Bohr and (not) his postulates

There are three Bohr’s postulates, but not exactly these which are presented in schools.

Young (28 yr) Ph.D. in Manchester in 1913 and 1915 published three articles, which created "old" quantum mechanics. Bohr didn’t risk his reputation predicating that:

  1. electrons travel on stationary orbits, where (from unknown reasons) they do not emit energy, like do  electrons in Hertz’s antenna (see experiments on exhibition “204 years of Volta’s pile”) and
  2. they emitting light with Planck frequency
    v =(En-Em)/h
    falling from orbit n to orbit m.
  3. As third postulate, school books quote that momentum rmv is quantized and equal to nh/2π.

In reality that result is Bohr’s conclusion but not a assumption. His assumption was a correspondence principle:

"electron emits the light of the frequency equal to the frequency of his orbital motion".

From this (and the emmision laws) the momentum condition is derived.

But in truth, the third Bohr’s postulate is the condition of a standing wave: the lengthλ of the de Brogile wave on the first orbit is such(h/mv) , that on the full circumference (2πr) stays one and only one its multiplicity.

Like these waves travelling in a bowl with water.

stojąca fala kolista stojąca fala kulista

A stationary circular wave. Here you can hear the "singing" bowl.