00:01
In part a, we're asked to find theta in phi.
00:03
The momentum of the photon before scattering, p0, is equal to h minus lambda 0.
00:10
And after scattering, it's p prime is equal to h times lambda prime.
00:15
And we also have conservation of momentum in the zx direction, and that's given by p0 is equal to p prime cosine theta plus p .e cosine theta, where pe is the electron momentum after scattering.
00:27
So we can use these equations now.
00:30
Lambda prime is equal to h or h lambda not is equal to h lambda prime plus p e times cosine of theta and in the wide direction we have conservation momentum so we have zero is equal to p prime sine theta minus p e sine theta so we can use these to solve for lambda prime and we also need to we have a shift in wavelength known as a compton effect so the compton effect equation is lambda prime minus lambda zero is equal to h mcc minus cosine theta, and we can use all of these equations to start putting it together to solve for theta.
01:09
So it would be lambda prime minus lambda not is equal to hmc times 1 minus cosine theta, times 2 lambda not cosine theta minus lambda not, and let's solve for theta, and we can plug in all of our values that we know.
01:23
So we have 0 .511 m .ev for mec squared, 0 .880 mev for e0, and we want to solve for theta.
01:33
So if we plug in our values, we get 0 .511 plus 0 .880 times 0 .8 .1 plus 0 .880 is equal to cosine of, inverse cosine of point is 0 .731.
01:46
So the scattering angle is 43 degrees...