Question

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

• A. 21/100R
• B. 100/21R
• C. 21R/100
• D. 100R/21

Answer 1

Answer: (B)

100/21R

Balmer series $\Rightarrow n_1=2$

The third line of Balmer series $\Rightarrow n_2=5$

Rydberg equation $\Rightarrow \frac{1}{\lambda }={Rz}^2[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$

$\Rightarrow \frac{1}{\lambda }=\left(10967800\right){\left(1\right)}^2$

$[\frac{1}{2^2}-\frac{1}{5^2}]$

$\frac{1}{\lambda }=\frac{21}{100}R$

Wavelength of $3^{rd}$ line of Balmer, $\lambda =\frac{100}{21R}$

So, the correct option is $B$