Finding particle momentum from energy and potential difference

[Stickybees]

Say I have the rest energy(mc^2) and the total energy of a particle (E), would getting the momentum energy of the particle be as simple as doing (E^2-(mc^2)^2)^(1/2) = pc?

And when accelerating a electron through a potential difference how would I work out its momentum, given I have its rest energy and the value for potential difference?

Thanks.

 

[zhermes]

That looks like the correct equation to use.

When an electron is accelerated through a potential difference, what happens to its total energy?

 

[Morgoth]

c=1 you have
E²= p²+m²

so you want to know the momentum you do what you said

p=√ [E²-m²]

by the time you say "total energy E" it means that the kinetical energy is within your already known parameter, so is there a potential, is there not- you know E, you know mass, so you know its mommentum.

 

[Stickybees]

I am assuming that for a p.d. of for example 1 MV, this will create an energy difference of 1 MeV for an electron and with the rest energy of around 0.5 MeV for an electron, it would simply equal 1.5 MeV/c for the momentum, but I think this is wrong, but I don't understand why.

 

[Matterwave]

Assuming all the energy was kinetic, your formula works. If there is also potential energy involved, then you have to take that into account as well.