Chapter 27, Problem 33P

To determine

The amount of total kinetic energy produced.

Answer to Problem 33P

Solution:

Electron- positron pair has $2.618\text{MeV}$ total kinetic energy when produced by a $3.64\text{MeV}$ photon.

Explanation of Solution

Given:

Energy of the photon: $3.64\text{MeV}$

Mass of the electron & positron: $9.1\times {10}^{-31}\text{kg}$

Formula Used:

$\text{KE}=hf-2m_0{c}^2$

Calculation:

Total kinetic energy of the electron- positron pair produced by a $3.64\text{MeV}$ photon can be calculated by using the formula as

$\begin{array}{c}\text{KE}=hf-2m_0{c}^2\\ =3.64\text{MeV-2(0}\text{.511MeV)}\\ \text{=}2.618\text{MeV}\end{array}$

So, the total kinetic energy of the electron- positron pair is found to be $2.618\text{MeV}$.