Bohr Model Postulates: Understand Discrete Angular Momentum Orbits

[Bassalisk]

Hello,

I am interested if anybody knows, how did Bohr came to the conclusion that only discrete angular momentum orbits are stable? In other words,

m*v*r=n*h/(2*pi)

and how did de Broglie came to the same conclusion, just through another way 2*pi*r=n*h/(m*v)

Thanks

 

[PhilDSP]

Hi Bassalisk,

Bohr didn't come to that conclusion. He was already familiar with the various formulas for determining the ratios between the various discrete wavelengths or frequencies of emission of a hydrogen atom. He apparently intuitively recognized the pattern could likely be derived from a model of the electron orbiting the proton and set about creating the most simple model possible using energies (kinetic and potential) balanced in a standard classical model.

De Broglie's analysis is based on wave mechanics and phase invariance in any frame of reference. Numerically, it happened to coincide with Bohr's model (for hydrogen only) But a full analysis of how wave mechanics restricts the possible modes of radiation didn't really come until Bohm had studied and documented the situation ("Quantum Theory" -David Bohm) That particular book is general and doesn't involve his variant of "Pilot Wave" theory.

 

[Bassalisk]

Thank you very much, you answer was very helpful!