Question

Use the idea of energy conservation to explain why the hydrogen atom only emits light of specific wavelengths.

What is it about the structure of the hydrogen atom that leads to this?

Answer 1

a)
energy of hydrogen atom when electron is in nth orbit,

En = -13.6 eV/n^2

whenever electron jumps from jigher energy stationary state to lower energy stationary state,

it emits a photon with energy equal to difference of the two energy states.

E_photon = -13.6 eV*(1/ni^2 - 1/nf^2)

E_photn = 13.6eV*(1/nf^2 - 1/ni^2) (here ni > nf)

b) electron revolve around the nucleus in a particular ststaionary states in which the angular momentum

of the electrion is conserved.

Ln = n*h/(2*pi)

this conservation of angular momentum is led to the hydrogen atom only emits light of specific wavelengths.