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I know that conventionally the unit of $E$ in $E=mc^2$ is taken as joules when mass is in $\mathrm{kg}$. But I am doing some calculations of my own with different units of energy ($\mathrm{keV}$,$\mathrm{MeV}$ etc.). So my question is whether we have to convert $\mathrm{keV}$ or $\mathrm{MeV}$ to joules in order to calculate mass or we can keep the values of $\mathrm{KeV}$, $\mathrm{MeV}$ units and then find mass (I think this method is easier)? If we are keeping $\mathrm{keV}$ and $\mathrm{MeV}$ then what will be the unit of mass, will it still be $\mathrm{kg}$? I am a chemist so please forgive if I asked an irrational question.

Advanced thanks for your help

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  • $\begingroup$ The easy conversion is that 1GeV is 1 proton, or 1 gram divided by 1 mole. $\endgroup$
    – Ron Maimon
    Commented Feb 23, 2012 at 16:00

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The unit can be anything as long as you carry out the proper conversion. If you're using $KeV$ and $MeV$, there isn't any complete unit system that specifies the units of speed (which we need to convert to mass).

Usually, particle physicists use $MeV$ as a mass unit as well as energy (thereby setting $c=1$ in this unit system). Later on stuff can be converted to SI by normal $eV$-to-Joules conversion, followed by division by $c^2$ in SI if we want mass. This unit system may be helpful for you calculations.

One can't generally ask "If so-and-so is in abc unit, what is the unit of xyz?", unless more examples are provided. For example, you can ask the above question as "If energy is in MeV, and speed is in ly/s (made-up useless unit), then what's the unit of mass?". Here, the answer would be $\frac{MeV\times s^2}{ly^2}$.

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    $\begingroup$ You'll also occasionally see the mass unit written as $\frac{\rm MeV}{c^{2}}$. $\endgroup$
    – Zo the Relativist
    Commented Feb 22, 2012 at 15:54
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In general the units of energy will be $\frac{\text{[Mass]}\text{[distance]}^2}{\text{[time]}^2}$, where you substitute in the units for mass, distance and time that you have chosen.

It is the relationship between them that matters, not what you call them.

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