Question

What is the relationship between the energy differences of the orbits in an atom and the light emitted by the atom?

Answer 1

One of the postulates of Bohr's atom is -

When an electron makes a transition from a level of higher energy `E_h` to a level of lower energy `E_l`, then it emits a single photon of frequency,

`nu = (E_h - E_l)/h` where `h` is the Planck's constant.

Thus energy levels and transitions between these levels determine what frequency of light is emitted when an electron returns from a higher energy orbit to a lower energy orbit.

This is what gives rise to the discrete lines in the emission line spectra of a particular element. Where each line corresponds to a particular frequency which in turn corresponds to a particular transition between orbits in the atom.