Question

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

Answer 1

Wavelength of light emitted in Lyman series $\frac{1}{\lambda }=R(\frac{1}{1}-\frac{1}{n^2})$
where $n=2,3,4...$
For shortest wavelength, $n=\infty$
$⟹{\lambda }_s=R(\frac{1}{1}-\frac{1}{{\infty }^2})=\frac{1}{R}$
${\lambda }_s=\frac{1}{1.097\times {10}^7}m=91.2\times {10}^{-9}m=9.12\times {10}^{-8}m=91.2nm$