00:01
Derive for the content scattering process, the recoil energy t as a function of incident photon energy and the electron angle scattering.
00:16
So in this problem, we have, content scattering is when we have some incident photon and we have an electron and it ends up scattering at some angle, at some angle of what's call this alpha.
00:31
And there's some recoil as well.
00:36
Okay, so from our momentum conservation, we have hv over c is equal to hv over c cosine of alpha plus mv cosine of phi e.
00:50
And zero is equal to hv prime over c, sine alpha plus mv sine phi e.
00:59
And the y -axis.
01:01
This is for the x -axis, and this is our y -axis.
01:05
From energy conservation, we have hv plus m -0 c squared is equal to hv -prime plus mc squared.
01:16
Now, from our expression above, this expression, we'll call this one, we have mvc cosine of phi -e is equal to h -v -c, and v minus v prime cosine of our angle and then we also have mvc sine of phi e is equal to h v prime sine of alpha let's call this set two if we square the equation and add them we should get um squared v squared c squared is equal to h squared v squared plus v squared v prime squared minus 2 v v prime, cosine of alpha.
02:07
And we have another expression, mc squared, is equal to h, new minus new prime, plus m0 c squared.
02:18
And if we square these equations, this is what one of all resulting equations will be.
02:27
We know m is equal to m0 divided by the square root 1 minus v squared over c squared...