Kinetic energy level

[silverek]

I am having trouble with this problem,

According to Bohr's quantization rules, the angular momentum of the electron in a given orbit is quantized according to P=nh. Find an equation for the possible kinetic energy levels for the electron orbiting in circles in a magnetic field, B. Calculate the kinetic energy level spacing if B=10T.

[Kane O'Donnell]

Try it like this: the magnetic field is what generates the centripetal force on the electron, causing it to go in a circle. So:

\frac{mv^2}{r} = qvB

(assuming the electron is travelling perpendicular to the field, which is the case if we want the electron going in a circle)

You can fiddle with this to get an expression for v which you can sub into the kinetic energy equation. You can then introduce the quantisation condition by going back to the equation above, fiddling to get an expression for L = mvr and then replacing it with n\hbar (note that it's h-bar, not just h), then substituting in your energy equation. You will get an equation for kinetic energy that depends on n and is independent of v and r. Indeed, you should get a very familiar expression!

Cheerio!

Kane