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Q18E

Expert-verifiedFound in: Page 556

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 $1.2TeV$ .

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

**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, $9.1\times {10}^{-31}\text{kg}$ ,h is reduced Planck's constant, $6.63\times {10}^{-34}\text{J}\xb7\text{s}$ , $\lambda $ is the size of an object to be examined and is the velocity of light, $3\times {10}^{8}\text{m/s}$ .

Substitute the numerical values in equation (1) as:

$\begin{array}{rcl}E& =& \frac{\left(6.63\times {10}^{-34}J\xb7s\right)\left(3\times {10}^{8}m/s\right)}{\left({10}^{-18}m\right)}\\ E& =& 1.989\times {10}^{-7}J\\ & =& 1.2TeV\\ & & \end{array}$

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 $1.2TeV$ .

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