Question

The ratio of series limit frequencies of Balmer series to that of Bracket series for a $H-atom$ is

• A. $16:1$
• B. $1:16$
• C. $4:1$
• D. $1:4$

Answer 1

Answer: (C)

$4:1$

$\begin{array}{c}\text{* For Balmer series}(n_1=2)\\ \text{By Rydberg's law-}\\ \begin{array}{cc}\frac{1}{\lambda }=R_H[\frac{1}{n_1^2}-\frac{1}{n_2^2}]& \text{where}\lambda =\text{wavelength}\\ \Rightarrow \nu =c\cdot R_4[\frac{1}{n_1^2}-\frac{1}{n_2^2}]\text{where}c=\text{speed of light}& \\ v=\text{frequency}& \\ \Rightarrow v_{max}=c\cdot R_H[\frac{1}{4}-\frac{1}{\infty }]& =\frac{R_H\cdot c}{4}\end{array}\end{array}$

$\begin{array}{c}\text{For Bracket series}(n_1=4)\\ \Rightarrow {\nu }_{max}=c\cdot R_H[\frac{1}{16}-\frac{1}{\infty }]=\frac{R_4\cdot c}{16}\\ \Rightarrow \text{Ratio}\frac{{\partial }_{max}\left(\text{Balmer}\right)}{D_{\text{max}}\left(\text{Boacket}\right)}=\frac{16}{4}=\frac{4}{1}\\ \text{Ratio}=4:1\\ \text{Hence, option}\left(c\right)\text{is the correct answer.}\end{array}$