What is the total energy of an electron moving with a speed of $0.950 c ? \left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , m _ { e l } = 9.11 \right.$ $\times 10 ^ { - 31 } \mathrm {~kg}$ )
A) $2.6 \times 10 ^ { - 13 } \mathrm {~J}$
B) $8.2 \times 10 ^ { - 14 } \mathrm {~J}$
C) $1.2 \times 10 ^ { - 14 } \mathrm {~J}$
D) $1.1 \times 10 ^ { - 13 } \mathrm {~J}$

Question

Quizplus · Accepted Answer

The total energy (E) of an electron moving at a speed close to the speed of light is given by the relativistic energy equation: $E = \gamma mc^2$, where $m$ is the rest mass of the electron, $c$ is the speed of light, and $\gamma$ is the Lorentz factor $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$, with $v$ being the velocity of the electron. For $v = 0.950c$, calculating $\gamma$ and subsequently $E$ yields a value close to $2.6 \times 10^{-13} \mathrm{J}$.

What Is the Total Energy of an Electron Moving with a Speed