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## Homework Statement

Show that the quantization of angular momentum implies that the kinetic energy of the electron is quantized as K=nhf

_{orb}/2, where f

_{orb}is the frequency of rotation. Assume circular orbit.

## Homework Equations

Radial acceleration:

a

_{rad}= v

^{2}/r = (4π

^{2}r/T = 2*π*v/Tr = nħ

KE = mv

^{2}/2

We have covered the Bohr model of the atom, as well as the Rutherford model.

## The Attempt at a Solution

I did a bunch of moving around of variables and have been able to get to the following expressions, but not the one I need:

K = m*a

_{rad}*vf

_{orb}/2nh = ½mnħr = vmf

_{orb}/4π

Your input is much appreciated!