Question

Ratio of series limit of Brackett and Pfund series of hydrogen ato spectrum is

• A. $\frac{1}{4}$
• B. $\frac{4}{9}$
• C. $\frac{9}{16}$
• D. $\frac{16}{25}$

Answer 1

The correct option is C $\frac{9}{16}$

$\begin{array}{c}\text{Bracket series}{\text{n}}_1=3,n_2=4,5,\dots \\ \frac{1}{\text{series limit}}\propto [\frac{1}{3^2}-\frac{1}{n_2^2}]\\ \propto \frac{1}{9}\end{array}$

$\begin{array}{c}\text{Pfund series}{n}_1=4,n_2=5,6,\dots \\ \frac{1}{\text{series limit}}\propto [\frac{1}{4^2}-\frac{1}{(n_2{)}^2}]\propto \frac{1}{16}\\ \text{Ratio of series limit}=9/16\end{array}$