Why isn't the scaling factor included when stating particle mass in eV?

[Jrs580]

Homework Statement

Silly question I know…but…the energy mass relationship is E=mc^2 with E in units of Joules. Which means mass = E/c^2 and if we take c = 1, mass = joules. So where did the conversion factor of e go when we state particle mass in eV?

Relevant Equations

E=mc^2

not technically a homework question, just figured it fit here.

 

[Orodruin]

What conversion factor? eV is a unit of energy just as Joule is.

 

[PeroK]

Homework Statement:: Silly question I know…but…the energy mass relationship is E=mc^2 with E in units of Joules.

This equation holds for any consistent system of units. E.g energy in joules, mass in kilograms and speed in metres per second.

Or, energy in electron volts and mass in electron volts over $c^2$. For example, the mass of an electron is about $0.5 MeV/c^2$.

In that case, you are free to choose any units for length and time. If you choose units where $c =1$ then the mass of an electron in those units is $0.5 MeV$.

 

[Jrs580]

What conversion factor? eV is a unit of energy just as Joule is.

 

[Jrs580]

Ok let me try again, lol. E=mc^2 where m:kg and E:joules.

E/1.6e-19 = energy in eV = E’ = (mc^2)/1.6e-19

m = E’(1.6e-19)/c^2

So to get mass in kg you have to do the prescription above to the energy measured in eV. But when particle mass is stated, it doesn’t include this scaling factor.

 

[Jrs580]

I believe the major point is that you can quote mass in any of these units (eV, joules, kg) because you can always convert between them. They are all the same. Just as a week a month or a year can be used to describe a given amount of time.

 

[PeroK]

Ok let me try again, lol. E=mc^2 where m:kg and E:joules.

E/1.6e-19 = energy in eV = E’ = (mc^2)/1.6e-19

m = E’(1.6e-19)/c^2

So to get mass in kg you have to do the prescription above to the energy measured in eV. But when particle mass is stated, it doesn’t include this scaling factor.

I'm not sure I follow this. The mass of the electron is $9.1 \times 10^{-31}kg$. So, its rest energy is:
$$E = mc^2 = (9.1 \times 10^{-31}kg)\times(9 \times 10^{16} m^2/s^2) = 8.2 \times 10^{-14}J$$To convert from joules to $eV$ we have $1J = 6.24 \times 10^{18} eV$, so:
$$E = (8.2 \times 10^{-14}J)\times (6.24 \times 10^{18} eV/J) = 0.51 MeV$$Finally, using $E = mc^2$ in $eV$, we have:
$$m = E/c^2 = 0.51 MeV/c^2$$is the mass of the electron in $eV$.

 

[vela]

Ok let me try again, lol. E=mc^2 where m:kg and E:joules.

E/1.6e-19 = energy in eV = E’ = (mc^2)/1.6e-19

m = E’(1.6e-19)/c^2

So to get mass in kg you have to do the prescription above to the energy measured in eV. But when particle mass is stated, it doesn’t include this scaling factor.

Because mass doesn't have to be given in units of kg. Your question is kind of like asking: when a mass of a nickel is given as 5 grams, how come there's no factor of 0.001 thrown in (to convert it to kg)?

The unit ${\rm eV}/c^2$ is just another unit of mass, like a gram is.