The total energy of a free electron moving through empty space is E=1.5mc^2, where m is the mass of the electron and c is the speed of light. What is this electronâ€™s speed? 1. c (the speed of light) 2. 0.7453c 3. 0.8660c 4. 0.9428c 5. 0.9950c 6. 0.9999c I thought since that Etotal = 1.5mc^2 then.... Etotal = KE = .5mv^2 1.5mc^2 = .5mv^2 and solve for v (masses would cancel which is what I was looking for) What is wrong about this approach?
I believe that the proper relativistic kinetic energy equation would be [tex]E_k = (\gamma - 1)mc^2[/tex] Or did you make that mistake on purpose, Doc Al?
oh shoot...i forgot about that. Do I need to use the non-approximated version of KE? (I can never remember it.. but i'm looking it up right now)
Oh, I get it... the total energy of the free electron is the sum of its kinetic energy and the energy from the mass-energy equivalence? The potential energy of the electron is zero, since it's free, right? [tex]E_{total}= (\gamma - 1)mc^2 + mc^2[/tex] [tex]\ \ \ = \gamma mc^2[/tex] Is this so?