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So what is an MeV?

The standard unit of energy is the Joule, such that 1 Joule is equal to the work done by a force of 1 Newton in moving a distance of 1 metre (in direction of the force).   However using this for particles seems a bit silly when everything occurs on such a small scale.  Physicists have found that a more useful unit of energy is the MeV or 106eV, i.e. Mega electron Volt or 106 electron Volts - an electron volt?  1 eV is defined to be the energy required to move an electron through a potential difference of 1 Volt.  As the charge on the electron is -1.6x10-19C. it means that there are 6.25x1018eV in 1 Joule (or conversely 1 eV is 1.6x10-19 Joules).

and a GeV?

Just as an M means 106, so a G represents 109 (Giga), which is useful as we head to higher energy physics