A-level Physics (Advancing Physics)/Pair Production and Annihilation

Pair Production
Sometimes, a photon turns into a particle and its antiparticle, for example, an electron and a positron. It could not turn into just an electron, since this would leave the lepton number unbalanced. The photon must have enough energy to create the masses of the two particles. The energy required to create one of the particles is given by:

$$E = mc^2$$,

where m is the mass of the particle, and c is the speed of light (3 x 108 ms−1). However, two particles must be created. Since the two particles are each other's antiparticle, they have identical masses. So, the total energy required is:

$$E = 2mc^2$$

Annihilation
When a particle meets its antiparticle, the two annihilate each other to form 2 photons (due to conservation of momentum) with sum total energy equivalent to the total mass-energy of both particles.

Sometimes, a pair of particles annihilates, but then the photon produces another pair of particles. Also, a photon could produce a pair of particles which then annihilate each other.

Questions
h = 6.63 x 10−34 Js

1. The mass of an electron is 9.11 x 10−31 kg. What is the minimum amount of energy a photon must have to create an electron?

2. A 1.1 MeV electron annihilates with a 1.1 MeV positron. What is the total energy of the photon produced?

3. What is its frequency?

4. What is its wavelength?

5. A newly produced electron-positron pair are likely to annihilate almost immediately. Under what circumstances can this be avoided?

/Worked Solutions/