Question

Photons corresponding to the $10 \rightarrow 2$ transition of $He ^{+}$ ion sample is used to excite the $H$-atom sample in ground state. If electrons make transition up to ground state after excitation in $H$-atom sample, then find out the maximum number of spectral lines produced in the infrared region.

Answer 1

$10 \rightarrow 2$ transition of $He ^{+}$will cause $1 \rightarrow 5$ transition in $H$-atom.
$\therefore $ maximum number of spectral line
$=\frac{5(5-1)}{2}=10$
$\therefore $ number of lines in infrared region
$=10-4-3=3$.