# Calculation of some electron properties

1. May 3, 2010

### Lissajoux

1. The problem statement, all variables and given/known data

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 $MeV/c^{2}$

2. Relevant equations

Within the problem statement and solution attempt.

3. 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.

2. May 3, 2010

### 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.

3. May 3, 2010

### Lissajoux

Yeah think I've figured it out now