How did DeBroglie's hypothesis account for the fact that the energy in a hydrogen atom is quantised?

1 Answer
Michael
Jan 16, 2015

Bohr assumed that electrons move in an orbit around the central nucleus and only certain orbits are allowed.

The electron can be considered as a standing wave. This means that only an integral number of wavelengths can fit into a circular orbit. So we can write:

#nlambda =2pir#

#n# is an integer

#lambda# = wavelength of electron

#r# = radius of orbit.

The wavelength of the electron is given by the de Broglie expression:

#lambda =(h)/(mv)#

Where:

#h# = the Planck Constant

#m# = mass of electron

#v# = velocity of electron

Substituting for #lambda# into the 1st equation we get:

#(nh)/(mv)=2pir#

The angular momentum of the electron = #mvr# so rearranging we get:

#mvr = (nh)/(2pi)#

This is an important result in that it tells us that the angular momentum of the electron can only take integral values of #(h)/(2pi)# I.e it is quantised.

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