Question

What is meant by pair production and annihilation?

Answer 1

Hint:Recall the terms photoelectric effect and Compton Effect. As the name suggests, the pair production results in formation of two particles. The name annihilation suggests loss in the particles.

Complete step by step answer:
We know from photoelectric effect and Compton Effect, the incident photon gives up some of its energy to the colliding particle. This rises to two processes: pair production and annihilation. We know in pair production, the original photon containing high energy splits into two particles of the same mass but opposite charge. These two particles are generally electron and its anti-electron commonly known as positron. We express the process of pair production as follows,
$$h\nu =2\left(m_0{c}^2\right)+K_e+K_{-e}$$
Here, $$h\nu$$ is the energy of the original photon, $$m_0$$ is the rest mass of electron, c is the speed of light, $$K_e$$ is the kinetic energy of electron and $$K_{-e}$$ is the kinetic energy of positron.
We know the annihilation is the reverse process of pair production in which the electron and positron collides with each other and the result of this is the annihilation of both electron and positron. After annihilation of electrons and positrons, the energy is emitted in the form of electromagnetic radiation whose frequency is $$\nu$$. Two photons emit after the annihilation of electrons and positrons. We can express the energy balance in annihilation process as,
$$2\left(m_0{c}^2\right)+K_e+K_{-e}=2h\nu$$
The factor 2 in the above equation represents the rest mass energy of the electron and positron. The pair production generally occurs in solids.


Note:To answer this question, students must understand the photoelectric effect and Compton Effect. In the above energy balance equations, students might wonder why the two photons emit after the annihilation while in pair production, only one photon splits into electron and positron. Because in pair production, the energy of the photon is greater enough to split into electron and positron but in annihilation, the energy of each photon is less as compared to the incident photon in the pair production.