Question

Number of possible spectral lines which may be emitted in Brackett series in $H$-atom, if electrons in $9th$ excited state returns to ground state are:

• A. $5$
• B. $45$
• C. $6$
• D. $21$

Answer 1

The correct option is D $21$

Since, the first excited state is $2^{nd}$ orbit. Similarly, the ninth excited state is ${10}^{th}$ orbit.

For spectral lines in Brackett series in H-atom.

$n_1=4$

Formula for number of possible spectral lines

$=\frac{(n_2-n_1)(n_2-n_1+1)}{2}$

Here, $n_2=10$ , $n_1=4$

Maximum spectral lines $=\frac{(10-4)(10-4+1)}{2}$

$=\frac{6\ast 7}{2}$

$=21$