# When is it safe to use eV units and when do we have to convert eV units into kg?

1. Dec 27, 2012

### DunWorry

1. The problem statement, all variables and given/known data
I have a misunderstanding of when I can safely use eV units in a formula. For example in the formula p = $\sqrt{\frac{E^{2} - m^{2}c^{4}}{c^{2}}}$ I can put the energy and mass in terms of MeV and get an answer with units MeV/C, which makes sense. But then there was this formula I was using e$^{-\sqrt{\frac{2m (V-E)}{h^{2}}}x}$

where m is mass, v is potential, e is energy, h bar squared on bottom (I couldnt find symbol) and x is in metres. It is supposed to give probability which is dimensionless. However, if I put in mass, potential and energy in terms of eV, I get a wrong answer. if I convert the mass into kg, put potential and energy in terms of joules then I get the correct answer. Why could I use eV in the first case but had to convert in the second case? is it because I am multiplying by x which is in metres so it somehow does not work with eV? what if I had another formula with mass/energy and was multiplying by a speed with units m/s? would I again have to convert all eV units into kg/joules etc?

Are there any general rules I should keep in mind whilst working with eV?

Thanks

2. Dec 27, 2012

### tiny-tim

Welcome to PF!

Hi DunWorry! Welcome to PF!

(it's the obvious … \hbar )

The only unit you've changed is the mass unit (by a factor MeV/kg).

If the terms in the top line of your formula all contain MeV, then since the bottom line (c2) doesn't contain mass at all, there's no difficulty: the result will be in MeV.

In your second formula, the bottom line ($\hbar$2) does contain mass, so it won't work unless you rewrite h in terms of Mev.

(so the general rule is that it's ok to change the mass unit, so long as you change it everywhere)​