calculate the wavelength of the light emitted when an electron in a hydrogen atom n=2 to n=1

when an electron moved from a higher energy level to a lower energy level, it releases energy in the form of light, the formular for calculating such energy is given by

E = -E₀/n²

where  E₀ is the at the ground state and is E₀ = 13.6 eV (1 eV = 1.602×10^-19 Joules) and n is the number of energy levels.

therefore

For the above example,

we start by , say

E₁ = -E₀/n²

-13.6 eV/1²

=-13.6 eV

and

E₂ = -E₀/n²

13.6 eV/2²

=-3.4

 our energy now is the difference between these two energy levels

-13.6 -(-3.4)

=-13.26 eV

our wavelength will now be calculated as

λ=h⋅c/E

but  our energy E is equal to 13.26  * 1.67 *10^-19J