Answer
$n_i=3, n_f=2$
Work Step by Step
We can find the initial and final states as follows:
$\frac{1}{\lambda}=(R)(\frac{1}{n_f^2}-\frac{1}{n_i^2})$
This simplifies to:
$n_i=(\frac{1}{n_f^2}-\frac{1}{\lambda R})^{\frac{-1}{2}}$
We plug in the known values to obtain:
$n_i=[\frac{1}{2^2}-\frac{1}{(656\times 10^{-9})(1.097\times 10^7)}]^{(\frac{-1}{2})}$
$n_i=3$
Thus, the initial and final states are: $n_i=3, n_f=2$
