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


$vr = nh/(2mπ)$


or


$vr = constant$


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?




What you're missing is that the electron (or rather, Bohr's version thereof) moves in a curved path because of the centripetal force provided by electrostatic attraction to the proton. You therefore have


$mvr=nh/2\pi$, quantized angular momentum


*and*


$mv^2/r=\epsilon\_0e^2/r$ centripetal force from electrostatic attraction


For each quantum number $n$ we have just one shell radius $r$ and one speed $v$ meeting both requirements.


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