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

The diagram is shown below:

Rydberg’s formula is given as:

where

Z is atomic number

R is Rydberg’s constant, R = 1.9074 x 10⁷ m-1

h is planck’s constant and is equal to 6.64 × 10^-34 Js

c is speed of light and is equal to 3.0 × 10⁸ m/s

substituting the values we get,

⇒

⇒

⇒

⇒

⇒ λ = 8.2012 × 10^-7 m ~ 820.12 × 10^-9 m ~

Or λ = 820 nm

(∵ 10^-9 m = 1nm)