00:02
For this question, part a, it says to show that it's not possible for only one photon to be produced.
00:08
So to show that it's not possible for only one photon to be produced, we're going to consider a conservation law.
00:13
Which conservation law then is the question that we should be considering? so initially there are only two particles, the electron and the positron.
00:21
And they're moving in opposite directions to annihilate with one another.
00:23
But the mass is the same since a positron is just a positive electron.
00:28
So maybe since the masses are the same, we know they're going to have the same, momentum is just going to be in opposite directions.
00:34
So this is a momentum conservation.
00:36
So how we can answer this is we can say m sub e minus.
00:40
So we'll call that the mass of the electron is equal to m sub e plus the mass of the positron.
00:48
Therefore, this leads to the momentum of the electron, we'll call this p e minus, and it's a vector because it has direction, is equal and opposite to the momentum of the positron.
01:05
So since the momentums are conserved, if one of these emits a photon, the other must also emit a photon.
01:12
Because if one emits a photon and the other does not, then the momentum would no longer be conserved.
01:17
So we can answer this by saying, since momentum is conserved, two photons must be emitted.
01:34
If the momentum is to continue to be conserved in the system.
01:47
Okay, so all of that would be the answer to part a.
01:50
Part b is another conceptual question.
01:54
It says, show that if only two photons are produced, they must travel in opposite directions and have equal energy.
02:03
Okay, so again, do conservation of momentum, the momentum of the photon, we'll call gamma that's coming from the negative electron, so we'll call this gamma minus, has to be equal and opposite to the photon that's coming from the positron.
02:24
We'll call that gamma plus.
02:25
Since the masses are the same, they must have opposite, they must be traveling in opposite directions.
02:32
So we can say, since masses are the same, they must travel in opposite directions.
02:46
Okay, it also says to show that they have to have the same energy.
02:49
Well, how can we show that they have the same energy? so to continue part b, the energy here is equal to, what is it, one half mv squared, okay? but m here is the same for both, right? but what is momentum? this is also equal to p squared over 2m, since momentum is mass times velocity.
03:23
So, therefore, if both have the same momentum, the energies are the same.
03:31
We can say, since momentum is equal, the energies are the same.
03:48
And lastly, part c says to calculate the wavelength of each of the photons in part b, and what part of the electromagnetic spectrum do they lie? okay, so to calculate the wavelength, we need to find the frequency of the photon.
04:10
This is because the wavelength is equal to c, the speed of light, divided by the frequency.
04:15
Well, we know the speed of light, so we just need to find the frequency.
04:18
So to find the frequency, we need to find the energy...