An electron is accelerated to a speed where its total energy is 187 times larger

ID: 1272137 • Letter: A

Question

An electron is accelerated to a speed where its total energy is 187 times larger than its rest energy. A) How many times is the kinetic energy of the electron larger than its rest energy?
B) What is the kinetic energy of the electron?
C) What is the speed of the electron in terms of the speed of light? (In this part of the problem you have to enter your answer with a precision of seven or eight digits!)
D) What is the momentum of the electron measured in MeV/c units? (Enter only a number without the MeV/c unit.) An electron is accelerated to a speed where its total energy is 187 times larger than its rest energy. A) How many times is the kinetic energy of the electron larger than its rest energy?
B) What is the kinetic energy of the electron?
C) What is the speed of the electron in terms of the speed of light? (In this part of the problem you have to enter your answer with a precision of seven or eight digits!)
D) What is the momentum of the electron measured in MeV/c units? (Enter only a number without the MeV/c unit.)
B) What is the kinetic energy of the electron?
C) What is the speed of the electron in terms of the speed of light? (In this part of the problem you have to enter your answer with a precision of seven or eight digits!)
B) What is the kinetic energy of the electron?
C) What is the speed of the electron in terms of the speed of light?
D) What is the momentum of the electron measured in MeV/c units? (Enter only a number without the MeV/c unit.)

Explanation / Answer

Total energy E = Mc^2 and e = mc^2; when E = 187e we have M = 187 m

E^2 = e^2 + k^2 = (187e)^2 so k^2 = (186e)^2 and k = sqrt(186)e ANS a)

k = sqrt(186)*.511 = 6.969 MeV. ANS b)

since M = m/L((v/c) that means 1/187 = sqrt(1 - (v/c)^2)

so that (1/187)^2 = 1 - (v/c)^2

v/c = sqrt(1 - (1/187)^2) = 0.99998570 so v = 0.99998570 c ANS. c

k/c = Mv = (6.969E6)/(0.99998570*3*10^8) = 0.02323 ANS d)

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An electron is accelerated to a speed where its total energy is 187 times larger

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