Bohr assumed angular momentum was quantized as ##L=n\hbar##. But really it is quantized as ##L=\hbar \sqrt{l(l+1)}##.(adsbygoogle = window.adsbygoogle || []).push({});

What he does to derive,e.g., the Bohr radius is consider that the total energy of an electron orbiting a proton is

## E=\frac{L^2}{2mr^2}-\frac{k e^2}{r} ##

and then he makes some clever substitutions. However, Bohr substituted the formula for ##L_z## (##n\hbar##) not the actual ##L## (which is ##h\sqrt{l(l+1)}##). So why then does his procedure work?

Up until now I have considered this a mere accident but I've heard about people considering the so-called "Gravitational Bohr Radius" which is derived using the same procedure.

I don't understand why we asume its validity for the simple system of one particle orbiting another if we've got the wrong formula for angular momentum.

So then:

Why does his procedure work?

Why do we take on the similar (and wrong) derivation to the gravitational case?

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# Why does Bohr's derivation work?

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