1.67262192e-27
kg
1.00727647
u
938.2721
MeV
1,836.152673
0
1.67262192e-27
kg
1.00727647
u
938.2721
MeV
1,836.152673
0
The proton rest mass mp = 1.67262192369 × 10⁻²⁷ kg = 938.272 MeV/c² is the mass of the hydrogen nucleus and the most abundant baryon in the observable universe. Unlike the electron mass, which is a fundamental parameter of the Standard Model, the proton mass is a derived quantity emerging from the complex dynamics of quarks and gluons described by quantum chromodynamics (QCD).
Only about 1% of the proton mass comes from the rest masses of its three valence quarks (two up quarks at ~2.3 MeV each and one down quark at ~4.8 MeV). The remaining ~99% comes from the kinetic energy of quarks (confined by QCD to a region ~1 fm = 10⁻¹⁵ m in size), the gluon field energy binding them, and contributions from virtual quark-antiquark pairs. This is the most dramatic illustration of E = mc² in nature: 99% of everyday matter's mass is pure energy.
The proton-to-electron mass ratio m_p/m_e = 1836.15267343 is one of the dimensionless constants of nature. Its precise value determines the structure of atomic spectra, the stability of molecules, and the possibility of chemistry as we know it. If this ratio were significantly different, the periodic table, chemical bonds, and presumably life would all be fundamentally changed.
In atomic mass units, the proton mass is mp = 1.007276466621 u, slightly less than 1 u due to the definition of the atomic mass unit (1/12 of C-12, which includes electron masses and nuclear binding energy). The hydrogen atom mass is 1.007825 u = proton (1.007276 u) + electron (0.000549 u).
At the Large Hadron Collider, protons are accelerated to 6.5 TeV — approximately 6,930 proton rest masses. The Lorentz factor γ ≈ 6930, making each proton relativistically 6930 times heavier than at rest. When two such protons collide head-on, up to 13 TeV of energy is available for creating new particles.
Select the calculation: proton rest energy (938.272 MeV), hydrogen atom binding energy (13.6 eV = 1 Rydberg), relativistic kinetic energy at a given speed fraction of c, or proton magnetic moment information. CODATA 2018 value mp = 1.67262192369 × 10⁻²⁷ kg is used throughout.
The proton rest energy (938 MeV) is about 1836 times the electron rest energy (511 keV). Relativistic effects become significant for proton kinetic energies above ~100 MeV. Proton-antiproton annihilation produces about 1876 MeV of energy (gamma rays and pions).
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Results
At v=0.5c, γ = 1.1547. Relativistic KE = (γ-1)×938.272 = 0.1547×938.272 = 145 MeV. Non-relativistic KE would give ½ × 938.272 × 0.25 = 117 MeV — an error of ~19%.
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Results
The proton magnetic moment is 2.7928 nuclear magnetons (μN). The fact that it is not exactly 1 μN (as Dirac's equation would predict for a point particle) was the first evidence that the proton has internal structure — quarks.
The proton contains three valence quarks (uud) with total rest mass ~9.8 MeV. The remaining ~928 MeV comes from: kinetic energy of quarks (~330 MeV), gluon field energy (~490 MeV), and contributions from virtual quark-antiquark pairs. This is calculated using lattice QCD, which confirmed in 2008 that ~99% of the proton mass is dynamically generated by the strong force — not from the Higgs mechanism.
The proton's charge radius is approximately 0.84-0.88 fm (femtometres), measured by electron-proton scattering and hydrogen spectroscopy. The 'proton radius puzzle' emerged when muonic hydrogen measurements gave r_p = 0.84087 ± 0.00039 fm, 7σ smaller than earlier CODATA values of ~0.877 fm. Recent electron-proton experiments now support the smaller value, suggesting the discrepancy was in measurement systematics.
The proton appears to be stable: experimental lower bounds on the proton lifetime exceed 10³⁴ years for certain decay modes, much longer than the age of the universe (1.4 × 10¹⁰ years). Grand Unified Theories predict proton decay, but none of the predicted modes (p → e⁺ + π⁰, etc.) have been observed in large underground detectors like Super-Kamiokande.
Deep inelastic scattering experiments at SLAC (1968-1970) showed that high-energy electrons bouncing off protons behaved as if they were scattering from point-like objects inside — the quarks (called 'partons' by Feynman). The angular distribution matched scattering from spin-1/2 particles, consistent with quarks. This discovery won the 1990 Nobel Prize in Physics for Friedman, Kendall, and Taylor.
The nuclear magneton μN = eℏ/(2m_p) = 5.0507837461 × 10⁻²⁷ J/T is the natural magnetic moment scale for nuclear particles. The proton's magnetic moment is 2.7928 μN (not 1 μN as Dirac theory would predict), and the neutron's is -1.9130 μN (negative despite being uncharged!). These anomalous values indicate quark substructure.
Proton-antiproton annihilation (p + p̄ → mesons + γ) releases 2 × 938.272 MeV = 1876.5 MeV per event. The energy goes into pions and other mesons which quickly decay. This reaction has potential applications: 1 gram of antiprotons annihilating with 1 gram of protons releases 1.7 × 10¹⁷ J — equivalent to ~40 megatons TNT. Production costs currently exceed $10⁶² per kilogram.
The neutron is slightly heavier than the proton: m_n - m_p = 1.293332 MeV/c². This small mass difference, arising from the up-down quark mass difference and electromagnetic corrections, is responsible for the fact that free neutrons decay (n → p + e⁻ + ν̄_e, half-life 10.24 minutes) but free protons are stable. If m_n < m_p, protons would decay into neutrons and positrons, and the universe as we know it would not exist.
In a cyclotron, protons spiral outward in a magnetic field, receiving energy boosts from an alternating electric field twice per revolution. The cyclotron frequency is f = qB/(2πm) = eB/(2πm_p) ≈ 15.2 MHz/T. At relativistic energies, the proton's mass increases (γm_p), requiring the frequency to decrease with increasing energy — hence the synchrocyclotron or synchrotron designs used in modern particle accelerators.
Proton therapy uses beams of protons (typically 60-250 MeV) to treat cancer. Unlike X-rays which deposit energy continuously, protons exhibit a sharp Bragg peak at the end of their range where most energy is deposited. The range can be adjusted to place the peak precisely at the tumor, sparing surrounding tissue. The range of a 100 MeV proton in tissue is about 7.7 cm.
In QCD, the proton is a color-neutral bound state of three quarks held together by gluons — the mediators of the strong force. Color confinement prevents free quarks or gluons from being observed; they are always found in colorless combinations. The QCD Lagrangian has only six quark masses and one coupling constant (αs) as parameters, yet describes the entire spectrum of hadrons.
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