Question

An electron absorbs a photon of light of frequency $7.312 \times 10^{14} \,s ^{-1}$ in the first excited state of hydrogen and jumps from there to $n ^{\text {th }}$ excited state. The value of $n$ is ____

Answer 1

$v =7.312 \times 10^{14} s ^{-1} \rightarrow \bar{v}=\frac{v}{ c }=2437200\, m ^{-1}$
$\bar{v}$ in $cm ^{-1}=24372\, cm ^{-1}$
For Ist excited state $n =2$
$24372=109677\left[\frac{1}{4}-\frac{1}{ n _{2}^{2}}\right]$
$n _{2}=6$, i.e., $5^{\text {th }}$ excited state