An electron makes a transition from $7^{th}$ excited state to $2^{nd}$ energy level in a $H$-atom sample. Find the maximum spectral lines observed.

The correct option is B $21$
$7^{th}$ excited state means $8^{th}$ orbit so $n_2$ will be 8. and $n_1$ will be 2
Value of $\Delta n=(n_2-n_1)=8-2=6$
where n is the Bohr's orbit of H-atom
Maximum spectal lines observed $=\Delta n\times \frac{\Delta n+1}{2}$
$=6\times \frac{\left(7\right)}{2}=21$