Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What units are used after eV, MeV, GeV, etc, are divided by c^2?

  1. Feb 16, 2011 #1
    I know that the mass of subatomic particles is usually given in electronvolts, and that c[tex]^{2}[/tex] is set to 1 so that we can say, "This particle has a mass of 13 eV." However, if you divide 13 eV by c[tex]^{2}[/tex], you get an answer, x. What units is this in?

    Oh, also, what units do we use c in in the first place? km/s, m/s, mi/s?
  2. jcsd
  3. Feb 16, 2011 #2


    User Avatar

    Staff: Mentor

    I believe it is Kilograms or grams since that is the unit of mass. Cant say for the c.
  4. Feb 16, 2011 #3


    User Avatar

    Staff: Mentor

    This is sloppy language which is unfortunately commonly used by physicists.

    The electron-volt (eV) is a unit of energy, equal to 1.602e-19 joule.

    When someone says "the mass of an electron is 511 keV" he really means, "the energy-equivalent of the mass of an electron is 511 keV" or "the rest-energy of an electron is 511 keV" or "the mass of an electron is 511 keV/c^2." Mathematically,

    [tex]m_e c^2 = 511 \rm{ keV}[/tex]

    Dividing through by c^2 we get

    [tex]m_e = 511 \rm{ keV}/c^2[/tex]

    so the eV/c^2 is a unit of mass, equal to (1.602e-19 J)/(2.998e8 m/s)^2 = 1.782e-36 kg.

    To check this, 511 keV = 511 x 1000 x 1.782e-36 kg = 9.108e-31 kg which is indeed the mass of an electron in kg.
    Last edited: Feb 16, 2011
  5. Feb 17, 2011 #4


    User Avatar
    Science Advisor

    This language is fortunately commonly used by physicists.
    There are several systems of units in which c=1 and is dimensionless.
    (Distance in light-years and time in years is one.)
    All of those systems are more useful than kg or joules in describing an electron.
  6. Feb 17, 2011 #5


    User Avatar

    Staff: Mentor

    I wouldn't call "light-years per year" dimensionless.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?