# Why do we use the electron volt?

Why do we use the electron volt?

Why did it come to be the electron volt and not, say, just a prefix of the joule, like the nanojoule?

Does the electron volt represent anything particular as far as the mathematics goes? I am guessing that it does, and if so, what is it that the electron volt exactly represents in terms of the mass of a particle, as I have seen it used for both the energy of a photon and the mass of subatomic particles?

• For the same reason why we use AU instead of meters in astronomy. – Dmitry Grigoryev Nov 23 '16 at 10:31
• It's simply convenient: I work with fluorophores and photonics, and an electron volt is a handy size here: roughly the energy of an optical photon (more precisely, a 1.24um wavelength one). Bond energies in chemistry are also of the order of electron volts. – Selene Routley Nov 23 '16 at 11:44
• For the same reason we use 1 lightyear instead of 9,460,730,472,580,800 meters – Ghoti and Chips Nov 23 '16 at 11:53
• Follow-up question: why do we use TeV instead of µJ? 13 TeV is only about 2 µJ :P – Nick T Nov 23 '16 at 23:51
• I don't buy the order of magnitude argument. SI prefixes exist for a reason; 1 eV = 0.16 aJ = 160 zJ, 100 eV = 16 aJ. Saying "attojoule" is as short as or shorter than "electron-volt". The Oort Cloud is ~15 PM out, next star ~50 PM. The Mliky Way is ~1 ZM in diameter. The observable universe is ~865 YM in diametre, not at all an impractically large number to talk about). It all just boils down to what a community is used to, which is why we have wavenumbers in $cm^{-1}$, lengths in Å, etc. – gerrit Nov 25 '16 at 9:24

The electron-volt is a convenient unit of energy when considering electrons moving between points at different potentials. The convenience came from having numerical values which are around or greater than one, $1 \rm eV = 1.6 \times 10^{-19} \rm J$. It was first used in the 1930s.

So one perhaps has a better "feel" for the difference between 1 and 100 eV than $1.6 \times 10^{-19} \rm J$ and $1.6 \times 10^{-17} \rm J$ and the value in electron volts is easier to write.
Electron energy levels are conveniently quoted in electron-volts and then nuclear energy levels in MeV show a clear difference in terms of scale.

Then using eV/c² with the appropriate prefix as a unit of mass also becomes convenient; e.g. the mass of the electron as 500 keV/c² and that of the proton as 1 GeV/c².

It is not an SI unit but is retained because as well as being convenient it was and still is in widespread use in the scientific community.

• This is just the same argument as to why we use mpg and mph in US/UK - convention and familiarity breeds convenience and intuition. But I don't think we should make the mistake of thinking that it's a quality of the unit: it's a quality of the people. I remember that once I really understood an atom ~= angstrom = 0.1nm, all sorts of relative scales fell into place, diameter of cells in atoms, width of a wire on an IC. – SusanW Nov 25 '16 at 12:16

Addressing only why it is used/useful in science today, not why or how it came about

The other answers seem to come from a particle physicist's point of view; for a chemist the electronvolt is convenient as well:

Please note these are "order of magnitude" ranges.

• +1 I like this answer, I think it is useful to have a chemist pov here :-) (BTW: I wrote my answer from the particle physics pov because OP used the tag particle-physics so that I assumed that they were mostly interested in that branch, but your answer is useful as well, at least to me) – AccidentalFourierTransform Nov 22 '16 at 22:33
• -1 You make it sound like these are co-incidences. Each of these processes are Physical processes. The same ones that Physicist deal with. The reason that these processes are all in the range of eV, is because they all involve electrons AND we defined the Volt from a Chemical process. – Aron Nov 23 '16 at 7:00
• @Aron No, he doesn't. Perhaps it's just something you're projecting into the answer? Electronvolts are convenient, that's it. – Luaan Nov 23 '16 at 10:40
• @Luaan No, Aron has a strong point there. There is no natural voltage scale: an electronvolt is equal to $(e/1\:\rm{C})\:\rm J$, and the definition of the Coulomb is arbitrary. As it happens, the SI volt was chosen at the order of magnitude of the output of Daniell and Clark cells, which produce a constant voltage that comes from chemical processes. This means that pentane's first point isn't a coincidence - it is the reason why we chose the volt at that magnitude to begin with. – Emilio Pisanty Nov 23 '16 at 18:00
• @EmilioPisanty I agree that the answer might benefit from including this relevant information. But pentane's main point is still that it's convenient for chemistry. Sure, that follows from the first interesting batteries being chemical batteries, but that's just historical trivia - important for particle physicsts, but not for chemists, where it's simply a rather convenient unit exactly because chemistry is mostly concerned with bound electrons, especially the outermost electrons that aren't too much shielded. It's not like there's anything natural about the meter, V isn't special. – Luaan Nov 23 '16 at 18:11

"Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences because a particle with charge $q$ has an energy $E = qV$ after passing through the potential $V$; if $q$ is quoted in integer units of the elementary charge and the terminal bias in volts, one gets an energy in eV."
source

Further, you will have to admit that energies written as $x \cdot 10^{-19} \textrm{J}$ are not the most useful numbers to work with. Using an arbitrary standard quantity (e.g. Angstrom) as comparison to obtain numbers that do actually mean something to us and that make it easier for us to talk about them is quite a widespread custom in physics.

• I think it is really because people started measuring particle masses in accelerators in which initially, most of the accelerating was done through electric fields - which made this a pretty "natural" scale. Giving masses in energies is I guess mostly due to Einstein and the fact that the masses again would become quite nasty numbers - and using a second arbitrary standard (e.g. proton mass) probably seemed to be less attractive than being able to speak of everything with one "custom standard". – Sanya Nov 22 '16 at 21:54
• Ok, yes, I think I understand what you mean here. – Benjamin Rogers-Newsome Nov 22 '16 at 21:58
• Does anyone really actually write out 10^-19J? (Yes, they do - so Why?) Why not use prefixes, like everybody else? 1aJ, 100zJ ... ? Other than convention, of course. – SusanW Nov 25 '16 at 12:29
• This is why physicists sometimes use natural units (like Planck units). Making calculations with them is much simpler because many constants disappear. – Jaime Gallego Nov 26 '16 at 16:21
• @Sanya Why a particle has that amount of energy when moving through an electric field? Is gravity neglected? – Antonios Sarikas Jun 12 at 11:59

It is just a convention, and not a particularly convenient one. In particle physics we hardly ever use $\mathrm{eV}$; it is much more common to use $\mathrm{MeV}$, $\mathrm {GeV}$ or even $\mathrm{TeV}$. The electronvolt scale is not a natural scale for particle physics: typical energies are, at least, a million times higher than that (except for neutrinos). We use it for historical reasons, but I guess you'll agree that it is more convenient that Joules: an electronvolt is somewhat closer to the mass of a proton than a Joule ($m_p\sim 10^{-10}\ \mathrm{J}\sim10^9\ \mathrm{eV}$).

Perhaps I should add that in solid state physics electronvolts are sometimes a natural scale.

• @BenjaminRogers-Newsome youre welcome, of course. A natural scale means that you use units "that make sense", so to speak. For example, it makes no sense to measure the mass of a person using tonnes, because the mass is usually in the scale of kg. It neither makes sense to use micrograms for the same reason: you are using units that are very far from the scale you want to measure. – AccidentalFourierTransform Nov 22 '16 at 21:55
• I think most of this misses the point. I'm pretty sure the question isn't "Why do people use eV instead of MeV, GeV, etc.?" but "Why do people use the electron-volt as a base unit instead of the joule?" – David Richerby Nov 23 '16 at 23:56
• @DavidRicherby yes, and my answer to that question is: "in particle physics, for historical reasons. In particle physics electronvolts are not useful but just customary". In other branches of physics, electronvolts have a reason, but in particle physics they do not: they are not really convenient. (OP asked about eV in the context of particle physics, so I dont thing Im missing the point...) – AccidentalFourierTransform Nov 24 '16 at 9:40

Originally, eV might have been the right unit for electron energy used by people who were doing experiments with cathodic tubes. In those experiments, a cathode was emitting electrons if there was a cathode-anode bias. The multiples of eV are the right unit if you do accelerator physics. MeV, GeV, TeV are chosen because they are also closest to the order of magnitude of the electron energies in those accelerators. So, as a rule of thumb, one chooses the unit closest to the order of magnitude of the energy in the type of physical phenomenon of interest.

For example, if you do electron transport in nanostructures (like carbon nanotubes) you might want to use meV for energies, nm for distances, and fs for time. If you are interested in the band structure of solids, the best unit is eV, as the band gaps for insulators are usually a few eV's.

On the other hand, if you do engineering and you work mostly with macroscopic objects, you will work with SI units.

• I think this misses the point. I'm pretty sure the question isn't "Why do people use eV instead of MeV, GeV, etc.?" but "Why do people use the electron-volt as a base unit instead of the joule?" – David Richerby Nov 23 '16 at 23:55
• @DavidRicherby I think it really is the same reason. You would use J if you studied problems like ballistics of handguns. The kinetic energy of a bullet would be in the range a 10-100J. – Magicsowon Nov 24 '16 at 8:29