66.25: Fundamental Physical Constants — Extensive Listing
- Page ID
- 91955
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Table \(\PageIndex{1}\): Universal Fundamental Constants
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| speed of light in vacuum | \(c\) |
\(299\; 792\; 458\) |
\(\mathrm{~m} \mathrm{~s}^{-1}\) | exact |
| vacuum magnetic permeability \(4 \pi \alpha \hbar / e^2 c\) | \(\mu_0\) | \(1.25663706212(19) \times 10^{-6}\) | \(\mathrm{NA}^{-2}\) | \(1.5 \times 10^{-10}\) |
| \(\mu_0 /\left(4 \pi \times 10^{-7}\right)\) | \(1.00000000055(15)\) | \(\mathrm{NA}^{-2}\) | \(1.5 \times 10^{-10}\) | |
| vacuum electric permittivity \(1 / \mu_0 c^2\) | \(\epsilon_0\) | \(8.8541878128(13) \times 10^{-12}\) | \(\mathrm{~F} \mathrm{~m}^{-1}\) | \(1.5 \times 10^{-10}\) |
| characteristic impedance of vacuum \(\mu_0 c\) | \(Z_0\) | \(376.730313668(57)\) | \(\Omega\) | \(1.5 \times 10^{-10}\) |
| Newtonian constant of gravitation | \(G\) | \(6.67430(15) \times 10^{-11}\) | \(\mathrm{~m}^3 \mathrm{~kg}^{-1} \mathrm{~s}^{-2}\) | \(2.2 \times 10^{-5}\) |
| \(G / \hbar c\) | \(6.70883(15) \times 10^{-39}\) | \(\left(\mathrm{GeV} / c^2\right)^{-2}\) | \(2.2 \times 10^{-5}\) | |
| Planck constant* | \(h\) | \(6.62607015 \times 10^{-34}\) | \(\mathrm{~J} \mathrm{~Hz}^{-1}\) | exact |
| \(4.135667696 \ldots \times 10^{-15}\) | \(\mathrm{eV} \mathrm{Hz}^{-1}\) | exact | ||
| \(\hbar\) | \(1.054571817 \ldots \times 10^{-34}\) | \(J s\) | exact | |
| \(6.582119569 \ldots \times 10^{-16}\) | \(\mathrm{eV} \mathrm{s}\) | exact | ||
| \(\hbar c\) | \(197.3269804 \ldots\) | \(\mathrm{MeV} \mathrm{fm}\) | exact | |
| Planck mass (\(\hbar c / G)^{1 / 2}\) | \(m_{\mathrm{P}}\) | \(2.176434(24) \times 10^{-8}\) | \(\mathrm{~kg}\) | \(1.1 \times 10^{-5}\) |
| energy equivalent | \(m_{\mathrm{P}} c^2\) | \(1.220890(14) \times 10^{19}\) | \(\mathrm{GeV}\) | \(1.1 \times 10^{-5}\) |
| Planck temperature \(\left(\hbar c^5 / G\right)^{1 / 2} / k\) | \(T_{\mathrm{P}}\) | \(1.416784(16) \times 10^{32}\) | \(K\) | \(1.1 \times 10^{-5}\) |
| Planck length \(\hbar / m_{\mathrm{P}} c=\left(\hbar G / c^3\right)^{1 / 2}\) | \(l_{\mathrm{P}}\) | \(1.616255(18) \times 10^{-35}\) | \(\mathrm{~m}\) | \(1.1 \times 10^{-5}\) |
| Planck time \(l_{\mathrm{P}} / c=\left(\hbar G / c^5\right)^{1 / 2}\) | \(t_{\mathrm{P}}\) | \(5.391247(60) \times 10^{-44}\) | \(s\) | \(1.1 \times 10^{-5}\) |
Table \(\PageIndex{2}\): Electromagnetic Constants
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| elementary charge | \(e\) | \(1.602176634 \times 10^{-19}\) | \(\mathrm{C}\) | exact |
| \(e / \hbar\) | \(1.519267447 \ldots \times 10^{15}\) | \(\mathrm{~A} \mathrm{~J}^{-1}\) | exact | |
| magnetic flux quantum \(2 \pi \hbar /(2 e)\) | \(\Phi_0\) | \(2.067833848 \ldots \times 10^{-15}\) | \(\mathrm{~Wb}\) | exact |
| conductance quantum \(2 e^2 / 2 \pi \hbar\) | \(G_0\) | \(7.748091729 \ldots \times 10^{-5}\) | \(\mathrm{~S}\) | exact |
| \(\quad\) inverse of conductance quantum | \(G_0^{-1}\) | \(12906.40372 \ldots\) | \(\Omega\) | exact |
| Josephson constant \(2 e / h\) | \(K_{\mathrm{J}}\) | \(483597.8484 \ldots \times 10^9\) | \(\mathrm{~Hz} \mathrm{~V}^{-1}\) | exact |
| von Klitzing constant \(\mu_0 c / 2 \alpha=2 \pi \hbar / e^2\) | \(R_{\mathrm{K}}\) | \(25812.80745 \ldots\) | \(\Omega\) | exact |
| Bohr magneton \(e \hbar / 2 m_{\mathrm{e}}\) | \(\mu_{\mathrm{B}}\) | \(9.2740100783(28) \times 10^{-24}\) | \(\mathrm{~J} \mathrm{~T}^{-1}\) | \(3.0 \times 10^{-10}\) |
| \(5.7883818060(17) \times 10^{-5}\) | \(\mathrm{eV} \mathrm{T}^{-1}\) | \(3.0 \times 10^{-10}\) | ||
| \(\mu_{\mathrm{B}} / h\) | \(1.39962449361(42) \times 10^{10}\) | \(\mathrm{~Hz} \mathrm{~T}^{-1}\) | \(3.0 \times 10^{-10}\) | |
| \(\mu_{\mathrm{B}} / h c\) | \(46.686447783(14)\) | \(\left[\mathrm{m}^{-1} \mathrm{~T}^{-1}\right]^{\dagger}\) | \(3.0 \times 10^{-10}\) | |
| \(\mu_{\mathrm{B}} / k\) | \(0.67171381563(20)\) | \(\mathrm{K} \mathrm{T}^{-1}\) | \(3.0 \times 10^{-10}\) | |
| nuclear magneton \(e \hbar / 2 m_{\mathrm{p}}\) | \(\mu_{\mathrm{N}}\) | \(5.0507837461(15) \times 10^{-27}\) | \(\mathrm{~J} \mathrm{~T}^{-1}\) | \(3.1 \times 10^{-10}\) |
| \(3.15245125844(96) \times 10^{-8}\) | \(\mathrm{eV} \mathrm{T}^{-1}\) | \(3.1 \times 10^{-10}\) | ||
| \(\mu_{\mathrm{N}} / h\) | \(7.6225932291(23)\) | \(\mathrm{MHz} \mathrm{T}^{-1}\) | \(3.1 \times 10^{-10}\) | |
| \(\mu_{\mathrm{N}} / h c\) | \(2.54262341353(78) \times 10^{-2}\) | \(\left[\mathrm{~m}^{-1} \mathrm{~T}^{-1}\right]^{\dagger}\) | \(3.1 \times 10^{-10}\) | |
| \(\mu_{\mathrm{N}} / k\) | \(3.6582677756(11) \times 10^{-4}\) | \(\mathrm{~K} \mathrm{~T}^{-1}\) | \(3.1 \times 10^{-10}\) |
Table \(\PageIndex{3}\): General Atomic and Nuclear Constants
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| fine-structure constant \(e^2 / 4 \pi \epsilon_0 \hbar c\) | \(\alpha\) | \(7.2973525693(11) \times 10^{-3}\) | \(1.5 \times 10^{-10}\) | |
| \(\quad\) inverse fine-structure constant | \(\alpha^{-1}\) | \(137.035999084(21)\) | \(1.5 \times 10^{-10}\) | |
| Rydberg frequency \(\alpha^2 m_{\mathrm{e}} c^2 / 2 h=E_{\mathrm{h}} / 2 h\) | \(c R_{\infty}\) | \(3.2898419602508(64) \times 10^{15}\) | \(\mathrm{~Hz}\) | \(1.9 \times 10^{-12}\) |
| \(\quad\) energy equivalent | \(h c R_{\infty}\) | \(2.1798723611035(42) \times 10^{-18}\) | \(\mathrm{~J}\) | \(1.9 \times 10^{-12}\) |
| \(13.605693122994(26)\) | \(\mathrm{eV}\) | \(1.9 \times 10^{-12}\) | ||
| Rydberg constant | \(R_{\infty}\) | \(10973731.568160(21)\) | \(\left[\mathrm{m}^{-1}\right]^{\dagger}\) | \(1.9 \times 10^{-12}\) |
| Bohr radius \(\hbar / \alpha m_{\mathrm{e}} c=4 \pi \epsilon_0 \hbar^2 / m_{\mathrm{e}} e^2\) | \(a_0\) | \(5.29177210903(80) \times 10^{-11}\) | \(\mathrm{~m}\) | \(1.5 \times 10^{-10}\) |
| Hartree energy \(\alpha^2 m_{\mathrm{e}} c^2=e^2 / 4 \pi \epsilon_0 a_0=2 h c R_{\infty}\) | \(E_{\mathrm{h}}\) | \(4.3597447222071(85) \times 10^{-18}\) | \(\mathrm{~J}\) | \(1.9 \times 10^{-12}\) |
| \(27.211386245988(53)\) | \(\mathrm{eV}\) | \(1.9 \times 10^{-12}\) | ||
| quantum of circulation | \(\pi \hbar / m_{\mathrm{e}}\) | \(3.6369475516(11) \times 10^{-4}\) | \(\mathrm{~m}^2 \mathrm{~s}^{-1}\) | \(3.0 \times 10^{-10}\) |
| \(2 \pi \hbar / m_{\mathrm{e}}\) | \(7.2738951032(22) \times 10^{-4}\) | \(\mathrm{~m}^2 \mathrm{~s}^{-1}\) | \(3.0 \times 10^{-10}\) | |
Table \(\PageIndex{4}\): Electroweak Constants
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| Fermi coupling constant \({ }^{\ddagger}\) | \(G_{\mathrm{F}} /(\hbar c)^3\) | \(1.1663787(6) \times 10^{-5}\) | \(\mathrm{GeV}^{-2}\) | \(5.1 \times 10^{-7}\) |
| \(\sin ^2 \theta_{\mathrm{W}}=s_{\mathrm{W}}^2 \equiv 1-\left(m_{\mathrm{W}} / m_{\mathrm{Z}}\right)^2\) | \(\sin ^2 \theta_{\mathrm{W}}\) | \(0.22290(30)\) | \(1.3 \times 10^{-3}\) | |
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| electron mass | \(m_{\mathrm{e}}\) | \(9.1093837015(28) \times 10^{-31}\) | \(\mathrm{kg}\) | \(3.0 \times 10^{-10}\) |
| \(5.48579909065(16) \times 10^{-4}\) | \(\mathrm{u}\) | \(2.9 \times 10^{-11}\) | ||
| energy equivalent | \(m_{\mathrm{e}} c^2\) | \(8.1871057769(25) \times 10^{-14}\) | \(J\) | \(3.0 \times 10^{-10}\) |
| \(0.51099895000(15)\) | \(\mathrm{MeV}\) | \(3.0 \times 10^{-10}\) | ||
| electron-muon mass ratio | \(m_{\mathrm{e}} / m_\mu\) | \(4.83633169(11) \times 10^{-3}\) | \(2.2 \times 10^{-8}\) | |
| electron-tau mass ratio | \(m_{\mathrm{e}} / m_\tau\) | \(2.87585(19) \times 10^{-4}\) | \(6.8 \times 10^{-5}\) | |
| electron-proton mass ratio | \(m_{\mathrm{e}} / m_{\mathrm{p}}\) | \(5.44617021487(33) \times 10^{-4}\) | \(6.0 \times 10^{-11}\) | |
| electron-neutron mass ratio | \(m_{\mathrm{e}} / m_{\mathrm{n}}\) | \(5.4386734424(26) \times 10^{-4}\) | \(4.8 \times 10^{-10}\) | |
| electron-deuteron mass ratio | \(m_{\mathrm{e}} / m_{\mathrm{d}}\) | \(2.724437107462(96) \times 10^{-4}\) | \(3.5 \times 10^{-11}\) | |
| electron-triton mass ratio | \(m_{\mathrm{e}} / m_{\mathrm{t}}\) | \(1.819200062251(90) \times 10^{-4}\) | \(5.0 \times 10^{-11}\) | |
| electron-helion mass ratio | \(m_{\mathrm{e}} / m_{\mathrm{h}}\) | \(1.819543074573(79) \times 10^{-4}\) | \(4.3 \times 10^{-11}\) | |
| electron to alpha particle mass ratio | \(m_{\mathrm{e}} / m_\alpha\) | \(1.370933554787(45) \times 10^{-4}\) | \(3.3 \times 10^{-11}\) | |
| electron charge to mass quotient | \(-e / m_{\mathrm{e}}\) | \(-1.75882001076(53) \times 10^{11}\) | \(\mathrm{C} \mathrm{kg}^{-1}\) | \(3.0 \times 10^{-10}\) |
| electron molar mass \(N_{\mathrm{A}} m_{\mathrm{e}}\) | \(M(\mathrm{e}), M_{\mathrm{e}}\) | \(5.4857990888(17) \times 10^{-7}\) | \(\mathrm{~kg} \mathrm{~mol}^{-1}\) | \(3.0 \times 10^{-10}\) |
| reduced Compton wavelength \( \hbar / m_{\mathrm{e}} c=\alpha a_0\) | \(\lambda_{\mathrm{C}}\) | \(3.8615926796(12) \times 10^{-13}\) | \(\mathrm{~m}\) | \(3.0 \times 10^{-10}\) |
| Compton wavelength | \(\lambda_{\mathrm{C}}\) | \(2.42631023867(73) \times 10^{-12}\) | \([\mathrm{~m}]^{\dagger}\) | \(3.0 \times 10^{-10}\) |
| classical electron radius \(\alpha^2 a_0\) | \(r_{\mathrm{e}}\) | \(2.8179403262(13) \times 10^{-15}\) | \(\mathrm{~m}\) | \(4.5 \times 10^{-10}\) |
| Thomson cross section \((8 \pi / 3) r_{\mathrm{e}}^2\) | \(\sigma_{\mathrm{e}}\) | \(6.6524587321(60) \times 10^{-29}\) | \(\mathrm{~m}^2\) | \(9.1 \times 10^{-10}\) |
| electron magnetic moment | \(\mu_{\mathrm{e}}\) | \(-9.2847647043(28) \times 10^{-24}\) | \(\mathrm{~J} \mathrm{~T}^{-1}\) | \(3.0 \times 10^{-10}\) |
| to Bohr magneton ratio | \(\mu_{\mathrm{e}} / \mu_{\mathrm{B}}\) | \(-1.00115965218128(18)\) | \(1.7 \times 10^{-13}\) | |
| to nuclear magneton ratio | \(\mu_{\mathrm{e}} / \mu_{\mathrm{N}}\) | \(-1838.28197188(11)\) | \(6.0 \times 10^{-11}\) | |
| electron magnetic moment | ||||
| anomaly \(\left|\mu_{\mathrm{e}}\right| / \mu_{\mathrm{B}}-1\) | \(a_{\mathrm{e}}\) | \(1.15965218128(18) \times 10^{-3}\) | \(1.5 \times 10^{-10}\) | |
| electron g-factor \((-2\left(1+a_{\mathrm{e}}\right)\)) | \(g_{\mathrm{e}}\) | \(-2.00231930436256(35)\) | \(1.7 \times 10^{-13}\) | |
| electron-muon magnetic moment ratio | \(\mu_{\mathrm{e}} / \mu_\mu\) | \(206.7669883(46)\) | \(2.2 \times 10^{-8}\) | |
| electron-proton magnetic moment ratio electron to shielded proton magnetic |
\(\mu_{\mathrm{e}} / \mu_{\mathrm{p}}\) | \(-658.21068789(20)\) | \(3.0 \times 10^{-10}\) | |
| moment ratio \(\left(\mathrm{H}_2 \mathrm{O}\right., sphere, \left.25^{\circ} \mathrm{C}\right)\) | \(\mu_{\mathrm{e}} / \mu_{\mathrm{p}}^{\prime}\) | \(-658.2275971(72)\)\) | \(1.1 \times 10^{-8}\) | |
| electron-neutron magnetic moment ratio | \(\mu_{\mathrm{e}} / \mu_{\mathrm{n}}\) | \(960.92050(23)\) | \(2.4 \times 10^{-7}\) | |
| electron-deuteron magnetic moment ratio electron to shielded helion magnetic |
\(\mu_{\mathrm{e}} / \mu_{\mathrm{d}}\) | \(-2143.9234915(56)\) | \(2.6 \times 10^{-9}\) | |
| moment ratio (gas, sphere, \(25^{\circ} \mathrm{C}\) ) | \(\mu_{\mathrm{e}} / \mu_{\mathrm{h}}^{\prime}\) | \(864.058257(10)\) | \(1.2 \times 10^{-8}\) | |
| electron gyromagnetic ratio \(2\left|\mu_{\mathrm{e}}\right| / \hbar\) | \(\gamma_{\mathrm{e}}\) | \(1.76085963023(53) \times 10^{11}\) | \(\mathrm{~s}^{-1} \mathrm{~T}^{-1}\) | \(3.0 \times 10^{-10}\) |
| \(28024.9514242(85)\) | \(\mathrm{MHz}\mathrm{T}^{-1}\) | \(3.0 \times 10^{-10}\) | ||
Table \(\PageIndex{6}\): Muon, \(mu_{-}\)
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| muon mass | \(m_\mu\) | \(1.883531627(42) \times 10^{-28}\) | \(\mathrm{~kg}\) | \(2.2 \times 10^{-8}\) |
| \(0.1134289259(25)\) | \(\mathrm{u}\) | \(2.2 \times 10^{-8}\) | ||
| energy equivalent | \(1.692833804(38) \times 10^{-11}\) | \(\mathrm{~J}\) | \(2.2 \times 10^{-8}\) | |
| \(m_\mu c^2\) | \(105.6583755(23)\) | \(\mathrm{MeV}\) | \(2.2 \times 10^{-8}\) | |
| muon-electron mass ratio | \(m_\mu / m_{\mathrm{e}}\) | \(206.7682830(46)\) | \(2.2 \times 10^{-8}\) | |
| muon-tau mass ratio | \(m_\mu / m_\tau\) | \(5.94635(40) \times 10^{-2}\) | \(6.8 \times 10^{-5}\) | |
| muon-proton mass ratio | \(m_\mu / m_{p}\) | \(0.112 609 5264(25)\) | \(2.2 \times 10^{-8}\) | |
| muon-neutron mass ratio | \(m_\mu / m_{\mathrm{n}}\) | \(0.1124545170(25)\) | \(2.2 \times 10^{-8}\) | |
| muon molar mass \(N_{\mathrm{A}} m_\mu\) | \(M(\mu), M_\mu\) | \(1.134289259(25) \times 10^{-4}\) | \(\mathrm{~kg} \mathrm{~mol}^{-1}\) | \(2.2 \times 10^{-8}\) |
| reduced muon Compton wavelength \(\hbar / m_\mu c\) | \(\lambda_{\mathrm{C}, \mu}\) | \(1.867594306(42) \times 10^{-15}\) | \(\mathrm{~m}\) | \(2.2 \times 10^{-8}\) |
| \(\quad\) muon Compton wavelength | \(\lambda_{\mathrm{C}, \mu}\) | \(1.173444110(26) \times 10^{-14}\) | \([\mathrm{~m}]^{\dagger}\) | \(2.2 \times 10^{-8}\) |
| muon magnetic moment | \(\mu_\mu\) | \(-4.49044830(10) \times 10^{-26}\) | \(\mathrm{~J} \mathrm{~T}^{-1}\) | \(2.2 \times 10^{-8}\) |
| \(\quad\) to Bohr magneton ratio | \(\mu_\mu / \mu_{\mathrm{B}}\) | \(-4.84197047(11) \times 10^{-3}\) | \(2.2 \times 10^{-8}\) | |
| \(\quad\) to nuclear magneton ratio | \(\mu_\mu / \mu_{\mathrm{N}}\) | \(-8.89059703(20)\) | \(2.2 \times 10^{-8}\) | |
| muon magnetic moment anomaly | \(5.4 \times 10^{-7}\) | |||
| \(\left|\mu_\mu\right| /\left(e \hbar / 2 m_\mu\right)-1\) | \(a_\mu\) | \(1.16592089(63) \times 10^{-3}\) | \(6.3 \times 10^{-10}\) | |
| muon g-factor \(-2\left(1+a_\mu\right)\) | \(g_\mu\) | \(-2.0023318418(13)\) | \(2.2 \times 10^{-8}\) | |
| muon-proton magnetic moment ratio | \(\mu_\mu / \mu_{\mathrm{p}}\) | \(-3.183345142(71)\) | ||
Table \(\PageIndex{7}\): Tau, \(tau_{-}\)
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| tau mass | \(m_\tau\) | \(3.16754(21) \times 10^{-27}\) | \(\mathrm{~kg}\) | \(6.8 \times 10^{-5}\) |
| \(1.90754(13)\) | \(\mathrm{u}\) | \(6.8 \times 10^{-5}\) | ||
| energy equivalent | \(m_\tau c^2\) | \(2.84684(19) \times 10^{-10}\) | \(\mathrm{~J}\) | \(6.8 \times 10^{-5}\) |
| \(1776.86(12)\) | \(\mathrm{MeV}\) | \(6.8 \times 10^{-5}\) | ||
| tau-electron mass ratio | \(m_\tau / m_{\mathrm{e}}\) | \(3477.23(23)\) | \(6.8 \times 10^{-5}\) | |
| tau-muon mass ratio | \(m_\tau / m_\mu\) | \(16.8170(11)\) | \(6.8 \times 10^{-5}\) | |
| tau-proton mass ratio | \(m_\tau / m_{\mathrm{p}}\) | \(1.89376(13)\) | \(6.8 \times 10^{-5}\) | |
| tau-neutron mass ratio | \(m_\tau / m_{\mathrm{n}}\) | \(1.89115(13)\) | \(6.8 \times 10^{-5}\) | |
| tau molar mass \(N_{\mathrm{A}} m_\tau \) | \(M_{\mathrm{C}, \tau}\) | \(1.90754(13) \times 10^{-3}\) | \(\mathrm{~kg} \mathrm{~mol}^{-1}\) | \(6.8 \times 10^{-5}\) |
| reduced tau Compton wavelength \(\hbar / m_\tau c \) | \(\lambda_{\mathrm{C}, \tau}\) | \(1.110538(75) \times 10^{-16}\) | \([\mathrm{~m}]^{\dagger}\) | \(6.8 \times 10^{-5}\) |
| tau Compton wavelength | \(\lambda_{\mathrm{C}, \tau}\) | \(6.97771(47) \times 10^{-16}\) | \([m]\) | \(6.8 \times 10^{-5}\) |
Table \(\PageIndex{8}\): Proton, p
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| proton-tau mass ratio | \(m_{\mathrm{p}} / m_\tau\) | \(0.528051(36)\) | \(6.8 \times 10^{-5}\) | |
| proton-neutron mass ratio | \(m_{\mathrm{p}} / m_{\mathrm{n}}\) | \(0.99862347812(49)\) | \(4.9 \times 10^{-10}\) | |
| proton charge to mass quotient | \(e / m_{\mathrm{p}}\) | \(9.5788331560(29) \times 10^7\) | \(\mathrm{C} \mathrm{kg}^{-1}\) | \(3.1 \times 10^{-10}\) |
| proton molar mass \(N_{\mathrm{A}} m_{\mathrm{p}}\) | \(M(\mathrm{p}), M_{\mathrm{p}}\) | \(1.00727646627(31) \times 10^{-3}\) | \(\mathrm{~kg} \mathrm{~mol}^{-1}\) | \(3.1 \times 10^{-10}\) |
| reduced proton Compton wavelength \(\hbar / m_{\mathrm{p}} c\) | \(\lambda_{\mathrm{C}, \mathrm{p}}\) | \(2.10308910336(64) \times 10^{-16}\) | \(\(\mathrm{~m}\) | \(3.1 \times 10^{-10}\) |
| \(\quad\) proton Compton wavelength | \(\lambda_{\mathrm{C}, \mathrm{p}}\) | \(1.32140985539(40) \times 10^{-15}\) | \([\mathrm{~m}]^{\dagger}\) | \(3.1 \times 10^{-10}\) |
| proton rms charge radius | \(r_{\mathrm{p}}\) | \(8.414(19) \times 10^{-16}\) | \(\mathrm{~m}\) | \(2.2 \times 10^{-3}\) |
| proton magnetic moment | \(\mu_{\mathrm{p}}\) | \(1.41060679736(60) \times 10^{-26}\) | \(\mathrm{~J} \mathrm{~T}^{-1}\) | \(4.2 \times 10^{-10}\) |
| \(\quad \) to Bohr magneton ratio | \(\mu_{\mathrm{p}} / \mu_{\mathrm{B}}\) | \(1.52103220230(46) \times 10^{-3}\) | \(3.0 \times 10^{-10}\) | |
| \(\quad\) to nuclear magneton ratio | \(\mu_{\mathrm{p}} / \mu_{\mathrm{N}}\) | \(2.79284734463(82)\) | \(2.9 \times 10^{-10}\) | |
| proton g-factor \(2 \mu_{\mathrm{p}} / \mu_{\mathrm{N}}\) | \(g_{\mathrm{p}}\) | \(5.5856946893(16)\) | \(2.9 \times 10^{-10}\) | |
| proton-neutron magnetic moment ratio | \(\mu_{\mathrm{p}} / \mu_{\mathrm{n}}\) | \(-1.45989805(34)\) | \(2.4 \times 10^{-7}\) | |
| shielded proton magnetic moment |
\(\mu_{\mathrm{p}}^{\prime}\) | \(1.410570560(15) \times 10^{-26}\) | \(\mathrm{~J} \mathrm{~T}^{-1}\) | \(1.1 \times 10^{-8}\) |
| \(\left(\mathrm{H}_2 \mathrm{O} \text {, sphere, } 25^{\circ} \mathrm{C}\right)\) | ||||
| \(\quad\) to Bohr magneton ratio | \(\mu_{\mathrm{p}}^{\prime} / \mu_{\mathrm{B}}\) | \(1.520993128(17) \times 10^{-3}\) | \(1.1 \times 10^{-8}\) | |
| \(\quad\) to nuclear magneton ratio | \(\mu_{\mathrm{p}}^{\prime} / \mu_{\mathrm{N}}\) | \(2.792775599(30)\) | \(1.1 \times 10^{-8}\) | |
| proton magnetic shielding correction | ||||
| \(1-\mu_{\mathrm{p}}^{\prime} / \mu_{\mathrm{p}}\left(\mathrm{H}_2 \mathrm{O}\right., sphere, \left.25^{\circ} \mathrm{C}\right)\) | \(\sigma_{\mathrm{p}}^{\prime}\) | \(2.5689(11) \times 10^{-5}\) | \(4.2 \times 10^{-4}\) | |
| proton gyromagnetic ratio 2 \(\mu_{\mathrm{p}} / \hbar\) | \(\gamma_{\mathrm{p}}\) | \(2.6752218744(11) \times 10^8\) | \(\mathrm{~s}^{-1} \mathrm{~T}^{-1}\) | \(4.2 \times 10^{-10}\) |
| \(42.577 478 518(18)\) | \(\mathrm{MHz} \mathrm{T}^{-1}\) | \(4.2 \times 10^{-10}\) | ||
| shielded proton gyromagnetic ratio | ||||
| \(2 \mu_{\mathrm{p}}^{\prime} / \hbar\left(\mathrm{H}_2 \mathrm{O}\right., sphere, \left.25^{\circ} \mathrm{C}\right)\) | \(\gamma_{\mathrm{p}}^{\prime}\) | \(2.675153151(29) \times 10^8\) | \(\mathrm{~s}^{-1} \mathrm{~T}^{-1}\) | \(1.1 \times 10^{-8}\) |
| \(42.57638474(46)\) | \(\mathrm{MHz} \mathrm{T}^{-1}\) | \(1.1 \times 10^{-8}\) |
Table \(\PageIndex{9}\): Neutron, n
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| neutron mass | \(m_{\mathrm{n}}\) | \(1.67492749804(95) \times 10^{-27}\) |
\(\mathrm{kg}\) |
\(5.7 \times 10^{-10}\) |
| \(1.008 664 915 95(49)\) | \(\mathrm{u}\) | \(4.8 \times 10^{-10}\) | ||
| \(\quad \)energy equivalent | \(m_{\mathrm{n}} c^2\) | \(1.50534976287(86) \times 10^{-10}\) |
\(\mathrm{J}\) | \(5.7 \times 10^{-10}\) |
| \(939.565 420 52(54)\) | \(\mathrm{MeV}\) | \(5.7 \times 10^{-10}\) | ||
| neutron-electron mass ratio | \(m_{\mathrm{n}} / m_{\mathrm{e}}\) | \(1838.68366173(89)\) | \(4.8 \times 10^{-10}\) | |
| neutron-muon mass ratio | \(m_{\mathrm{n}} / m_\mu\) | \(8.89248406(20)\) | \(2.2 \times 10^{-8}\) | |
| neutron-tau mass ratio | \(m_{\mathrm{n}} / m_\tau\) | \(0.528779(36)\) | \(6.8 \times 10^{-5}\) | |
| neutron-proton mass ratio | \(m_{\mathrm{n}} / m_{\mathrm{p}}\) | \(1.00137841931(49)\) | \(4.9 \times 10^{-10}\) | |
| neutron-proton mass difference | \( m_{\mathrm{n}}-m_{\mathrm{p}}\) | \(2.30557435(82) \times 10^{-30 }\) |
\(\mathrm{kg}\) |
\(3.5 \times 10^{-7}\) |
| \(1.38844933(49) \times 10^{-3}\) | \(\mathrm{u}\) | \(3.5 \times 10^{-7}\) | ||
| \(\quad \)energy equivalent | \( \left(m_{\mathrm{n}}-m_{\mathrm{p}}\right) c^2\) | \(2.07214689(74) \times 10^{-13}\) |
\(\mathrm{J}\) |
\(3.5 \times 10^{-7}\) |
| \(1.29333236(46)\) | \(\mathrm{MeV}\) | \(3.5 \times 10^{-7}\) | ||
| neutron molar mass \(N_{\mathrm{A}} m_{\mathrm{n}}\) | \( M(\mathrm{n}), M_{\mathrm{n}}\) | \(1.00866491560(57) \times 10^{-3}\) | \(\mathrm{~kg} \mathrm{~mol}^{-1}\) | \(5.7 \times 10^{-10}\) |
| reduced neutron Compton wavelength \(\hbar / m_{\mathrm{n}} c\) |
\( \lambda_{\mathrm{C}, \mathrm{n}\) | \(2.1001941552(12) \times 10^{-16}\) |
\(\mathrm{m }\) |
\(5.7 \times 10^{-10}\) |
| neutron Compton wavelength | \( \lambda_{\mathrm{C}, \mathrm{n}\) | \(1.31959090581(75) \times 10^{-15}\) | \([\mathrm{m}]^{\dagger}\) | \(5.7 \times 10^{-10}\) |
| neutron magnetic moment |
\( \mu_{\mathrm{n}}\) |
\(-9.6623651(23) \times 10^{-27}\) | \(\mathrm{~J} \mathrm{~T}^{-1}\) | \(2.4 \times 10^{-7}\) |
| \(\quad \)to Bohr magneton ratio | \( \mu_{\mathrm{n}} / \mu_{\mathrm{B}}\) | \(-1.04187563(25) \times 10^{-3}\) | \(2.4 \times 10^{-7}\) | |
| \(\quad \)to nuclear magneton ratio | \( \mu_{\mathrm{n}} / \mu_{\mathrm{N}}\) | \(-1.91304273(45)\) | \(2.4 \times 10^{-7}\) | |
| neutron g-factor \(2 \mu_{\mathrm{n}} / \mu_{\mathrm{N}}\) | \( g_{\mathrm{n}}\) | \(-3.82608545(90)\) | \(2.4 \times 10^{-7}\) | |
| neutron-electron magnetic moment ratio | \(\mu_{\mathrm{n}} / \mu_{\mathrm{e}}\) | \(1.04066882(25) \times 10^{-3}\) | \(2.4 \times 10^{-7}\) | |
| neutron-proton magnetic moment ratio | \(\mu_{\mathrm{n}} / \mu_{\mathrm{p}}\) | \(-0.68497934(16)\) | \(2.4 \times 10^{-7}\) | |
| neutron to shielded proton magnetic | ||||
| \(\quad \) moment ratio \(\left(\mathrm{H}_2 \mathrm{O}\right., sphere, \left.25^{\circ} \mathrm{C}\right)\) | \(\mu_{\mathrm{n}} / \mu_{\mathrm{p}}^{\prime}\) | \(-0.68499694(16)\) | \(2.4 \times 10^{-7}\) | |
| neutron gyromagnetic ratio \(2\left|\mu_{\mathrm{n}}\right| / \hbar\) | \(\gamma_{\mathrm{n}}\) | \(1.83247171(43) \times 10^8\) | \(\mathrm{~s}^{-1} \mathrm{~T}^{-1}\) | \(2.4 \times 10^{-7}\) |
| \(29.1646931(69)\) | \(\mathrm{MHz} \mathrm{T}^{-1}\) | \(2.4 \times 10^{-7}\) |
Table \(\PageIndex{10}\): Deuteron, d
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| deuteron mass | \( m_{\mathrm{d}}\) | \( 3.3435837768(10) \times 10^{-27}\) | kg | \( 3.1 \times 10^{-10}\) |
| \( 2.013553212544(15)\) | u | \( 7.4 \times 10^{-12}\) | ||
| iivalent | \( m_{\mathrm{d}} c^2 \) | \( 3.00506323491(94) \times 10^{-10}\) | J | \( 3.1 \times 10^{-10}\) |
| deuteron-electron mass ratio | \( m_{\mathrm{d}} / m_{\mathrm{e}} \) | \( 3670.4829676555(63)\) | MeV | \( 3.1 \times 10^{-10}\) |
| deuteron-proton mass ratio | \( m_{\mathrm{d}} / m_{\mathrm{p}} \) | \( 1.9990075012699(84)\) | \( 1.7 \times 10^{-11}\) | |
| deuteron molar mass \(N_{\mathrm{A}} m_{\mathrm{d}}\) | \( M(\mathrm{~d}), M_{\mathrm{d}} \) | \( 2.01355321466(63) \times 10^{-3}\) | \( 4.2 \times 10^{-12}\) | |
| deuteron rms charge radius | \( r_{\mathrm{d}} \) | \( 2.12778(27) \times 10^{-15}\) | \( \mathrm{~kg} \mathrm{~mol}^{-1} | \( 3.1 \times 10^{-10}\) |
| deuteron magnetic moment | \( \mu_{\mathrm{d}} \) | \( 4.330735087(11) \times 10^{-27}\) | \mathrm{~m}^{-1} | \( 1.3 \times 10^{-4}\) |
| to Bohr magneton ratio | \( \mu_{\mathrm{d}} / \mu_{\mathrm{B}} \) | \( 4.669754568(12) \times 10^{-4}\) | \( 2.6 \times 10^{-9}\) | |
| to nuclear magneton ratio | \( \mu_{\mathrm{d}} / \mu_{\mathrm{N}} \) | \( 0.8574382335(22)\) | \( 2.6 \times 10^{-9}\) | |
| deuteron g-factor \(\mu_{\mathrm{d}} / \mu_{\mathrm{N}}\) | \( g_{\mathrm{d}} \) | \( 0.8574382335(22)\) | \( 2.6 \times 10^{-9}\) | |
| deuteron-electron magnetic moment ratio | \( \mu_{\mathrm{d}} / \mu_{\mathrm{e}} \) | \( -4.664345550(12) \times 10^{-4}\) | \( 2.6 \times 10^{-9}\) | |
| deuteron-proton magnetic moment ratio | \( \mu_{\mathrm{d}} / \mu_{\mathrm{p}} \) | \( 0.30701220930(79)\) | \( 2.6 \times 10^{-9}\) | |
| deuteron-neutron magnetic moment ratio | \( \mu_{\mathrm{d}} / \mu_{\mathrm{n}} \) | \( -0.44820652(11)\) | \( 2.6 \times 10^{-9}\) | |
Table \(\PageIndex{11}\): Triton, t
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| triton mass | \( m_{\mathrm{t}}\) | \( 5.0073567512(16) \times 10^{-27}\) | kg | \( 3.1 \times 10^{-10}\) |
| \( 3.01550071597(10)\) | u | \( 3.4 \times 10^{-11}\) | ||
| energy equivalent | \( m_{\mathrm{t}} c^2\) | \( 4.5003878119(14) \times 10^{-10}\) | J | \( 3.1 \times 10^{-10}\) |
| \( 2808.92113668(88)\) | MeV | \( 3.1 \times 10^{-10}\) | ||
| triton-electron mass ratio | \( m_{\mathrm{t}} / m_{\mathrm{e}}\) | \( 5496.92153551(21)\) | \( 3.8 \times 10^{-11}\) | |
| triton-proton mass ratio | \( m_{\mathrm{t}} / m_{\mathrm{p}}\) | \( 3.4 \times 10^{-11}\) | ||
| triton molar mass \( N_{\mathrm{A}} m_{\mathrm{t}}\) | \( M(\mathrm{t}), M_{\mathrm{t}}\) | \( 3.01550071913(94) \times 10^{-3}\) | \( \mathrm{~kg} \mathrm{~mol}^{-1}\) | \( 3.1 \times 10^{-10}\) |
| triton magnetic moment | \( \mu_{\mathrm{t}}\) | \( 1.5046095178(30) \times 10^{-26}\) | \( \mathrm{~J} \mathrm{~T}^{-1}\) | \( 2.0 \times 10^{-9}\) |
| to Bohr magneton ratio | \( \mu_{\mathrm{t}} / \mu_{\mathrm{B}}\) | \( 1.6223936648(32) \times 10^{-3}\) | \( 2.0 \times 10^{-9}\) | |
| to nuclear magneton ratio | \( \mu_{\mathrm{t}} / \mu_{\mathrm{N}}\) | \( 2.9789624650(59)\) | \( 2.0 \times 10^{-9}\) | |
| triton g-factor \( 2 \mu_{\mathrm{t}} / \mu_{\mathrm{N}}\) | \( g_{\mathrm{t}}\) | \( 2.0 \times 10^{-9}\) | ||
Table \(\PageIndex{12}\): Helion, h
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| helion mass | \( m_{\mathrm{h}}\) | \( 5.0064127862(16) \times 10^{-27}\) | kg | \( 3.1 \times 10^{-10} 25 \times 10^{-11} \) |
| \( 3.014932246932(74)\) | \( 2.5 \times 10^{-11}\) | |||
| energy equivalent | \( m_{\mathrm{h}} c^2\) | \( 4.4995394185(14) \times 10^{-10}\) | J | \( 3.1 \times 10^{-10}\) |
| \( 2808.39161112(88)\) | MeV | \( 3.1 \times 10^{-10}\) | ||
| helion-electron mass ratio | \( m_{\mathrm{h}} / m_{\mathrm{e}}\) | \( 5495.88527984(16)\) | \( 2.9 \times 10^{-11}\) | |
| helion-proton mass ratio | \( m_{\mathrm{h}} / m_{\mathrm{p}}\) | \( 2.993152671552(70)\) | \( 2.4 \times 10^{-11}\) | |
| helion molar mass \( N_{\mathrm{A}} m_{\mathrm{h}}\) | \( M(\mathrm{~h}), M_{\mathrm{h}}\) | \( 3.01493225010(94) \times 10^{-3}\) | \( \mathrm{~kg} \mathrm{~mol}^{-1}\) | \( 3.1 \times 10^{-10}\) |
| helion magnetic moment | \( \mu_{\mathrm{h}}\) | \( -1.07461755198(93) \times 10^{-26}\) | \( \mathrm{~J} \mathrm{~T}^{-1}\) | \( 8.7 \times 10^{-10}\) |
| to Bohr magneton ratio | \( \mu_{\mathrm{h}} / \mu_{\mathrm{B}}\) | \( -1.15874098083(94) \times 10^{-3}\) | \( 8.1 \times 10^{-10}\) | |
| to nuclear magneton ratio | \( \mu_{\mathrm{h}} / \mu_{\mathrm{N}}\) | \( -2.1276253498(17)\) | \( 8.1 \times 10^{-10}\) | |
| helion g-factor \( 2 \mu_{\mathrm{h}} / \mu_{\mathrm{N}}\) | \( g_{\mathrm{h}}\) | \( -4.2552506995(34)\) | \( 8.1 \times 10^{-10}\) | |
| shielded helion magnetic moment (gas, sphere, \( 25^{\circ} \mathrm{C} )\) |
\( \mu_{\mathrm{h}}^{\prime}\) | \( -1.07455311035(93) \times 10^{-26}\) | \( \mathrm{~J} \mathrm{~T}^{-1} | \( 8.7 \times 10^{-10}\) |
| to Bohr magneton ratio | \( \mu_{\mathrm{h}}^{\prime} / \mu_{\mathrm{B}}\) | \( -1.15867149457(94) \times 10^{-3}\) | \( 8.1 \times 10^{-10}\) | |
| to nuclear magneton ratio | \( \mu_{\mathrm{h}}^{\prime} / \mu_{\mathrm{N}}\) | \( -2.1274977624(17)\) | \( 8.1 \times 10^{-10}\) | |
| shielded helion to proton magnetic moment ratio (gas, sphere, \( 25^{\circ} \mathrm{C} )\) shielded helion to shielded proton magnetic |
\( \mu_{\mathrm{h}}^{\prime} / \mu_{\mathrm{p}}\) | \( -0.76176657721(66)\) | \( 8.6 \times 10^{-10}\) | |
| moment ratio (gas / \( \mathrm{H}_2 \mathrm{O}, spheres, 25^{\circ} \mathrm{C} )\) | \( \mu_{\mathrm{h}}^{\prime} / \mu_{\mathrm{p}}^{\prime}\) | \( -0.761 7861334(31)\) | \( 4.0 \times 10^{-9}\) | |
| shielded helion gyromagnetic ratio | ||||
| \( 2\left|\mu_{\mathrm{h}}^{\prime}\right| / \hbar \text { (gas, sphere, } 25^{\circ} \mathrm{C} \text { ) }\) | \( \gamma_{\mathrm{h}}^{\prime}\) | \( 2.0378946078(18) \times 10^8\) | \( \mathrm{s}^{-1} \mathrm{~T}^{-1}\) | \( 8.7 \times 10^{-10}\) |
| \( 32.434100033(28)\) | \( \mathrm{MHz} \mathrm{T}^{-1}\) | \( 8.7 \times 10^{-10}\) |
Table \(\PageIndex{13}\): Alpha particle, \(\alpha\)
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| alpha particle mass | \(m_\alpha\) | \(6.6446573450(21) \times 10^{-27}\) | kg | \(3.1 \times 10^{-10}\) |
| energy equivalent | \(4.001506179129(62)\) | u | \(1.6 \times 10^{-11}\) | |
| \(m_\alpha c^2\) | \(5.9719201997(19) \times 10^{-10}\) | J | \(3.1 \times 10^{-10}\) | |
| alpha particle to electron mass ratio | \(3727.3794118(12)\) | MeV | \(3.1 \times 10^{-10}\) | |
| alpha particle to proton mass ratio | \(m_\alpha / m_{\mathrm{e}}\) | \(7294.29954171(17)\) | \(2.4 \times 10^{-11}\) | |
| alpha particle rms charge radius | \(m_\alpha / m_{\mathrm{p}}\) | 3.972599690252(70)\) | \(1.8 \times 10^{-11}\) | |
| alpha particle molar mass \(N_{\mathrm{A}} m_\alpha\) | \(r_\alpha\) | \(1.6785(21) \times 10^{-15}\) | m | \(1.2 \times 10^{-3}\) |
| \(M(\alpha), M_\alpha\) | \(4.0015061833(12) \times 10^{-3}\) | \(\mathrm{~kg} \mathrm{~mol}^{-1} | \(3.1 \times 10^{-10}\) | |
Table \(\PageIndex{14}\): Physicochemical Constants
| Quantity | Symbol | Value | Unit | Relative std. uncert. u_{\mathrm{r}} |
|---|---|---|---|---|
| Avogadro constant |
\( N_{\mathrm{A}}\) | \( 6.02214076 \times 10^{23}\) | \( \mathrm{~mol}^{-1}\) | exact |
| Boltzmann constant | k | \( 1.380649 \times 10^{-23}\) | \( \mathrm{~J} \mathrm{~K}^{-1}\) | exact |
| \( 8.617333262 \ldots \times 10^{-5}\) | \( \mathrm{eV} \mathrm{K}^{-1}\) | exact | ||
| k / h | \( 2.083661912 \ldots \times 10^{10}\) | \( \mathrm{~Hz} \mathrm{~K}^{-1}\) | exact | |
| k / h c | \( 69.50348004 \ldots\) | \( \left[\mathrm{m}^{-1} \mathrm{~K}^{-1}\right]^{\dagger}\) | exact | |
| atomic mass constant | ||||
| \( m_{\mathrm{u}}=\frac{1}{12} m\left({ }^{12} \mathrm{C}\right)=2 h c R_{\infty} / \alpha^2 c^2 A_{\mathrm{r}}(\mathrm{e})\) | \( m_{\mathrm{u}} \) | \( 1.66053906892(52) \times\) 10^{-27}\) | kg | \( 3.1 \times 10^{-10}\) |
| equivalent energy | \( m_{\mathrm{u}} c^2\) | \)\( 1.49241808768(46) \times 10^{-10}\) | J | \( 3.1 \times 10^{-10}\) |
| \( 931.49410372(29)\) | MeV | \( 3.1 \times 10^{-10}\) | ||
| molar mass constant\( { }^{\|}\) | \( M_{\mathrm{u}}\) | \( 1.00000000105(31) \times 10^{-3}\) | \( \mathrm{~kg} \mathrm{~mol}^{-1}\) | \( 3.1 \times 10^{-10}\) |
| molar mass" of carbon-12 \( A_{\mathrm{r}}\left({ }^{12} \mathrm{C}\right) M_{\mathrm{u}}\) | \( M\left({ }^{12} \mathrm{C}\right)\) | \( 12.0000000126(37) \times 10^{-3}\) | \( \mathrm{~kg} \mathrm{~mol}^{-1}\) | \( 3.1 \times 10^{-10}\) |
| molar Planck constant | \( N_{\mathrm{A}} h\) | \( 3.990312712 \ldots \times 10^{-10}\) | \( \mathrm{~J} \mathrm{~Hz}^{-1} \mathrm{~mol}^{-1}\) | exact |
| molar gas constant \( N_{\mathrm{A}} k\) | R | \( 8.314462618 \ldots\) | \( \mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\) | exact |
| Faraday constant \( N_{\mathrm{A}} e\) | F | \( 96485.33212 \ldots\) | \( \mathrm{C} \mathrm{mol}^{-1}\) | exact |
| standard-state pressure | \( 100000\) | Pa | exact | |
| standard atmosphere | \( 101325\) | Pa | exact | |
| molar volume of ideal gas R T / p | ||||
| T=273.15 \( \mathrm{~K}, p=100 \mathrm{kPa}\) or standard-state pressure |
\( V_{\mathrm{m}}\) | \( 22.71095464 \ldots \times 10^{-3}\) | \( \mathrm{~m}^3 \mathrm{~mol}^{-1}\) | exact |
| Loschmidt constant \( N_{\mathrm{A}} / V_{\mathrm{m}}\) molar volume of ideal gas R T / p |
\( n_0\) | \( 2.651645804 \ldots \times 10^{25}\) | \( \mathrm{~m}^{-3}\) | exact |
| \( T=273.15 \mathrm{~K}, p=101.325 \mathrm{kPa}\) or standard atmosphere |
\( V_{\mathrm{m}}\) | \( 22.41396954 \ldots \times 10^{-3}\) | \(\mathrm{~m}^3 \mathrm{~mol}^{-1}\) | exact |
| Loschmidt constant \( N_{\mathrm{A}} / V_{\mathrm{m}}\) | \( n_0\) | \( 2.686780111 \ldots \times 10^{25}\) | \(\mathrm{~m}^{-3}\) | exact |
| Sackur-Tetrode (absolute entropy) constant** | ||||
|
\(\frac{5}{2}+\ln \left[\left(m_{\mathrm{u}} k T_1 / 2 \pi \hbar^2\right)^{3 / 2} k T_1 / p_0\right]\) \(T_1=1 \mathrm{~K}, p_0=100 \mathrm{kPa} \) |
\( S_0 / R\) | \(-1.15170753496(47)\) | \(4.1 \times 10^{-10}\) | |
| \( T_1=1 \mathrm{~K}, p_0=101.325 \mathrm{kPa} \) or standard atmosphere |
\(-1.16487052149(47)\) | \(4.0 \times 10^{-10}\) | ||
| Stefan-Boltzmann constant \( \left(\pi^2 / 60\right) k^4 / \hbar^3 c^2\) |
\( \sigma\) | \(5.670374419 \ldots \times 10^{-8}\) | \(\mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}\) | exact |
| first radiation constant for spectral | ||||
| radiance \( 2 h c^2 \mathrm{sr}^{-1}\) | \( c_{1 \mathrm{~L}}\) | \( 1.191042972 \ldots \times 10^{-16}\) | \( \left[\mathrm{~W} \mathrm{~m}^2 \mathrm{sr}^{-1}\right]^{\dagger}\) | exact |
| first radiation constant \( 2 \pi h c^2=\pi \mathrm{sr} c_{1 \mathrm{~L}}\) | \( c_1\) | \( 3.741771852 \ldots \times 10^{-16}\) | \( \left[\mathrm{~W} \mathrm{~m}^2\right]^{\dagger}\) | exact |
| second radiation constant h c / k | \( c_2\) | \( 1.438776877 \ldots \times 10^{-2}\) | \( [\mathrm{~m} \mathrm{~K}]^{\dagger}\) | exact |
| Wien displacement law constants | ||||
| \( b=\lambda_{\max } T=c_2 / 4.965114231 \ldots\) | b | \( 2.897771955 \ldots \times 10^{-3}\) | \( [\mathrm{~m} \mathrm{~K}]^{\dagger}\) | exact |
| \( b^{\prime}=\nu_{\max } / T=2.821439372 \ldots c / c_2\) | \( b^{\prime}\) | \( 5.878925757 \ldots \times 10^{10}\) | Hz K | exact |
* The energy of a photon with frequency \(\nu\) expressed in unit Hz is \(E=h \nu\) in J . Unitary time evolution of the state of this photon is given by \(\exp (-i E t / \hbar)|\varphi\rangle\), where \(|\varphi\rangle\) is the photon state at time \(t=0\) and time is expressed in unit s. The ratio \(E t / \hbar\) is a phase.
\({ }^{\dagger}\) The symbol \([\mathrm{m}]\) denotes \(\mathrm{m} /(\mathrm{Hz} \mathrm{s})\). If angles are dimensionless, as in the current SI , then \(\mathrm{Hz} \mathrm{s}=1\). If angles have a dimension, then \(\mathrm{Hz} \mathrm{s}=\) cycle.
‡ Value recommended by the Particle Data Group (Workman, et al., 2022).
\({ }^8\) Based on the ratio of the masses of the W and Z bosons \(m_{\mathrm{W}} / m_{\mathrm{Z}}\) recommended by the Particle Data Group (Workman, et al., 2022). The value for \(\sin ^2 \theta_{\mathrm{W}}\) they recommend, which is based on a variant of the modified minimal subtraction \((\overline{\mathrm{MS}})\) scheme, is \(\sin ^2 \hat{\theta}_{\mathrm{W}}\left(M_{\mathrm{Z}}\right)=0.23122(4)\).
\({ }^{\text {II }}\) This and other constants involving \(m_\tau\) are based on \(m_\tau c^2\) in MeV recommended by the Particle Data Group (Workman, et al., 2022). atomic mass constant and u is the unified atomic mass unit. Moreover, the mass of particle \(X\) is \(m(X)=A_{\mathrm{r}}(X) \mathrm{u}\) and the molar mass of \(X\) is \
(M(X)=A_{\mathrm{r}}(X) M_{\mathrm{u}}\), where \(M_{\mathrm{u}}=N_{\mathrm{A}} \mathrm{u}\) is the molar mass constant and \(N_{\mathrm{A}}\) is the Avogadro constant.
\({ }^{* *}\) The entropy of an ideal monoatomic gas of relative atomic mass \(A_{\mathrm{r}}\) is given by \(S=S_0+\frac{3}{2} R \ln A_{\mathrm{r}}-R \ln \left(p / p_0\right)+\frac{5}{2} R \ln (T / \mathrm{K})\).