Question

The wavelength of the third line of the Balmer series for a hydrogen atom is:

• A. $\frac{21}{100R_H}$
• B. $\frac{100R_H}{21}$
• C. $\frac{21R_H}{100}$
• D. $\frac{100}{21R_H}$

Answer 1

The correct option is D $\frac{100}{21R_H}$

We know,
$\frac{1}{\lambda }=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})$ for the H atom.
For the Balmer series,
$n_1=2$ and $n_2=5$ (for the third line).
$\frac{1}{\lambda }=R_H(\frac{1}{2^2}-\frac{1}{5^2})=\frac{21}{100}{R}_H\therefore \lambda =\frac{100}{21R_H}$