12.3 What is the shortest wavelength present in the Paschen series of spectral lines?

12.3 Rydberg's formula is given as:

$\frac{hc}{?}$ = 21.76 $*{10}^{-19}\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$

Where, h = Planck's constant = 6.6 $*{10}^{-34}$ Js

c = speed of light = 3 $*{10}^8$ m/s

$?$ = Wavelength

$n_1$ and $n_2$ are integers.

The shortest wavelength present in the Paschen series of the spectral lines is given for the values $n_1=3$ and $n_2=?$

Therefore, $\frac{hc}{?}$ = 21.76 $*{10}^{-19}\left[\frac{1}{3^2}-\frac{1}{{?}^2}\right]$

$\frac{hc}{?}=$ 2.42 $*{10}^{-19}$

$?=\frac{6.6*{10}^{-34}*3*{10}^8}{2.42*{10}^{-19}}$ = 8.189 $*{10}^{-7}$ m= 8