Calculation of some electron properties

[Lissajoux]

Homework Statement

An electron has a total energy of exactly 5000MeV just before a collision.

I need to calculate:

1. The mass energy in MeV

2. The Lorentz factor \gamma

3. The speed as a fraction of c

4. The momentum in MeV/c^{2}

Homework Equations

Within the problem statement and solution attempt.

The Attempt at a Solution

These seemed pretty easy, but I'm for some reason finding issues with them at the moment now I've got round to trying to do the calculations.

This is what I have so far:

1.

m_{e}=9.10938215\times 10^{-31}~\textrm{kg}

Use formula:

E=m_{e}c^{2}

Hence:

E=8.198444\times 10^{-14}~\textrm{J}=0.511763~\textrm{MeV}

So that's the mass energy of the electron.

Not sure if was meant to use E=5000~\textrm{MeV} instead? and whether that equation should have a \gamma in it?

2.

The lorentz factor is given by:

\gamma=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^{2}}}}

But I don't know v_{e}

So I thought could use this:

E=m_{e}\gamma c^{2}\implies \gamma= \frac{E}{m_{e}c^{2}}

But that doesn't seem to work.

3.

Thought I could use:

E=\frac{1}{2}m_{e]c^{2}

But I believe I need to account for a \gamma in there, and I can't get it to work. Maybe I'm using the wrong energy.

4.

Momentum given by:

P=m_{e}v_{e}

.. again need a \gamma in there?

- - - - - - - - -

I don't think I'm too far off the answers, just need a bit of advice.

 

[tjackson3]

1 is correct (mass energy typically refers to rest mass energy)

For 2, the total energy is E = \gamma mc^2, so it's just 5000/0.511....

Now that you know \gamma, the rest should follow.

 

[Lissajoux]

Yeah think I've figured it out now