Calculate the amount of energy needed to accelerate an electron from $0.8880$ to $0.991 \mathrm { c }$ Express your answer in $\mathrm { MeV }$ 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 energy needed is calculated using the relativistic energy formula: $ E = \gamma mc^2 $, where $\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$. Calculate $\gamma$ for both velocities, find the difference in energy, and convert to MeV. The correct calculation gives approximately 2.71 MeV.

Calculate the Amount of Energy Needed to Accelerate an Electron 0.88800.88800.8880

Calculate the Amount of Energy Needed to Accelerate an Electron $0.8880$