00:01
All right, so let's say we have a positron with a kinetic energy of 2mev strikes a stationary electron, and they annihilate into two photons.
00:09
And so we want to know the energy of each of these photons.
00:12
So the initial energy of the system is going to be the kinetic energy plus twice the rest mass energy of the system, because a positron and electron have the same rest mass.
00:25
So that means our final energy, which is going to be the energy of, one photon.
00:32
Sorry, let's put it this way.
00:33
The energy of one photon plus the energy of our second photon has to add up to this value.
00:39
And this is going to be, so this is two million electron volts plus two times 0 .511 m .ev.
00:48
And so this is 3 .022 m .v.
00:53
Now we also have momentum conservation.
00:55
So the initial momentum of the system we can find because it's going to be the square root of the energy, the total energy of our positron, which will be basically k plus the rest mass energy minus the m squared c to the fourth term.
01:19
And then this, sorry, this will be divided by the speed of light.
01:23
So, and this should be squared.
01:25
All right, so this should be about 2 .46 mev per c.
01:32
That's our initial momentum of our system...