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

Question:

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

Solution:

Rydberg’s formula is given as:

$\frac{h c}{\lambda}=21.76 \times 10^{-19}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$

Where,

h = Planck’s constant = 6.6 × 10−34 Js

= Speed of light = 3 × 10m/s

(n1 and n2 are integers)

The shortest wavelength present in the Paschen series of the spectral lines is given for values n1 = 3 and n2 = ∞.

$\frac{h c}{\lambda}=21.76 \times 10^{-19}\left[\frac{1}{(3)^{2}}-\frac{1}{(\infty)^{2}}\right]$

$\lambda=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8} \times 9}{21.76 \times 10^{-19}}$

$=8.189 \times 10^{-7} \mathrm{~m}$

$=818.9 \mathrm{~nm}$