Chapter 32, Problem 44GP

To determine

The total energy and wavelength of proton.

Answer to Problem 44GP

Energy, $E=2,59\times {10}^{10}\text{ eV}$

Wavelength, $\lambda =4.7\times {10}^{-17}\text{ m}$

Explanation of Solution

Given:

Kinetic energy of proton, $KE=25\text{ GeV}$

Rest energy of proton, $RE=938.27\text{ MeV}$

Formula used:

  $E=KE+RE$

  $E=\frac{hc}{\lambda }$

Where, $h$ = Planck's constant

  $\lambda$ = wavelength

   c = speed of light

Calculation:

The total energy of is calculated as,

  $\begin{array}{l}E=KE+RE\\ E=\left(25\times {10}^9\right)+\left(938.27\times {10}^6\right)\\ E=2.59\times {10}^{10}\text{ eV}\end{array}$

The wavelength is calculated as,

  $\begin{array}{l}E=\frac{hc}{\lambda }\\ \lambda =\frac{hc}{E}\\ \lambda =\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{2.59\times {10}^{10}\times 1.6\times {10}^{-19}}\\ \lambda =4.7\times {10}^{-17}\text{ m}\end{array}$