If the total energy of an electron in an accelerator is three times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s) A)2.00 × 10⁸ m/s B)1.30 × 10⁸ m/s C)1.41 × 10⁸ m/s D)2.98 × 10⁸ m/s E)2.83 × 10⁸ m/s

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Quizplus · Accepted Answer

The total energy (E) of an electron is given by $E = \gamma mc^2$, where $m$ is the rest mass of the electron, $c$ is the speed of light, and $\gamma$ is the Lorentz factor, defined as $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$, with $v$ being the velocity of the electron. If the total energy is three times the rest energy ($mc^2$), then $\gamma = 3$. Solving the equation $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ for $v$ when $\gamma = 3$ gives $v \approx 0.9428c$, which is approximately $2.83 \times 10^8 m/s$, matching choice E.

If the Total Energy of an Electron in an Accelerator