calculate the wavelength of the light emitted when an electron in a hydrogen atom moved from n=4 to n=2"

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

E₄ = -E₀/n²

13.6 eV/4²

=-0.85 eV

and

E₂ = -E₀/n²

13.6 eV/2²

=-3.4

 our energy now is the difference between these two energy levels

-0.85-(-3.4) =

= 2.55 Ev

 IS THE ENRGY  RELEASED

λ=h⋅c/E

 therefore

 the wavelength of the light is given as

λ=h⋅c/E

but  our energy E is equal to 2.55 * 1.67 *10^-19

h= 6.626⋅10^-34js

c =3.0⋅10⁸

wavelength = 4.667* 10^-7m