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Calculation of some electron properties

  1. May 3, 2010 #1
    1. The problem statement, all variables and given/known data

    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]

    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.

    [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. :smile:
     
  2. jcsd
  3. May 3, 2010 #2
    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.
     
  4. May 3, 2010 #3
    Yeah think I've figured it out now :smile:
     
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