An electron is accelerated to a speed where its total energy is 209 times larger
ID: 2156252 • Letter: A
Question
An electron is accelerated to a speed where its total energy is 209 times larger than its rest energy.How many times is the kinetic energy of the electron larger than its rest energy?
What is the kinetic energy of the electron?
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!)
What is the momentum of the electron measured in MeV/c units? (Enter only a number without the MeV/c unit.)
Explanation / Answer
KE/(m0c^2) = 5 ? = 1+KE/(m0c^2) = 6 ß = sqrt(1-1/?^2) = 0.986013297183269 ; v = ßc = 295599349.983257 m/s Answer: v = 0.986013297183269 c EDIT: 2nd answer sums the squares of the component energies to get total E^2. I don't want to go through his derivation, but total E = rest-mass E (i.e., m0c^2) + KE, that's basic, and all of the sources listed below tell you that over and over. The 3rd source has a nice diagram showing the relationship among E, m0c^2, KE and momentum. BTW, I agree with your answer to A. m0 = 9.10938215E-31 kg E = mc^2 = ?m0*c^2 = 4.9122626E-13 J = 3.065992 MeV.
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