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Bohr's Model of Atom

A particle of...

Question

A particle of mass $m$ moves around in a circular orbit in a centro symmetric potential field $u (r)$ = $K r^{2} / 2$ . Using Bohr's quantization rule, find the permissible energy levels.

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Solution

$F = \frac{d}{d r} u (r) = K r = \frac{m v^{2}}{r}$ or $m v = \sqrt{K r^{2} m}$
$m v r = n h$
$∴ r \sqrt{K r^{2} m} = n h$ or $r = {(\frac{n h}{\sqrt{K m}})}^{1 / 2}$ and
$m v^{2} = K r^{2} = K (\frac{n h}{\sqrt{K m}})$
$B E = K E + P E$

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