Solution

Problem

**14.5.1.** A stationary particle of mass $M$ decays into two $\gamma$-quanta. Determine the mass of each $\gamma$-quantum.

Solution

The total energy of the particle before decay:

$$E = M c^2$$

After the decay, two identical $\gamma$-quanta are produced. Since each $\gamma$-quantum has no rest mass but carries energy, it is convenient to introduce an equivalent relativistic mass $m$ corresponding to its energy:

$$E = 2 m c^2$$

Applying the law of conservation of energy:

$$M c^2 = 2 m c^2$$

Dividing both sides by $c^2$, we get:

$$M = 2m \quad \Rightarrow \quad m = \frac{M}{2}$$