A subatomic particle found in the nuclei of atoms, as well as free. The number of protons in an atom's nucleus determines what chemical element the atom is.

The proton has unit positive electric charge and spin = ½ and belongs to the class of atomic particles called baryons.

A proton is not point-like, nor is it like a billiard ball. While the protons with their positive charge are found in the center of an atom, an atom is not really like a minature solar system with the nucleus as its sun. A proton contains 3 quarks (2 up and 1 down)

What is the mass of a proton?

According to the 2018 CODATA recommended values, the mass of the proton is 1.672 621 923 69 × 10⁻²⁷ kg, with a standard uncertainty of 0.000 000 000 51 × 10⁻²⁷ kg. It is sometimes convenient to express the proton's mass in MeV (938.272 088 16 MeV) or in u (1.007 276 466 621 u). The proton is 1836.152 673 43 times more massive than an electron, and a neutron is a bit (2.305 574 35 × 10⁻³⁰ kg) more massive.

The proton's mass can be measured experimentally.¹ »read more Its mass can also be calculated from knowledge of its structure (e.g, quarks, gluons, etc.)²

The sources of the proton's mass, as estimated by Yang et al.³ are:

9% quarks, 32% energy of quarks' motion within the proton, 36% gluons, 23% quark-gluon interactions

1. F. Heiße, F. Köhler-Langes, S. Rau, J. Hou, S. Junck, A. Kracke, A. Moser, W. Quint, S. Ulmer, G. Werth, K. Blaum and S. Sturm.
High-Precision Measurement of the Proton’s Atomic Mass.
Physical Review Letters, vol. 119, iss. 3 (18 July 2017)

2. S. Dürr, Z. Fodor1, J. Frison, C. Hoelbling, R. Hoffmann, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, G. Vulvert.
Ab Initio Determination of Light Hadron Masses.
Science, vol. 322, issue 5905, pp. 1224-1227 (21 Nov 2008).

3. Yi-Bo Yang, Jian Liang, Yu-Jiang Bi, Ying Chen, Terrence Draper, Keh-Fei Liu and Zhaofeng Liu.
Proton mass decomposition from the QCD energy momentum tensor.
Physical Review Letters, vol 121, issue 21. (19 November 2018.

What is the radius of a proton?

The proton's diameter is the average distance between the quarks. Its size is usually described by tbe root-mean-square charge radius (symbol, rp).

estimated by scattering experiments, simialr to Rutherford's classic experiemnt, but using electrons as the "cannonballs" shot at the nucleus. a radius can be calculated from the angles at which the electrons are scattered.    

electron scattering

spectroscopy photons transitions between energy levels


In the 2006 CODATA values, rp was 0.8768 femtometers with a standard uncertainty of 0.0069 femtometers.

In 2010 a new study² using a novel technique found a value of 0.84184 femtometers, with a standard uncertainty of 0.0067 femtometers.Much smaller.

Suppose muons differ electrons in more than just mass? That would play havoc wit the standard model.


Further studies using new techniques, published in 2013³ and 2016⁴, also found a smaller proton.

In the 2018 CODATA recommended values (released 20 May 2019) the rp is given as 8.414 x 10⁻¹⁶ meters, with a standard uncertainty of 0.019 x 10⁻¹⁶ m. It was based on all experimental results available by the end of 2018, including two the physics community knew about though they hadn't yet been published:

W. Xiong, A. Gasparian, H. Gao, et al.
A small proton charge radius from an electron–proton scattering experiment.
Nature, vol. 575, 147–150 (6 Nov 2019).

2. Randolf Pohl et al.
The size of the proton.
Nature, vol 466, pages 213-216 (8 July 2010).

3. Antognini et al.
Proton structure from the measurement of 2S-2P transition frequencies of muonic hydrogen.
Science, vol. 339, issue 6118, pages 417-20 (25 January 2013).
doi: 10.1126/science.1230016.

Randolf Pohl.
Das Proton bleibt zu klein.
Physik in Unserer Zeit, vol. 44, no. 3, pages 110-111 (2 May 2013).
doi: 10.1002/piuz.201390041

4. Pohl et al.
Laser spectroscopy of muonic deuterium.
Science, vol. 353, issue 6300, pages 669-673 (12 Aug 2016).
doi: 10.1126/science.aaf2468

Natalie Wolchover.
New Measurement Deepens Proton Puzzle.
Quanta Magazine, 11 August 2016.

N. Bezginov, T. Valdez, M. Horbatsch, A. Marsman, A. C. Vutha and E. A. Hessels.
A measurement of the atomic hydrogen Lamb shift and the proton charge radius.
Science, vol. 365, pages 1007–1012 (6 September 2019)

6. Xiong

Do protons decay?

The question of whether protons spontaneously change into another particle (a positron, probably) remains one of the great unanswered questions of physics. In 1977 researchers looking for signs of radioactive decay in an ancient ore showed that, if protons do decay, they must have a half life of more than 1.6 × 10²⁵ years,¹ a result high enough to knock out several theories popular at the time. The subject continues to be investigated, especially through continued refinements at the giant Super-Kamiokande detector in Japan. In 2017 they reported: “Lower limits on the proton lifetime are set at τ/B(pe+π0) > 1.6 × 10³⁴ years and τ/B(pμ+π0) > 7.7 × 10³³ years at 90% confidence level.”²

1. John C. Evans, Jr. and Richard I. Steinberg.
Nucleon stability: A geochemical test independent of decay mode.
Science, volume 197, no. 4307, page 989. (2 Sept. 1977)

2. Makoto Miura (The Super-Kamiokande Collaboration)
Search for Proton Decay via pe+π0 and pμ+π0 in 0.31 megaton·years exposure of the Super-Kamiokande Water Cherenkov Detector.
Physical Review D 95, 012004 (2017).

further reading

Natalie Wolchover.
Grand unification dream kept at bay.
Quanta, 15 December 2016. online

Pressure inside the proton

10³⁵ pascals

P. E. Shanahan et al.
Pressure distribution and shear forces inside the proton.
Physical Review Letters, (2019).
doi:10.1103/PhysRevLett. 122.072003

want more on particles?

The Particle Data Group offers authoritative data, an interesting chart and links to related sites:

12. Jan C. Bernauer and Randolph Pohl.
The proton radius puzzle.
Scientific American, vol. 310, pages 32–39 (February 2014).

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