Kinetic energy of electron: Quantization of angular momentum

[yeshuamo]

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 = v²/r = (4π²r/T = 2*π*v/Tr = nħ

KE = mv²/2

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!

 

[yeshuamo]

This has been solved using the DeBroglie relationship, the idea that in a Bohr atom, the angular moment of an electron is
L = mvr = nħ
as well as classical definition of angular momentum
L = Iω, where I = mr²

Thank you for looking!