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

1. ### Juxtaroberto

14
I know that the mass of subatomic particles is usually given in electronvolts, and that c$$^{2}$$ 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$$^{2}$$, 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?

### Staff: Mentor

I believe it is Kilograms or grams since that is the unit of mass. Cant say for the c.

### 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,

$$m_e c^2 = 511 \rm{ keV}$$

Dividing through by c^2 we get

$$m_e = 511 \rm{ keV}/c^2$$

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
4. ### clem

1,276
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.

### Staff: Mentor

I wouldn't call "light-years per year" dimensionless.