-\left(E_{1}-E_{2}\right) / k_{b} T\right]$. The relative degeneracy $g_{2} / g_{1}$ is:
(a)2
(b)2/3
(c)$3 / 2$
(d)3
Answer
Answer (as printed): B
Explanation
The population ratio satisfies $\dfrac{n_{1}}{n_{2}}=\dfrac{g_{1}}{g_{2}}\exp\left[-\dfrac{E_{1}-E_{2}}{k_{b}T}\right]$ ......(1), where $g_{1}$ and $g_{2}$ are degeneracies.Given: $\dfrac{n_{1}}{n_{2}}=\dfrac{3}{2}\exp\left[-\dfrac{E_{1}-E_{2}}{k_{b}T}\right]$ ......(2).Comparing (1) and (2), $\dfrac{g_{1}}{g_{2}}=\dfrac{3}{2}$, so $\dfrac{g_{2}}{g_{1}}=\dfrac{2}{3}$.