The total energy of a moving electron is $0.758 \mathrm { MeV }$ What is the speed of the electron in terms of c? The rest mass energy of an electron is 0.511 MeV.

Question

Quizplus · Accepted Answer

The total energy ($E$) of the electron is given as $0.758 \mathrm{MeV}$, and the rest mass energy ($E_0$) is $0.511 \mathrm{MeV}$. The kinetic energy ($K$) of the electron can be found by subtracting the rest mass energy from the total energy: $K = E - E_0 = 0.758 \mathrm{MeV} - 0.511 \mathrm{MeV} = 0.247 \mathrm{MeV}$. The relativistic total energy of an object is given by $E = \gamma E_0$, where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$, and $v$ is the velocity of the electron. Solving for $v$ in terms of $c$ involves rearranging the equation to solve for $\gamma$ first, then $v$. Given the total energy and rest mass energy, we find that $v \approx 0.739c$, which matches choice A.

The Total Energy of a Moving Electron Is 0.758MeV0.758 \mathrm { MeV }0.758MeV

The Total Energy of a Moving Electron Is $0.758 \mathrm { MeV }$