Question

The number of spectral lines that are possible when electrons in the $7^{th}$ shell in a sample of hydrogen atoms return to the $3^{rd}$ shell is:

• A. $12$
• B. $15$
• C. $14$
• D. $10$

Answer 1

The correct option is D $10$

Higher energy state $n_2=7$ and lower energy state $n_1=3$
Number of spectral lines $=\frac{(n_2-n_1)(n_2-n_1+1)}{2}$
$=\frac{(7-3)(7-3+1)}{2}=10$