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.
A) 0.739 c
B) 0.794 c
C) 0.306 c
D) 0.933 c

Question

Quizplus · Accepted Answer

The total energy of a moving electron is given by:$$E = \sqrt{p^2c^2 + (mc^2)^2}$$where:* E is the total energy* p is the momentum* c is the speed of light* m is the rest massWe can solve for the speed by rearranging the equation:$$v = \frac{pc}{E}$$We can find the momentum by using the relativistic momentum equation:$$p = \frac{mv}{\sqrt{1 - v^2/c^2}}$$Substituting this into the equation for the speed, we get:$$v = \frac{mc}{\sqrt{E^2 - (mc^2)^2}}$$Plugging in the given values, we get:$$v = \frac{(0.511 \mathrm { MeV})(3 	imes 10^8 \mathrm { m/s})}{\sqrt{(0.758 \mathrm { MeV})^2 - (0.511 \mathrm { MeV})^2}} = 0.739c$$Therefore, the speed of the electron is 0.739c.

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

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