# I How can MeV be equal to MeV/c^2

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1. Mar 10, 2016

### Christoffer Zakrzews

How can 1 u be eaual to 931,5 MeV, and at the same time be equal to 931,5 MeV/c^2?

(1) 1 u = 931,5 MeV
(2) 1 u = 931,5 MeV/c^2

Becuase then 931,5 MeV would equal to 931,5 MeV/c^2?

1 u = 1 u
(1) = (2)
931,5 MeV = 931,5 MeV/c^2

I understand that you can derive both separately or say that 931,5 MeV energi is equal to 931,5 MeV/c^2 in mass (in line with E=mc^2), but isn't it inconsistent as you look at it.

Assume that
1 u = 931,5 MeV (*)

then
1 u = 931,5 MeV = 931,5*c^2 MeV/c^2 = 8,3*10^19 MeV/c^2 (and not 931,5 MeV/c^2)

1 u = 931,5 MeV/c^2 (**)

then
1 u = 931,5 MeV/c^2 = 931,5/c^2 MeV = 1,0*10^-14 MeV (and not 931,5 MeV)

So, is 1 u equal to 931,5 MeV or is it eaual to 1,0*10^-14 MeV?

PS.
Or at least how can I think to not screw things up, to not think:
huum... 1 u = 931,5 MeV/c^2 in the formula, but I don't won't in MeV/c^2, I want in MeV...
okey then I move /c^2 to the number (as I would do with a prefix). c is a number as well as a prefix is, so I can treat them in the same way. Move /c^2 to the number means divide 931,5 with c^2, and MeV is what's left:
931,5 MeV/c^2 = 931,5/c^2 MeV = 1,0*10^-14 MeV

pehaps I don't think
okey, I have mass (931,5 MeV/c^2) and I want energi, then I have to multiply mass with c^2 (as in einsteins) to get energi:
E=mc^2 = 931,5 MeV/c^2 * c^2 = 931,5 MeV

Last edited: Mar 10, 2016
2. Mar 10, 2016

### jambaugh

Remember that c in the appropriate units can be made equal to 1. It is now defined specifically a unit conversion constant (like 12in/1foot) rather than a physical parameter or observed quantity.

The units of eV or MeV depend on the units you chose for the unit of charge. That part is still ambiguous. Give the charge in coulombs and you get
931.5MeV = 931.5 times 1M times 1.60217662 × 10-19 Coulomb Volts or Joules.

If it helps then, view the /c^2 as being absorbed into (or factored out of) the unit choice of the electron charge.

[addendum] As to your specific question when you calculate 1u both answers are correct once you correctly express the units.

3. Mar 10, 2016

### Staff: Mentor

I can say from personal experience that when talking among themselves, and when writing for each other, particle physicists always refer to masses as MeV (or some other multiple of eV), instead of as MeV/c2. It's a bit sloppy, but everybody in the field understands it. We do the same thing for momentum: MeV instead of MeV/c.

Another way to think of it is that when we say "m = 931.5 MeV" and "p = 500 MeV" we really mean "mc2 = 931.5 MeV" and "pc = 500 MeV". This fits with the way we actually use these numbers in calculations most of the time. For example, a particle with the above-given mass and momentum has energy $$E = \sqrt{m^2 c^4 + p^2 c^2} = \sqrt{(mc^2)^2 + (pc)^2} = \sqrt{(931.5 \text{ MeV})^2 + (500 \text{ MeV})^2} = 1057.2 \text{ MeV}$$

4. Mar 10, 2016

### Christoffer Zakrzews

Okey, thanks.

Calculation * and (1) is wrong.
Calculation ** and (2) is right:

1 u = 931,5 MeV/c2
E(1u) = 1 u * c2 = 931,5 MeV/c2 * c2 = 931,5 MeV

And yes, there are no difference between prefixes and c2. Both are numbers and you can treat them in the same way.

Thus, is

1 u = 931,5 MeV/c2 = 931,5/c2 MeV = 1,0*10-14 MeV

right.

But what's deciving, and can let you in a mindtrap in your weakest moments is that, suddenly you wake up seing 1,0*10-14 MeV on your paper, thinking, but this number has MeV, a energy unit behind itself, and I want my answer in MeV, then I have my energy. Big mistake. 1,0*10-14 MeV is just an expression of a mass with a kinky unit.

You just have to worship Einstein...

so
1 u = 931,5 MeV = 1,0*10^-14 MeV ***

...but at the same time, Einstein let you write deciving things like that (***), mixing mass and energi interchangeably in the same equation. Because, after all, Einstein said: mass = energi.

However, I prefer two equations:
1 u = 931,5 MeV/c2
E(1u) = 931,5 MeV

Last edited: Mar 10, 2016