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gus_massa

> These data imply an upper bound of 0.9 eV, which goes down to 0.8 eV when combined with the earlier results.

For comparison, the mass of an electron is approximately 510,998.950 eV and the mass of a proton is 938,272,088. eV.

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(total layperson here but) why is mass measured in electron volts?

(also i would have expected an electron to be... 1 electron volt?)

My understanding is that an electron volt is the energy an electron needs to move against an electrical gradient of 1V (imagine like rowing against the current). It is a unit of energy, so at first glance it doesn't really make much sense to use it a a mass unit. However, since e = mc2, you can calculate the mass that is equivalent to 1 eV (which, in kg, turns out to be about 10 to the power of -36).

The electron volt is related to the electric charge of the electron, not to its mass. Similarly, a magnet weights more than its strength turned into mass.

Because eV is not (directly) a mass measure. Though of course it can translate into a mass. To C&P Wikipedia it's "the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum."

electron volts is a unit of energy. Using E = mc^2, one expresses masses in the equivalent energy quantity. It turns out that electron-volts is a convenient scale for the (energy equivalent) mass for elementary particles -- much better than trying to express the mass in kilograms.

Or energy in Joules, which are around 10^19 bigger. So you'd have the inverse of that everywhere as an inconvenient factor.

As it happens eV works nicely from meV up to TeV for particles in all the most useful contexts, from chemical bonds to particle experiments. You only start getting insanely huge factors when you stop being subatomic.

I may ask a very dumb question, but, in kilograms, how much would it be ?

From FranchuFranchu's comment above, about 10 to the power of -36.

It's a convenient size unit for particles! Also energy is natural when the energy of the particle can vary.

Also, the unit used for mass of particle is usually eV/c² or MeV/c² which is more correct (unless in c=1 units) but the c part is sometimes dropped by convention.

The sibling comments are good, but let me add my own version.

eV is a unit of energy, and eV/c^2 is a unit of mass. You can drop the c^2 if you are lazy, and if someone ask you can say that you using a system of units where c=1 and ħ=1. This is fine in the second half of a Physic degree, but you can get in trouble for forgetting the c^2 in the first half or during secondary school.

The technical definition is in a sibling comment, but an eV is similar to the energy that an electron gets or loose when it makes a jump inside a molecule or between two molecules. The exact number depends on the molecule and the jump, it may be x10 bigger or smaller.

For example if you connect a led to a battery, each electron gets like 1.5eV when it pass through the battery, and release that energy as a photon of light in the led. If you ignore a lot of technical details, the electron makes one or two jumps in the battery and a jump in the led, but this is a huge oversimplification.

Note that a led releases like 10^18 photons per second, so each photon with approximately 1eV has a tiny amount of energy.

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On the other hand, if you destroy an electron you get 511000eV of energy. You can't destroy a single electron, but you can make an electron colide with a positron that has the same mass and in total you gen 511000eV+511000eV of energy. So destroying an electron release much more energy than an electron that jumps inside a molecule.

In special relativity there is an equivalence between energy and mass, so if the energy you get while destroying an electron is 511000eV then the mass is 511000eV/c^2. You can also measure the mass directly without destroying the electron, and you get the same number (probably with a bigger uncertainly, I'm not sure how they measured so many digits).

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As an analogy, if you move around and climb some steps and make some jumps, each big movement absorbs or release approximately 1000J.

If someone makes a antimatter clone of you, and you both colide, your mass will be released as energy and they will get like 10^18J+10^18J = 1000000000000000000J+1000000000000000000J.

Changing the units, your mass is like 510^37eV/c^2 and if you colide with your antimatter evil clone, you both will release 510^37eV+5*10^37eV of energy.

Too many digits… TL;DR: .5 MeV and .9 GeV, respectively.

That's what the GP wrote. Their electron value has a decimal point before the last three digits. The GP values are approximately 510 keV and 938 MeV.

I prefer to use the same unit for all numbers because it makes the comparison easier. The bound of mass of the neutrino is really low. Using M and G hides it.

I was going to write:

> For comparison, the mass of an electron is approximately 500,000 eV and the mass of a proton is 900,000,000 eV.

But all the numbers I wrote are measured experimentally. Both values have a lot of experimentally measured digits! I only removed the part that overlaps with the uncertainty, because the notation with parenthesis is somewhat confusing.

> I prefer to use the same unit for all numbers because it makes the comparison easier.

Thank you; this is a style guideline I wish more writers would adopt.

Alternatively, you can use exponential notation to compare numbers of very different sizes while writing them similarly and using the same unit.

Yeah. The point is keeping the units consistent.

511 keV and 938 MeV would have been much clearer than a distinction via comma/point like in 510,998 -> . <- 950 eV and 938,272 -> , <- 088 eV.

I agree that the coma/point distinction is confusing. Also, I'd like to cut all the numbers in the same digit, but the next digit of the proton is too dubious.

What about this version:

> [an upper bound of 0.9 eV] For comparison, the mass of an electron is approximately 510998.9 eV and the mass of a proton is 938272088.0 eV.

I would just round to the nearest eV and keep the commas.

> the mass of an electron is approximately 510,999 eV and the mass of a proton is 938,272,088 eV.

This reads best to me.

I know we're just bikeshedding now, but

  neutrino:           0. 8 eV/c^2
  electron:     510 000. 0 eV/c^2
  proton:   940 000 000. 0 eV/c^2

(Note: neutrino mass is given as the upper limit.)

The first value has one, the others two significant figures in this example. The decimal point is also giving a false sense of certainty when used like this. You can find more about significant figures at Wikipedia:

https://en.m.wikipedia.org/wiki/Significant_figures

Yes, I know about significant figures. In fact, I considered adding a note about sig figs before deciding it was too minor of a nitpick to elaborate on. Elsewhere in this thread, people have already listed these masses to much greater precision than almost anyone needs (including me, a practicing physicist); obviously people can infer I'm rounding from context.

Of course, if you were to present the masses this way without context, you should add a note about rounding.

I find that significantly less clear.

In fact, I find it so unintuitive that I didn't even notice the units changed and thought you'd made a mistake in magnitude before I finished your sentence and I went back.

Comparisons should always be done in like units.

In contrast to some sibling comments, I think using the same unit is a great idea. It’s just that long numbers with commas are a bit hard to read. At least I think 511 keV and 938 000 keV would have been another clear way to present those numbers.

Writing out the digits gives a more visceral impression of the difference in weight, from roughly one, to a six-digit number, to a nine-digit number.

> the mass of a proton is 938,272,088. eV.

No it isn't. At least, not all of them. The mass of a proton varies.

I assume that is the mass of an unbound proton.

A proton in a hydrogen atom does not have the same mass as a proton in a Helium atom, nor do any protons in any particular element have the same mass as the protons in any of the other elements. Again, the mass of a proton varies.

Why does it vary? Changes in gluon/quark energy due to nucleon-nucleon interactions?

Yes, in nucleons of different sizes, the amount of binding energy changes according to quantum mechanics. The result is the average mass per proton is different in different isotopes. The mass differences are explained by the energy differences. Anyway, idk about you, but this really bothers me.

Depends on if it's been dieting recently.

approximately <8 significant digit value>, <9 significant digit value>.

Y'all use a lot of bits for an approximation. In how many digits is the uncertainty?

Proton: 938.27208816(29) MeV/c^2

Electron: 0.51099895000(15) MeV/c^2

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