Kinetic energy of electron: Quantization of angular momentum

  • #1
39
6

Homework Statement


Show that the quantization of angular momentum implies that the kinetic energy of the electron is quantized as K=nhforb/2, where forb is the frequency of rotation. Assume circular orbit.

Homework Equations


Radial acceleration:
arad = 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*arad*vforb/2nh = ½mnħr = vmforb/4π

Your input is much appreciated!
 

Answers and Replies

  • #2
39
6
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!
 

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