Question

Find the wavelength of the spectral line that corresponds to a transition in hydrogen from the n = 10 state to the ground state. In what part of the spectrum is this?

Answer 1

Given:

$n=10,\quad m=1$

The Rydberg formula says

$$\frac{1}{\lambda}=R\left(\frac{1}{m^2}-\frac{1}{n^2}\right)$$

$$\frac{1}{\lambda}=1.09677×10^7\:\rm m^{−1}\left(\frac{1}{1^2}-\frac{1}{10^2}\right)$$

$$\frac{1}{\lambda}=1.086\times 10^7\:\rm m^{-1}$$

$$\lambda=92\times 10^{-9}\;\rm m=92\: nm$$

This is the Lyman series.