2.13 What is the wavelength of light emitted when the electron in a hydrogen atom undergoes the transition from an energy level with n = 4 to an energy level with n = 2?


The ni = 4 to nf = 2 transition will give rise to a spectral line of the Balmer series. The energy involved in the transition is given by the relation,
E= 2.18 x 10-191ni2 - 1nf2
Substituting the values in the given expression of E:
E = 2.18 x 10-19142 - 122
= 2.18 x 10-181 -416
= 2.18 x 10-18 x -316
E = – (4.0875 × 10-19 J)
The negative sign indicates the energy of emission.
Wavelength of light emitted λ = hcE
since E = hcλ

Substituting the values in the given expression of λ:
λ = 6.626 x 10-343 x 1084.0875 x 10-19
λ = 4.8631 x 10-7 m
= 486.3 x 10-9 m
= 486 mm