Calculate the amount of energy needed to accelerate an electron from $0.888 c$ to $0.991 c$ Express your answer in $\mathrm { MeV }$ The rest mass energy of an electron is 0.511 MeV.

Question

Quizplus · Accepted Answer

The kinetic energy of the electron can be calculated using the relativistic formula:
$K = (\gamma -1)mc^2$
where $\gamma$ is the Lorentz factor given by $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$, $m$ is the rest mass of the electron and $v$ is its velocity.

At $v = 0.888c$,
$\gamma_1 = \frac{1}{\sqrt{1-\frac{(0.888c)^2}{c^2}}} = 2.023$

At $v = 0.991c$,
$\gamma_2 = \frac{1}{\sqrt{1-\frac{(0.991c)^2}{c^2}}} = 7.089$

So, change in kinetic energy of the electron is given by:
$\Delta K = (\gamma_2 - \gamma_1)mc^2 = (7.089 -2.023)	imes (0.511\ \mathrm{MeV})= 2.71\ \mathrm{MeV}$

Therefore, the correct answer is A.

Calculate the Amount of Energy Needed to Accelerate an Electron 0.888c0.888 c0.888c

Calculate the Amount of Energy Needed to Accelerate an Electron $0.888 c$