# Bohr's postulate of quantisation of angular momentum

The Bohr's postulate of quantisation of angular momentum can be written in a formula as $$mvr = nh/(2π)$$

where $$m$$ is mass of electron

$$v$$ is its velocity

$$r$$ is the radius of that shell

$$h$$ is Plank's constant

So, I was wondering that if, I want to find where approximately the thing with $$n=2$$ exists, or in other words, what is the velocity of electron and radius of its circular path in the second shell, I could rewrite it as

$$vr = nh/(2mπ)$$ $$vr = constant$$

So if I was to just increase the radius by a factor of say $$z$$ and velocity by a factor of $$1/z$$ it would give me the exact same value for $$vr$$ every time. Doesn't that mean I could indefinitely increase the radius and keep reducing the velocity and still stay in second shell forever?

• There are (were) additional constraints on the velocity because of classical mechanics: en.wikipedia.org/wiki/Bohr_model#Electron_energy_levels Anyway, I'd really discourage reading too much into the Bohr model. It is severely outdated; perhaps useful to know because it provides some historical perspective for the development of quantum mechanics, but not useful to analyse in a serious fashion beyond the fact that it didn't work. – orthocresol Sep 20 '19 at 8:38

$$mvr=nh/2\pi$$, quantized angular momentum
$$mv^2/r=\epsilon_0e^2/r$$ centripetal force from electrostatic attraction
For each quantum number $$n$$ we have just one shell radius $$r$$ and one speed $$v$$ meeting both requirements.