Solution
= Solution
Extracting 95 percent of the maximum available inversion <energy> means $\eta=0.95/\beta$, or $x=\beta\eta=0.95$. Substitution in <1/c/ii> gives
$$
\boxed{r=\frac{-\ln(0.05)}{0.95}=3.1534\ldots.}
$$
The degeneracy factor cancels because the target is a fraction of the maximum <energy> $N_i^*V_g\hbar\omega_L/\beta$, rather than a fraction of $N_i^*V_g\hbar\omega_L$ without that factor.