Answer to Question #185676 in Mechanics | Relativity for Bidisha mondal

Question

A positron and an electron at rest in frame S combine and annihilate another, producing two photons. (a) What is the energy and momentum of each photon in this frame? What quantities are conserved in this process? (b) Prove that the positron and electron cannot combine to produce only one photon.

Answer 1

(a) Conservation of energy,

$r^{,}m_oc^2+m_oc^2=E_{r^,}+E_{r^,}$

$E_{r^{,}}=\dfrac{(r^,+1)m_oc^2}{2}$

Conservation of momentum,

Horizontal,

$r^,m_ov=P_o=\dfrac{E_{r^,}}{c}cos\theta_1+\dfrac{E_{r^,}}{c}cos\theta_2$

Vertical,

$P_o=0$

Momentum and energy are conserved in this process

(b) Conservation of energy and linear momentum forbid the creation of only one photon.

In the most common case, two photons are created, each with energy equal to the rest energy of the electron or positron.

Conservation laws forbid the formation of only a single photon as the energy released clearly leads to the formation of two or more photons