Find the maximum number of spectral lines in Balmer series when an electron returns from the $7^{th}$ orbit to the $1^{st}$ orbit in a sample of hydrogen atoms.

The correct option is A 5
Maximum number of spectral lines$\left(N\right)$ corresponding to transition from $n_1=7$ to $n_2=1$ are:
$N=$ number of lines emitted $=\frac{1}{2}(n_1-n_2)(n_1-n_2+1)$
$=\frac{1}{2}(7-1)(7-1+1)$
$=21$
From total spectral lines, lines falling in Balmer series is
$five(7\to 2,6\to 2,5\to 2,4\to 2and3\to 2)$.
Number of transitions in Balmer series $=5$