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  • If   and   are the wavelengths of the first members of the Lyman and Paschen

If \lambda_1  and \lambda_2  are the wavelengths of the first members of the Lyman and Paschen series respectively, then \lambda_1: \lambda_2 is:
 

Option: 1

1: 9
 


Option: 2

 1: 27


Option: 3

 7: 54

 


Option: 4

 7: 108


Answers (1)

best_answer

According to Rydberg's formula \frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right]

For Lyman series,\mathrm{n}_1=1 \text{ and } \mathrm{n}_2=2 for first line

\therefore \frac{1}{\lambda_1}=\mathrm{R}\left[\frac{1}{1^2}-\frac{1}{2^2}\right]=\mathrm{R}\left[\frac{1}{1}-\frac{1}{4}\right]=\frac{3}{4} \mathrm{R}

For Paschen series, \mathrm{n}_1=3 and \mathrm{n}_2=4 for first line

\begin{aligned} & \therefore \frac{1}{\lambda_2}=\mathrm{R}\left[\frac{1}{3^2}-\frac{1}{4^2}\right]=\mathrm{R}\left[\frac{1}{9}-\frac{1}{16}\right]=\frac{7}{144} \mathrm{R} \\\\ & \frac{\lambda_1}{\lambda_2}=\frac{\frac{4}{3} \mathrm{R}}{\frac{144}{7} \mathrm{R}}=\frac{7}{108} \end{aligned}

Posted by

Pankaj Sanodiya

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