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Q18E

Expert-verified
Found in: Page 556

### Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

# Approximately what energy would electrons need to have to be useful as probes that could reveal features as small as ${{\mathbf{10}}}^{\mathbf{-}\mathbf{18}}{\mathbf{}}{\mathbf{m}}$, the approximate range of the weak force?

The energy would the electrons need to have to be useful as probes that could reveal features as small as ${10}^{-18}m$ , the approximate range of the weak force is $1.2TeV$ .

See the step by step solution

## Step 1: Given data

The size of an object, $\lambda ={10}^{-18}m$ .

## Step 2: Concept of Energy of electron

The energy of an electron is given as,

${{E}}^{{2}}{=}{{m}}^{{2}}{{c}}^{{4}}{+}{{p}}^{{2}}{{c}}^{{2}}$

${{E}}^{{2}}{\approx }{{p}}^{{2}}{{c}}^{{2}}\phantom{\rule{0ex}{0ex}}{E}{\approx }\frac{h}{\lambda }{c}\phantom{\rule{0ex}{0ex}}$

Where is the mass of an electron, $9.1×{10}^{-31}\text{kg}$ ,h is reduced Planck's constant, $6.63×{10}^{-34}\text{J}·\text{s}$ , $\lambda$ is the size of an object to be examined and is the velocity of light, $3×{10}^{8}\text{m/s}$ .

## Step 3: Calculation of the energy for an electron

Substitute the numerical values in equation (1) as:

$\begin{array}{rcl}E& =& \frac{\left(6.63×{10}^{-34}J·s\right)\left(3×{10}^{8}m/s\right)}{\left({10}^{-18}m\right)}\\ E& =& 1.989×{10}^{-7}J\\ & =& 1.2TeV\\ & & \end{array}$

The energy would the electrons need to have to be useful as probes that could reveal features as small as ${10}^{-18}m$ , the approximate range of the weak force is $1.2TeV$ .