Chapter 2, Problem 2.1P

To determine

Make:

A table showing electron's relativistic moment and electron's nonrelativistic moment.

Explanation of Solution

Given:

Mass of electron, $m=9.11\times {10}^{-31}\text{kg}$

At different speed, $\beta =0.1,0.5,0.9,0.99$

Formula Used:

The speed of the electron:

  $u=\beta c$

Non- relativistic momentum:

  $p_{\text{NonRel}}=mu$

Relativistic momentum:

  $p_{\text{rel}}=\frac{mu}{\sqrt{1-{\beta }^2}}$

Calculation:

  $\boxed{\begin{array}{cccc}& & \text{ Non relativistic momentum }& \text{Relativistic}\text{momentum}\\ \beta & u=\beta c& p_{\text{NonRel}}=mu& p_{\text{rel}}=\frac{mu}{\sqrt{1-{\beta }^2}}\\ 0.1& 0.1c& 0.273\times {10}^{-22}\text{kg}.\text{m}/\text{s}& 0.275\times {10}^{-22}\text{kg}.\text{m}/\text{s}\\ 0.5& 0.5c& 1.37\times {10}^{-22}\text{kg}.\text{m}/\text{s}& 1.58\times {10}^{-22}\text{kg}.\text{m}/\text{s}\\ 0.9& 0.9c& 2.46\times {10}^{-22}\text{kg}.\text{m}/\text{s}& 5.63\times {10}^{-22}\text{kg}.\text{m}/\text{s}\\ 0.99& 0.99c& 2.7\times {10}^{-22}\text{kg}.\text{m}/\text{s}& 19.2\times {10}^{-22}\text{kg}.\text{m}/\text{s}\\ & & & \end{array}}$