# Proton Mass

## Main Question or Discussion Point

I read on NIST CODATA that electron mass is a fundamental constant. I take from this that proton mass is not fundamental. I also read it is possible that proton-electron mass ratio may vary. So I wonder how proton mass is measured or derived. I have no training in physics, however in studying a way to describe electron and proton as superconducting electric current shells I find a ratio of 1860.308707, and this ratio makes possible an equation describing elementary charge (q). From what I read the possible ratio variation is not that large, but it makes me wonder.

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mgb_phys
Homework Helper
The proton mass shouldn't vary (in most normal cosmological models)
It's just that the electron is the smallest common stable particel and so it is easy to define all the other atomic masses in terms of it.
It is a bit more 'fundemental' than the proton in the sense that it doesn't have any constituent parts (that we have found yet!) whereas the proton is made up of three quarks.

Thank you MGB,

I am wondering how the proton mass is measured or derived, in the sense that the precision is pretty amazing to me – I can dimly understand that a specific value for the electron could be defined, then working from that value the experimenters or theorists would be able to somehow arrive at a value for the proton. I wonder how that is done. I assume they get some kind of a readout on some kind of instrument, then they do some figuring according to a theory – is that describable here? Or am I asking too much?

rbj
what NIST says is a "fundamental constant" might not be the same semantic that a physicist like John Baez would say is a fundamental constant. some folks might say that "fundamental constants" are the dimensionless ones that are expressed as the same number, no matter what unit system one uses. i would say that the proton/electron mass ratio is more fundamental than the electron_mass/kilogram ratio.

but, it's the quark and lepton masses (measured in terms of some natural units; i would vote for Planck units) that are the truly fundamental parameters.

mgb_phys
Homework Helper
Since the proton and electron have the same (but opposite) charge it's very easy to measure their relative masses.
Just shoot them with the same voltage through a magnetic field and measure the different curvature of the paths of the two particles - this gives you the relative mass directly.

It's the principle behind the mass spectrograph which can give you the mass of any atom/molecule to amazing accuracy.

rbj – I feel the same way: that it is the electron-proton ratio that is fundamental, not the electron-kilogram (particularly since the kilogram bar seems to be losing mass). (I have a problem with quarks as “fundamental” but I won’t go there for now.)

mgb – Thank you, that is what I was looking for. In the case of electron and proton, how is the curvature of the path measured?

jtbell
Mentor
how is the curvature of the path measured?
You can place the source and detector on the same plane, and shoot the particles from the source perpendicularly to the plane. The magnetic bends the path around in a semicircle back to the detector. The distance between the source and the "impact point" is twice the radius of the circle. This is the original classic "mass spectrograph" design, in which the detector is a sheet of photographic film.

Thank you folks for pointing me in the right direction, I appreciate it very much. The questions below may be scatter-brained, but I appreciate any response to help focus.

From google search it appears that mass spectrometers are measuring the mass-to-charge ratio of ions, which I take to mean protons. Do they also measure the mass-to-charge ratio of electrons? Does it matter whether the electron spin is up or down? I recall reading there is some energy difference in different spins.

Most interestingly, hydrogen at 1.008 has more mass than it “should have” since it has only a proton in its nucleus, so according to theory no strong nuclear force (to absorb mass-energy?). In the evolution of physics, is this where particle physics begins to come into the picture?

mgb_phys
Homework Helper
From google search it appears that mass spectrometers are measuring the mass-to-charge ratio of ions, which I take to mean protons.
Mass spec measures ions because in lab use you use them to meausre real molecules. You knock one electron off a molecule so you know it has a charge of one and then measure it's mass-charge ratio to get it's mass. You don't use them to measure the mass-charge of protons because everybody already knows the answer.
What I meant was that experiments using a similair principle were used to measure the mass/charge for the proton originally.

Do they also measure the mass-to-charge ratio of electrons? Does it matter whether the electron spin is up or down? I recall reading there is some energy difference in different spins.
Commercial mass spec machines don't measure electrons because they are built to run positive ions and anyway the mass/charge ratio for an electron would be out or range - they are normally built to ananylse heavy ions with a mass of 10-100protons not an electron with a mass off 1/2000 proton.

Most interestingly, hydrogen at 1.008 has more mass than it “should have” since it has only a proton in its nucleus,
The quoted chemical values are averages. A small proportion of hydrogen in a sample of real gas will contain some Deuterium (hydrogen with a neutron) the 1.008 is an average taking into account the proportion of hydrgone (mass=1) and Deuterium (mass=2).
Similairly Chlorine has a mass of 35.5 because it consists of about 50% Cl35 and Cl36.

Last edited:
ZapperZ
Staff Emeritus
The quoted chemical values are averages. A small proportion of hydrogen in a sample of real gas will contain some Deuterium (hydrogen with a neutron) the 1.008 is an average taking into account the proportion of hydrgone (mass=1) and Deuterium (mass=2).
Similairly Chlorine has a mass of 35.5 because it consists of about 50% Cl35 and Cl36.
Er... hum. Is this true?

I thought 1.008 is in atomic mass unit, which, by definition, is defined with respect to carbon 12 nucleus?

Zz.

jtbell
Mentor
Actually, the atomic mass of ordinary hydrogen is about 1.008 (more precisely 1.007825). Deuterium is 2.014102 and tritium is 3.016049.

The reason hydrogen isn't exactly 1.000 is because the atomic mass unit is defined as 1/12 the mass of a carbon-12 atom, so that carbon-12 has an atomic mass of exactly 12. This is for practical reasons, probably because it's easier to get a pure sample of carbon-12 for "calibrating" our mass spectrometers etc.

The fractions of an a.m.u. for the other elements come about because of differences in nuclear binding energy, via $E = mc^2$.

I seem to remember reading that at one time physicists and chemists used different definitions for the a.m.u. One group used 1/12 the mass of carbon-12, and the other group used 1/16 the mass of oxygen-16 (or maybe it was 1/16 the average atomic mass of oxygen?). I can't remember which group used which definition. Anyway, this obviously led to confusion until everybody agreed to use the same definition.

(0ops, Zz slipped in with his brevity while I was being verbose.)

mgb_phys
Homework Helper
Sorry my mistake - forgot that for hydrogen the binding energy mattered.
And D2 is only 0.01% so has no real effect on the chemical mass.

I think the fundamental physics is where I am looking. The problem which prompted me to post is as follows.

The CODATA respective values for the electron and proton masses in kilograms are 9.10938215 e-31 and 1.672621637 e-27. I am trying to follow an idea or scenario in which the electron and proton are superconducting electric currents (with slightly different characteristics) – that is, shells rotating at c. In effect, massless particles. Using the “equivalence” of E = mc^2 and E=hf, you get m=hf/c^2 and I see these values used in some places, i.e. in GeV “energies”.

I find that a slightly different set of values – and a slightly different electron-proton ratio “r”, namely 1860.308707 – gives an interesting result, namely that the elementary charge can be defined in terms of fine structure constant alpha, permittivity of space, c, and “r”. In other words, “r” is like a fundamental constant value rather than an observed or measured value. There is also an interesting relation to the Josephson constant i.e. 2q/h.

Therefore I guess I am wondering whether the electron and proton mass measurements are “defined” by a theory that could be subject to another theory, etc., leading to an observed value that reflects for example space-time curvature in general relativity, so the underlying event could have slightly different values. In other words a massless shell rotating at c would come under general relativity (whose math I do not understand), maybe leading to slightly different values.