Question

If the series limit frequency of the Lyman series is $v_L$ then the series limit frequency of the pfund series is :

• A. $v_L/16$
• B. $v_L/25$
• C. $25v_L$
• D. $16v_L$

Answer 1

The correct option is B $v_L/25$

$\begin{array}{c}\text{Lyman series frequeny}=v_L\\ \frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})\\ \text{for limiting}{n}_2=\infty \\ \text{for Lyman series}{n}_1=1\\ \text{For Pfund series}{n}_1=5\end{array}$

$\begin{array}{c}\text{For Lyman}\\ \frac{1}{{\lambda }_L}=R\left(\frac{1}{1^2}\right)\dots \text{(i)}\\ \frac{1}{{\lambda }_p}=R\left(\frac{1}{5^2}\right)\dots \text{(ii)}\\ \frac{1}{{\lambda }_R}=\frac{R}{25}\\ \text{Dividing (i)/(ii)}\end{array}$

$\begin{array}{c}\frac{{\lambda }_2}{{\lambda }_1}=\frac{25}{1}\\ \text{frequency}\propto \frac{1}{\lambda }\\ \frac{{\nu }_L}{{\nu }_p}=\frac{{\lambda }_p}{{\lambda }_L}=\frac{25}{1}\\ {\nu }_p=\frac{{\nu }_L}{25}\end{array}$