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E=mc^2 units

  1. Nov 22, 2015 #1
    Hi,
    I'm new to the site and not sure if I'm posting in the right place as this is not exactly a homework problem, but just a problem in general. I'm looking at E=mc2 and how the units can be broken down into eV=u (I think?). I don't know what happens to the distance units, though, if we keep seconds as the time units.

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

    What happens to the distance units when E=mc2 is converted from joules=(kg)(m/s)2 into eV=u? Where eV is electron volts and u is atomic mass units.

    2. Relevant equations

    1u= 1.66x10-27 kg
    1eV=1.6x10-19 J
    c2=9.315x108 eV/u

    3. Attempt at Solution

    I really don't know what to do here. Can it just stay meters?
    Any help is appreciated.
     
  2. jcsd
  3. Nov 22, 2015 #2

    Simon Bridge

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    Work out the required scale factor... i.e. if your mass were in 4-kilogram lots, then the distance would need to be in units of 2 meters to keep energy in joules. But if you needed the energy is units of a quarter joule, what do you need to do to the meter?
     
  4. Nov 22, 2015 #3

    mfb

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    You can convert them into each other using this equation, but they are not equal.

    Plugging in m = 1u = 1.66*10-27 kg gives an energy of mc^2 = 1.66*10-27 kg * (3*108 m/s)2 = 1.5*10-10 J = 1.5*10-10 J * (1eV / (1.6*10-19 J)) = 0.94 * 109 eV or about 940 MeV.

    The multiplication by 1eV / (1.6*10-19 J) works because this fraction is equal to 1, and 1 kg m2/s2 = 1 J.
     
  5. Nov 22, 2015 #4
    Oh, ok I get it. I guess I was over complicating it in my head. Thanks a lot.
     
  6. Nov 22, 2015 #5
    Thanks. This helps.
     
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