# Modern Physics... relativistic

by irony of truth
Tags: modern, physics, relativistic
 P: 91 How much mass does an electron gain if it is accelerated to an energy of 500 MeV? My solution: I am using the mass of the electron in terms of "energy units"... that is m_e = 0.511 MeV/c^2 where c is the speed of light. The total energy is E = Eo + ke, where ke is kinetic energy Am I right here... mc^2 = m_ec^2 + ke? I mean.. should my E be mc^2/(1 - v^2/c^2)^(1/2)? I am confused.. but if I were to use that "relativistic" formula, I am not given the value of v. Then m = m_e + ke/c^2. Let m_e = 0.511 MeV/c^2 and ke = 500MeV m = 500.511 MeV/c^2 Converting this mass to kilograms results to m = 8.9 x 10^-28 kg.
P: 333
 E = mc^2 = m_ec^2 + ke?
is correct

 should my E be mc^2/(1 - v^2/c^2)^(1/2)?

THis is right if that m is the rest mass of the electron/particle.

$$E = \gamma m_0 c^2$$

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