Question

The ratio of the wave number of $1st$ line of Balmer series to last line of Lyman series in $H-$atom is:

• A. $\frac{36}{5}$
• B. $\frac{5}{36}$
• C. $\frac{1}{3}$
• D. $3$

Answer 1

Answer: (C)

$\frac{1}{3}$

Here the answer is wrong, and the correct answer is not mentioned in option i.e., 4.

For the first balmer series:

$\frac{1}{{\lambda }_b}=R[\frac{1}{2^2}-\frac{1}{{\infty }^2}]$

${\lambda }_b=\frac{4}{R}$

For the last lyman series:

$\frac{1}{{\lambda }_1}=R[\frac{1}{2^2}-\frac{1}{{\infty }^2}]$

${\lambda }_1=\frac{1}{R}$

$\frac{{\lambda }_b}{{\lambda }_1}=\frac{\frac{4}{R}}{\frac{1}{R}}$

$\frac{{\lambda }_b}{{\lambda }_1}$=4

Here the option given is $3$ which is $\approx$ $4$ is the answer.