Question

The Rydberg constant for hydrogen atom is $1.097\times {10}^7{m}^{-1}$. Calculate the long wavelength limit of Lyman series.

Answer 1

Given data:
$R=1.097\times {10}^7{m}^{-1}$
For short wavelength limit of Lyman Series,
$n_1=1,n_2=\infty ,{\lambda }_s=?$
For long wavelength limit of Lyman series,
$n_1=1,n_2=2,{\lambda }_1?$
Solution:
The wave number for Lyman series is,
$\overline{v}=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
For short wavelength limit,
$\overline{v_s}=\frac{1}{{\lambda }_s}=R\left[\frac{1}{1^2}-\frac{1}{(\infty {)}^2}\right]=R$
or ${\lambda }_s=\frac{1}{R}=\frac{1}{1.097\times {10}^7}=911.6\stackrel{o}{A}$
For long wavelength limit
$\overline{v_1}=\frac{1}{{\lambda }_1}=R\left[\frac{1}{1^2}-\frac{1}{2^2}\right]=\frac{3}{4}$R
${\lambda }_l=\frac{4}{3R}=\frac{4}{3\times 1.097\times {10}^7}$
${\lambda }_l=$

$1215\stackrel{o}{A}$