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 of the electron* p is the momentum of the electron* m is the rest mass of the electron* c is the speed of lightWe are given that the total energy of the electron is 0.758 MeV and the rest mass energy of an electron is 0.511 MeV. Substituting these values into the equation above, we get:$$0.758 \mathrm { MeV } = \sqrt{p^2c^2 + (0.511 \mathrm { MeV })^2}$$Solving for p, we get:$$p = \sqrt{(0.758 \mathrm { MeV })^2 - (0.511 \mathrm { MeV })^2} = 0.665 \mathrm { MeV }/c$$The speed of the electron is then given by:$$v = \frac{p}{m} = \frac{0.665 \mathrm { MeV }/c}{0.511 \mathrm { MeV }} = 0.739c$$Therefore, the correct answer is A) 0.739 c.

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

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