Calculate the amount of energy needed to accelerate an electron from $0.888 \mathrm { c }$ to $0.991 \mathrm { c } .$ Express your answer in $\mathrm { MeV } \text {. }$ The rest mass energy of an electron is 0.511 MeV.
A)2.71 MeV
B)1.90 MeV
C)4.61 MeV
D)5.69 MeV

Question

Quizplus · Accepted Answer

The correct answer is A.The kinetic energy of an electron is given by:$$K = (\gamma - 1)mc^2$$where $\gamma$ is the Lorentz factor, $m$ is the rest mass of the electron, and $c$ is the speed of light.The Lorentz factor is given by:$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$where $v$ is the velocity of the electron.Substituting the given values into the equations, we get:$$K = \left(\frac{1}{\sqrt{1 - 0.888^2}} - 1\right)0.511 \mathrm { MeV } = 2.71 \mathrm { MeV }$$

Calculate the Amount of Energy Needed to Accelerate an Electron 0.888c0.888 \mathrm { c }0.888c

Calculate the Amount of Energy Needed to Accelerate an Electron $0.888 \mathrm { c }$