Question

Modify the Bohr model to include the wave properties of electrons. Use this to explain mission/absorption line spectra. (note that this modification was that due to de Broglie.)

Answer 1

Initially Bohr model depicts the atom as small positively charged nucleus surrounded by the electrons moving in circular orbits around the nucleus- just like our Solar System.

Later on he added that this motion could be saved if we can add one more assumption to it, i.e. certain " special states of motion" of electrons can exist with having different radii not emitting any radiation thus can persist in the orbit without falling into nucleus. Specifically he postulated that angular momentum of the electron is quantized with

   ( where n= any integer starting from 1)

where m= mass of electron

v=orbital velocity of the electron

r= radius of orbit

This is the first time when the concept of the quantum number comes into light.

Normally the electron is in its lowest allowed orbit. Upon excitation by the electrical discharge or by the ultrviolet light, the atom absorbs energy and gets excited to the higher state. These higher states are unstable, so after a very short time it returns to its lower orbit emitting radiatons of certain frequencies, resulating in different different spectras. Energies of emitted radiations can be measured by using Planck's Einstein Relation,

or   

also momentum associated with it is

where = de-broglie wavelength