Bohr's Intuition: How He Knew Angular Momentum Without Proof

[shravan]

there is no proof for the saying that the orbit in which an electron is moving is an integral multiple of angular momentum? how did bohr guess that it is angular momentum ;why didnot he try other angular variables?
my question is how he knew angular momentum without any proof.

 

[mezarashi]

The 'proof' is that the Bohr model solves the problem that classical theory could not explain regarding atomic stability. He didn't 'guess'. He made a bold proposal (at the time) that the radius of orbit was quantized. Consequently, its angular momentum must be as well. The concept of angular momentum is relatively classical in origin and was understood way back before Bohr. It has proved to apply in the quantum world as well.

 

[James R]

there is no proof for the saying that the orbit in which an electron is moving is an integral multiple of angular momentum? how did bohr guess that it is angular momentum ;why didnot he try other angular variables?

He started with the assumption that the electron is a de Broglie wave with wavelength given by the de Broglie formula:

$$\lambda = h/mv$$.

Then, he said that for such a wave "wrapped around" the nucleus to undergo constructive interference, it must satisfy the condition:

$$2 \pi r = n\lambda$$

where r is the orbital radius, and n is an integer greater than or equal to one.

From that formula, it is very easy to derive the quantisation of angular momentum:

$$L = mvr = n \hbar$$

Try it yourself. It only takes a couple of lines of working.