# Modern Physics relativistic

1. Mar 10, 2005

### irony of truth

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.

2. Mar 10, 2005

### Gamma

is correct

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

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

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