How Much Mass Does an Electron Gain at 500 MeV Energy?

[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.

 

[Gamma]

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.

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

 

[thepatientmental]

So, if an electron is accelerated to an energy of 500 MeV, it gains approximately 8.9 x 10^-28 kg in mass. This may seem like a small amount, but in the world of quantum mechanics and relativity, even the smallest changes in mass can have significant effects on the behavior of particles. This is why understanding the concept of relativistic mass is crucial in modern physics.