Momentum of electron from total energy of electron

[umwolv16]

Homework Statement

An electron has a total energy equal to five times its rest energy(0.511MeV).

--What is its momentum (in MeV/c)?

Homework Equations

E(total) = [mass(electron)*c^2]/[sq. root of (1- velocity^2/c^2)]
----I converted 2.555MeV (total energy) to 4.088e-13 J and plugged that in for E(total) to solve for velocity

The Attempt at a Solution

I used the EQN above to solve for velocity of the electron [in terms of c(speed of light)].
I then divided the total energy (2.555MeV) by this velocity (which I got to be 0.979680884c) and got the answer 2.61MeV/c. When I submit it, it says I'm within 10%, but I didn't round any numbers until the can't see what I did wrong...

 

[alphysicist]

Homework Statement

An electron has a total energy equal to five times its rest energy(0.511MeV).

--What is its momentum (in MeV/c)?

Homework Equations

E(total) = [mass(electron)*c^2]/[sq. root of (1- velocity^2/c^2)]
----I converted 2.555MeV (total energy) to 4.088e-13 J and plugged that in for E(total) to solve for velocity

The Attempt at a Solution

I used the EQN above to solve for velocity of the electron [in terms of c(speed of light)].
I then divided the total energy (2.555MeV) by this velocity

I don't believe that is correct; if you look at the equation you are using I think you'll find that you don't divide the energy by velocity to get momentum. What do you get?

 

[umwolv16]

I thought I solved for momentum because I found the velocity by the EQN i gave and I know the mass of an electron, but the units weren't right. I didn't know how to convert kg*m/s to MeV/c. I had energy in MeV and found my velocity in terms of c, so I couldn't think of anything else to do, but divide them. I feel like I'm using the right EQN, but I'm not sure how to derive my answer

 

[alphysicist]

I thought I solved for momentum because I found the velocity by the EQN i gave and I know the mass of an electron, but the units weren't right. I didn't know how to convert kg*m/s to MeV/c. I had energy in MeV and found my velocity in terms of c, so I couldn't think of anything else to do, but divide them. I feel like I'm using the right EQN, but I'm not sure how to derive my answer

I think what you are missing is the definition of the relativistic momentum:

momentum =(gamma) m v

Since you have already done the work to find v, you could actually just plug that in and solve it. However, to get the equation related to what you have already done, note that:

momentum = (gamma) m v
energy = (gamma) m c^2

putting these together gives:

(v / c) = p c / E

and since you already have E in MeV and v in terms of c, you can get momentum directly.