00:01
In this problem, we're going to talk about relativistic energy.
00:03
So remember that the rest energy of a particle is mc squared, m is the math of the particle, the total energy e is mc squared times gamma, and the kinetic energy is equal to the total energy minus the rest energy, which is mc squared, gamma minus 1.
00:28
And it's worth remembering that gamma is 1 over the square root of 1 minus v squared over c square.
00:37
Also, we need to remember that for an electron, i'm sorry for a photon, the energy, gamma is equal to hc divided by lambda, where lambda is the wavelength of the electron and an h is plunks constant.
00:52
So what we have in our problem are two particles, one electron and one positron that annihilate one another and produce two photons.
01:04
So photon one plus photon two.
01:07
And they both have the same wavelength.
01:13
And our goal is to find what is the wavelength of the two photons in this process.
01:21
So what i'm going to do is to consider that both, the electron and the positron are at rest initially.
01:31
So all the energy they have is rest energy.
01:36
And remember that the rest energy for each of the particles is mc squared, where m is 9 .1 times 10 to the minus 31 kilograms since the mass of the positron and the electron is the same...