Consider an electron moving at relativistic speed B) Suppose the total energy of

Question

Consider an electron moving at relativistic speed

B) Suppose the total energy of the electron is 6.5 times its rest energy. With what speed is the electron moving?

C) At this speed, determine the kinetic energy of the electron in electron-volts.

D)What is the magnitude of the electron's momentum?

Consider an electron moving at relativistic speed Determine the electron's rest energy in electron-volts (1 eV = 1.60 times 10-19 J). Suppose the total energy of the electron is 6.5 times its rest energy. With what speed is the electron moving? At this speed, determine the kinetic energy of the electron in electron-volts. What is the magnitude of the electron's momentum?

Explanation / Answer

Part A)
At rest, = mc^2

E = (9.11 X 10^-31)(3 X 10^8)^2

E = 8.199 X 10^-14 J which is 512438.5 eV

Part B)
E = moc^2/(sqrt 1 - v^2/c^2)

6.5(8.199 X 10^-14) = (9.11 X 10^-31)(3 X 10^8)^2/sqrt (1 - v^2/c^2)

v = 2.96 X 10^8 m/s which is .988c

Part C)

KE = mc^2 - moc^2

KE = (9.11 X 10^-31)(3 X 10^8)^2/sqrt (1 - 2.96 X 10^8^2.3 X 10^8)^2 - 9.11 X 10^-31(3 X 10^8)^2

KE = 4.51 X 10^-13 J which is 2.82 X 10^6 eV

Part D

p = mov/sqrt (1 - v^2/c^2)

p = (9.11 X 10^-31)(2.96 X 10^8)/sqrt (1 - .988^2)

p = 1.76 X 10^-21 kg m/s

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