Question

The wavelength of the third line of the Balmer series for a hydrogen atom is :
(Given $R_H=$ Rydberg constant)

• A. $\frac{21}{100R_H}$
• B. $\frac{100}{21R_H}$
• C. $\frac{21R_H}{1000}$
• D. $\frac{1000R_H}{21}$

Answer 1

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

For hydrogen atom, the wave number (reciprocal of wavelength) is given by
$\frac{1}{\lambda }=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
For the third line of Balmer series,
$n_1=2$ and $n_2=5$
$\frac{1}{\lambda }=R_H(\frac{1}{2^2}-\frac{1}{5^2})=\frac{21}{100}{R}_H\Rightarrow \lambda =\frac{100}{21R_H}$