Question

A sample of hydrogen atom is excited to n = 4 state. In the spectrum of emitted radiation, the number of lines in the ultraviolet and visible regions are respectively:

• A. 2 : 1
• B. 2 : 3
• C. 1 : 3
• D. 3 : 1

Answer 1

The correct option is A 2 : 1

Balmer series transition take place in visible region $\to$ n = 2
Lyman series transition take place in Ultraviolet $\to n=1$
$n_H=4$
Number of spectral lines in visible region
$=\frac{(n_H-n_L)(n_H-n_L+1)}{2}$
$=\frac{(4-2)(4-2+1)}{2}$
$=3$

Number of spectral lines in Ultraviolet region
$=\frac{(n_H-n_L)(n_H-n_L+1)}{2}$
$=\frac{(4-1)(4-1+1)}{2}$
$=6$

Ratio of spectral lines in UV and visible 6 : 3 = 2 : 1