Why Do Particles Emerge With 2kT Energy in the Stern-Gerlach Experiment?

[Bkkkk]

Electron "oven" In S-G Experiment

This isn't so much a homework problem but I guess it fits more here then in the other areas of the forum.

Whilst we were deriving and expression for the deflection of particles in the Stern-Gerlach experiment, the lecturer stated that the particles emerge from the oven or furnace with 2kT energy, when asked why that was rather then 1/2kT, 3/2kT or anything in between, he could not recall the exact reason.

Any idea why? I understand that the oven excites the particles to energies of the order of 3/2kT but then only particles in a particular direction are allowed to leave the oven, so I would expect the energy to be between 1/2kT and 3/2kT or if we include rotational energy it would be 2kT as mentioned, but is that the reason?

This energy was then used to derive the velocity Vx along the x-axis (perpendicular to the screen)

Thanks

 

[pam]

In averaging the energy of the particles leaving the oven, you should include another factor of v_x in your integral.

 

[Bkkkk]

Sorry, could you specify which integral you are referring to? I realize that the distribution of velocities follows a maxwell-boltzmann distribution, neither the RMS, mean or Most probable velocity result in the correct answer, the only one which comes close is the Mean velocity with 2.5kT.

 

[pam]

The average energy is calculated by an integral of (1/2)mv^2 times the M-B distribution.
The rate of energy leaving the oven is the integral v_x times this, integrated from 0 to
+ infinity.
You have to look in your textbook to see how these averages are calculated.