Calculation of some electron properties

[Lissajoux]

Homework Statement

An electron has a total energy of exactly [itex]5000MeV[/itex] just before a collision.

I need to calculate:

1. The mass energy in [itex]MeV[/itex]

2. The Lorentz factor [itex]\gamma[/itex]

3. The speed as a fraction of [itex]c[/itex]

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

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.

[tex]m_{e}=9.10938215\times 10^{-31}~\textrm{kg}[/tex]

Use formula:

[tex]E=m_{e}c^{2}[/tex]

Hence:

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

So that's the mass energy of the electron.

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

2.

The lorentz factor is given by:

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

But I don't know [itex]v_{e}[/itex]

So I thought could use this:

[tex]E=m_{e}\gamma c^{2}\implies \gamma= \frac{E}{m_{e}c^{2}}[/tex]

But that doesn't seem to work.

3.

Thought I could use:

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

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

4.

Momentum given by:

[tex]P=m_{e}v_{e}[/tex]

.. again need a [itex]\gamma[/itex] 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 [itex]E = \gamma mc^2[/itex], so it's just [itex]5000/0.511...[/itex].

Now that you know [itex]\gamma[/itex], the rest should follow.

 

[Lissajoux]

Yeah think I've figured it out now