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

• Jrs580
In summary: It is just a convenience unit that allows you to say things like "the mass of an electron is about ##0.5 MeV/c^2##".
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.

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

Jrs580 said:
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##.

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

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 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.

Jrs580 said:
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##.

Jrs580 said:
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.

PeroK

## 1. What is the unit of measurement for particle mass in eV?

The unit of measurement for particle mass in eV (electron volts) is a unit of energy commonly used in particle physics. It is equivalent to the amount of energy gained by an electron when it is accelerated through a potential difference of one volt.

## 2. How is particle mass measured in eV?

Particle mass in eV is typically measured using a particle accelerator, where particles are accelerated to high energies and their masses are calculated based on their velocity and energy. Other methods such as mass spectrometry can also be used to measure particle mass in eV.

## 3. What is the significance of measuring particle mass in eV?

Measuring particle mass in eV allows scientists to better understand the properties and behavior of particles at the subatomic level. It also helps in the development of new technologies and advancements in fields such as particle physics, nuclear energy, and medical imaging.

## 4. Can particle mass be measured in units other than eV?

Yes, particle mass can also be measured in other units such as kilograms, grams, or atomic mass units (amu). However, eV is a commonly used unit in particle physics because it is a more convenient and precise unit for measuring the masses of subatomic particles.

## 5. How is particle mass in eV related to other fundamental constants?

Particle mass in eV is related to other fundamental constants such as the speed of light, Planck's constant, and the elementary charge. These constants are used in equations to calculate the mass of particles in eV and help in understanding the fundamental nature of matter and energy.

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