Chapter 30, Problem 90A

To determine

The magnitude and direction of the momentum of gamma rays which are generated when electron-positron pair decays.

Explanation of Solution

Introduction:

A positron and electron annihilate to produce gamma energy.

Energy equivalent of mass of an electron, $E=0.51\text{eV}$

A positron and electron annihilate to produce gamma energy. It can be represented as follows:

  $e^{-}+e^{+}\to 2\gamma$

This means the energy equivalent mass of both electron and positron would be emitted which is: $2\times 0.51\text{eV= 1}\text{.02 eV}$

As the positron and electron were initially at rest, the final momentum of the two gamma rays would also be zero. Thus, the magnitude of the gamma rays would be equal but opposite in direction to each other.

Conclusion:

The magnitude of the gamma rays would be equal but opposite in direction to each other.