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%TCIDATA{<META NAME="Title" CONTENT="Reference/Physics/Physical Constants">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 20:35:54 1997}
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\begin{document}


\subsection{Physical Constants}

\subsubsection{General Constants}

\subparagraph{Universal Constants\label{Universal}}

\begin{tabular}{lll}
\hspace{2.7in} &  &  \\ 
\textbf{Quantity} & \textbf{Symbol \ \ \ \ \ \ } & \textbf{Value} \\ \hline
\end{tabular}

\begin{tabular}{lll}
\hspace{2.85in} & \hspace{0.6in} &  \\ 
Speed of light in vacuum & $c$ & $2.99792458\times 10^{8}\unit{m}\unit{s}%
^{-1}$ \\ 
Permeability of free space & $\mu _{0}$ & $1.25664\times 10^{-6}\unit{N}%
\unit{A}^{-2}$ \\ 
Permittivity of free space 
\CustomNote[*]{Note}{$1/\mu _{0}\unit{c}^{2}$} & $\epsilon _{0}$ & $%
8.854187817\times 10^{-12}\unit{F}\unit{m}^{-1}$ \\ 
Gravitation constant & $G$ & $6.67259\times 10^{-11}\unit{m}^{3}\unit{kg}%
^{-1}\unit{s}^{-2}$ \\ 
Planck's constant & $h$ & $6.6260755\times 10^{-34}\unit{J}\unit{s}$ \\ 
\ in electron volts 
\CustomNote[*]{Note}{$h/\{e\}$} &  & $4.135669\times 10^{-15}\unit{eV}\unit{s%
}$ \\ 
$\ h/2\pi $ & $\hbar $ & $1.05457266\times 10^{-34}\unit{J}\unit{s}$ \\ 
\ in electron volts 
\CustomNote[*]{Note}{$\hbar /\{e\}$} &  & $6.5821220\times 10^{-16}\unit{eV}%
\unit{s}$ \\ 
Planck mass 
\CustomNote[*]{Note}{$(\hbar c/G)^{\frac{1}{2}}$} & $m_{P}$ & $2.17671\times
10^{-8}\unit{kg}$ \\ 
Planck length 
\CustomNote[*]{Note}{$\hbar /m_{P}c=(\hbar G/c^{3})^{\frac{1}{2}}$} & $l_{P}$
& $1.61605\times 10^{-35}\unit{m}$ \\ 
Planck time 
\CustomNote[*]{Note}{$l_{P}/c=(\hbar G/c^{5})^{\frac{1}{2}}$} & $t_{P}$ & $%
5.39056\times 10^{-44}\unit{s}$%
\end{tabular}

\vspace{1pt}

\subparagraph{Electromagnetic Constants\label{Electromagnetic}}

\begin{tabular}{lll}
\hspace{2.85in} & \hspace{0.6in} &  \\ 
Electron charge & $e$ & $1.60217733\times 10^{-19}\unit{C}$ \\ 
e over h & $e/h$ & $2.41798836\times 10^{14}\unit{A}\unit{J}^{-1}$ \\ 
Magnetic flux quantum 
\CustomNote[*]{Note}{$h/2e$} & $\Phi _{0}$ & $2.06783461\times 10^{-15}\unit{%
Wb}$ \\ 
Josephson frequency-voltage ratio & $2e/h$ & $4.8359767\times 10^{14}\unit{Hz%
}\unit{V}^{-1}$ \\ 
quantized Hall conductance & $e^{2}/h$ & $3.87404614\times 10^{-5}\unit{S}$
\\ 
quantized Hall resistance 
\CustomNote[*]{Note}{$h/e^{2}=\mu _{0}c/2\alpha $} & $R_{H}$ & $25812.8056%
\unit{\UNICODE{0x3a9}}$ \\ 
Bohr magneton & $\mu _{B}$ & $9.2740154\times 10^{-24}\unit{J}\unit{T}^{-1}$
\\ 
\ in electron volts &  & $5.78838263\times 10^{-5}\unit{eV}\unit{T}^{-1}$ \\ 
\ in hertz &  & $1.39962418\times 10^{10}\unit{Hz}\unit{T}^{-1}$ \\ 
\ in wavenumbers &  & $46.686437\unit{m}^{-1}\unit{T}^{-1}$ \\ 
\ in kelvins &  & $0.6717099\unit{K}\unit{T}^{-1}$ \\ 
Nuclear magneton & $\mu _{N}$ & $5.0507866\times 10^{-27}\unit{J}\unit{T}%
^{-1}$ \\ 
\ in electron volts &  & $3.15245166\times 10^{-8}\unit{eV}\unit{T}^{-1}$ \\ 
\ in hertz &  & $7.6225914\unit{MHz}\unit{T}^{-1}$ \\ 
\ in wavenumbers &  & $2.54262281\times 10^{-2}\unit{m}^{-1}\unit{T}^{-1}$
\\ 
\ in kelvins &  & $3.658246\times 10^{-4}\unit{K}\unit{T}^{-1}$%
\end{tabular}

\vspace{1pt}

\subsubsection{Atomic Constants\label{Atomic}}

\begin{tabular}{cll}
\hspace{2.85in} & \hspace{0.6in} &  \\ 
\multicolumn{1}{l}{Fine-structure constant 
\CustomNote[*]{Note}{$\mu _{0}ce^{2}/2h$}} & $\alpha $ & $7.29735308\times
10^{-3}$ \\ 
\multicolumn{1}{l}{Inverse fine-structure constant} & $\alpha ^{-1}$ & $%
137.0359895$ \\ 
\multicolumn{1}{l}{Rydberg constant} & $R_{\infty }$ & $1.0973731534\times
10^{7}\unit{m}^{-1}$ \\ 
\multicolumn{1}{l}{\ in hertz} &  & $3.2898419499\times 10^{15}\unit{Hz}$ \\ 
\multicolumn{1}{l}{\ in joules} &  & $2.1798741\times 10^{-18}\unit{J}$ \\ 
\multicolumn{1}{l}{\ in electron volts} &  & $13.6056981\unit{eV}$ \\ 
\multicolumn{1}{l}{Bohr radius 
\CustomNote[*]{Note}{$\alpha /4\pi R_{\infty }$}} & $a_{0}$ & $%
0.529177249\times 10^{-10}\unit{m}$ \\ 
\multicolumn{1}{l}{Hartree energy} & $E_{h}$ & $4.3597482\times 10^{-18}%
\unit{J}$ \\ 
\multicolumn{1}{l}{\ in electron volts} &  & $27.2113961\unit{eV}$ \\ 
\multicolumn{1}{l}{Quantum of circulation} & $h/2m_{e}$ & $3.63694807\times
10^{-4}\unit{m}^{2}\unit{s}^{-1}$ \\ 
\multicolumn{1}{l}{} & $h/m_{e}$ & $7.27389614\times 10^{-4}\unit{m}^{2}%
\unit{s}^{-1}$%
\end{tabular}

\vspace{1pt}

\subparagraph{Electron\label{Electron}}

\begin{tabular}{lll}
\hline
\hspace{2.85in} & \hspace{0.6in} &  \\ 
Electron mass & $m_{e}$ & $9.1093897\times 10^{-31}\unit{kg}$ \\ 
in electron volts &  & $0.51099906\unit{MeV}$ \\ 
Electron-muon mass ratio & $m_{e}/m_{\mu }$ & $4.83633218\times 10^{-3}$ \\ 
Electron-proton mass ratio & $m_{e}/m_{p}$ & $5.44617013\times 10^{-4}$ \\ 
Electron-deuteron mass ratio & $m_{e}/m_{d}$ & $2.72443707\times 10^{-4}$ \\ 
Electron-$\alpha $-particle ratio & $m_{e}/m_{\alpha }$ & $1.37093354\times
10^{-4}$ \\ 
Electron specific charge & $-e/m_{e}$ & $-1.75881962\times 10^{11}\unit{C}%
\unit{kg}^{-1}$ \\ 
Electron molar mass & $M(e)$, $M_{e}$ & $5.48579903\times 10^{-7}\unit{kg}%
\unit{mol}^{-1}$ \\ 
Compton wavelength & $\lambda _{C}$ & $2.42631058\times 10^{-12}\unit{m}$ \\ 
$\lambda _{C}/2\pi =\alpha a_{0}=\alpha ^{2}/4\pi R_{\infty }$ &  & $%
3.86159323\times 10^{-13}\unit{m}$ \\ 
Classical electron radius & $r_{e}$ & $2.81794092\times 10^{-15}\unit{m}$ \\ 
Thomson cross section 
\CustomNote[*]{Note}{$(8\pi /3)r_{e}^{2}$} & $\sigma _{e}$ & $%
0.66524616\times 10^{-28}\unit{m}^{2}$ \\ 
Electron magnetic moment & $\mu _{e}$ & $9.2847701\times 10^{-24}\unit{J}%
\unit{T}^{-1}$ \\ 
\ in Bohr magnetons & $\mu _{e}/\mu _{B}$ & $1.001159652193$ \\ 
\ in nuclear magnetons & $\mu _{e}/\mu _{N}$ & $1838.282000$ \\ 
Electron magnetic moment\ anomaly \ 
\CustomNote[*]{Note}{$\mu _{e}/\mu _{B}-1$} & $a_{e}$ & $1.159652193\times
10^{-3}$ \\ 
Electron g-factor 
\CustomNote[*]{Note}{$2(1+a_{e})$} & $g_{e}$ & $2.002319304386$ \\ 
Electron-muon magnetic moment ratio & $\mu _{e}/\mu _{\mu }$ & $206.766967$
\\ 
Electron-proton magnetic moment ratio & $\mu _{e}/\mu _{p}$ & $658.2106881$%
\end{tabular}

\vspace{1pt}

\subparagraph{Muon\label{Muon}}

\begin{tabular}{lll}
\hline
\hspace{2.85in} &  &  \\ 
Muon mass & $m_{\mu }$ & $1.8835327\times 10^{-28}\unit{kg}$ \\ 
\ in electron volts 
\CustomNote[*]{Note}{$m_{\mu }c^{2}/\{e\}$} &  & $105.658389\unit{MeV}$ \\ 
Muon-electron mass ratio & $m_{\mu }/m_{e}$ & $206.768262$ \\ 
Muon molar mass & $M\left( \mu \right) $, $M_{\mu }$ & $1.13428913\times
10^{-4}\unit{kg}\unit{mol}^{-1}$ \\ 
Muon magnetic moment & $\mu _{\mu }$ & $4.4904514\times 10^{-26}\unit{J}%
\unit{T}^{-1}$ \\ 
\ in Bohr magnetons & $\mu _{\mu }/\mu _{B}$ & $4.84197097\times 10^{-3}$ \\ 
\ in nuclear magnetons & $\mu _{\mu }/\mu _{N}$ & $8.8905981$ \\ 
Muon magnetic moment anomaly 
\CustomNote[*]{Note}{$(\mu _{\mu }/(e\hbar /2m_{\mu }))-1$} & $a_{\mu }$ & $%
1.1659230\times 10^{-3}$ \\ 
Muon g-factor 
\CustomNote[*]{Note}{$2(1+a_{\mu })$} & $g_{\mu }$ & $2.002331846$ \\ 
Muon-proton magnetic moment ratio & $\mu _{\mu }/\mu _{p}$ & $3.18334547$%
\end{tabular}

\vspace{1pt}

\subparagraph{Proton\label{Proton}}

\begin{tabular}{lll}
\hline
\multicolumn{1}{c}{\hspace{2.85in}} &  &  \\ 
Proton mass & $m_{p}$ & $1.6726231\times 10^{-27}\unit{kg}$ \\ 
\ in electron volts 
\CustomNote[*]{Note}{$m_{p}c^{2}/\{e\}$} &  & $938.27231\unit{MeV}$ \\ 
Proton-electron mass ratio & $m_{p}/m_{e}$ & $1836.152701$ \\ 
Proton-muon mass ratio & $m_{p}/m_{\mu }$ & $8.8802444$ \\ 
Proton specific charge & $e/m_{p}$ & $9.5788309\times 10^{7}\unit{C}\unit{kg}%
^{-1}$ \\ 
Proton molar mass & $M\left( p\right) $, $M_{p}$ & $1.007276470\times 10^{-3}%
\unit{kg}\unit{mol}^{-1}$ \\ 
Proton Compton wavelength 
\CustomNote[*]{Note}{$h/m_{p}c$} & $\lambda _{C,p}$ & $1.32141002\times
10^{-15}\unit{m}$ \\ 
\ $\lambda _{C,p}/2\pi $ &  & $2.10308937\times 10^{-16}$ \\ 
Proton magnetic moment & $\mu _{p}$ & $1.41060761\times 10^{-26}\unit{J}%
\unit{T}^{-1}$ \\ 
\ in Bohr magnetons & $\mu _{p}/\mu _{B}$ & $1.521032202\times 10^{-3}$ \\ 
\ in nuclear magnetons & $\mu _{p}/\mu _{N}$ & $2.792847386$ \\ 
\ Diamagnetic shielding correction 
\CustomNote[*]{Note}{%
for protons in pure water, spherical sample, $25\unit{degC}$, $1-\mu
_{p}^{\prime }/\mu _{p}$} & $\sigma _{\text{H}_{\text{2}}\text{O}}$ & $%
25.689\times 10^{-6}$ \\ 
Shielded proton moment 
\CustomNote[*]{Note}{%
for protons in pure water, spherical sample, $25\unit{degC}$, $1-\mu
_{p}^{\prime }/\mu _{p}$} & $\mu _{p}^{\prime }$ & $1.41057138\times 10^{-26}%
\unit{J}\unit{T}^{-1}$ \\ 
\ in Bohr magnetons & $\mu _{p}^{\prime }/\mu _{B}$ & $1.520993129\times
10^{-3}$ \\ 
\ in nuclear magnetons & $\mu _{p}^{\prime }/\mu _{N}$ & $2.792775642$ \\ 
Proton gyromagnetic ratio & $\gamma _{p}$ & $26752.2128\times 10^{4}\unit{s}%
^{-1}\unit{T}^{-1}$ \\ 
& $\gamma _{p}/2\pi $ & $42.577469\unit{MHz}\unit{T}^{-1}$ \\ 
\ uncorrected 
\CustomNote[*]{Note}{%
for protons in pure water, spherical sample, $25\unit{degC}$, $1-\mu
_{p}^{\prime }/\mu _{p}$} & $\gamma _{p}^{\prime }$ & $26751.5255\times
10^{4}\unit{s}^{-1}\unit{T}^{-1}$ \\ 
& $\gamma _{p}^{\prime }/2\pi $ & $42.576375\unit{MHz}\unit{T}^{-1}$%
\end{tabular}

\vspace{1pt}

\subparagraph{Neutron\label{Neutron}}

\begin{tabular}{cll}
\hline
\hspace{2.85in} &  &  \\ 
\multicolumn{1}{l}{Neutron mass} & $m_{n}$ & $1.6749286\times 10^{-27}\unit{%
kg}$ \\ 
\multicolumn{1}{l}{\ in electron volts 
\CustomNote[*]{Note}{$m_{n}c^{2}/\{e\}v$}} &  & $939.56563\unit{MeV}$ \\ 
\multicolumn{1}{l}{Neutron-electron mass ratio} & $m_{n}/m_{e}$ & $%
1838.683662$ \\ 
\multicolumn{1}{l}{Neutron-proton mass ratio} & $m_{n}/m_{p}$ & $1.001378404$
\\ 
\multicolumn{1}{l}{Neutron molar mass} & $M\left( n\right) $, $M_{n}$ & $%
1.008664904\times 10^{-3}\unit{kg}\unit{mol}^{-1}$ \\ 
\multicolumn{1}{l}{Neutron Compton wavelength 
\CustomNote[*]{Note}{$h/m_{n}c$}} & $\lambda _{C,n}$ & $1.31959110\times
10^{-15}\unit{m}$ \\ 
\multicolumn{1}{l}{\ $\lambda _{C,n}/2\pi $} &  & $2.10019445\times 10^{-16}%
\unit{m}$ \\ 
\multicolumn{1}{l}{Neutron magnetic moment} & $\mu _{n}$ & $0.96623707\times
10^{-26}\unit{J}\unit{T}^{-1}$ \\ 
\multicolumn{1}{l}{\ in Bohr magnetons} & $\mu _{n}/\mu _{B}$ & $%
1.04187563\times 10^{-3}$ \\ 
\multicolumn{1}{l}{\ in nuclear magnetons} & $\mu _{n}/\mu _{N}$ & $%
1.91304275$ \\ 
\multicolumn{1}{l}{Neutron-electron magnetic moment ratio} & $\mu _{n}/\mu
_{e}$ & $1.04066882\times 10^{-3}$ \\ 
\multicolumn{1}{l}{Neutron-proton magnetic moment ratio} & $\mu _{n}/\mu
_{p} $ & $0.68497934$ \\ 
\multicolumn{1}{l}{\hspace{2.85in}} &  & 
\end{tabular}

\vspace{1pt}

\subparagraph{Deuteron\label{Deuteron}}

\begin{tabular}{cll}
\hline
\hspace{2.85in} &  &  \\ 
\multicolumn{1}{l}{Deuteron mass} & $m_{d}$ & $3.3435860\times 10^{-27}\unit{%
kg}$ \\ 
\multicolumn{1}{l}{\ in electron volts} &  & $1875.61339\unit{MeV}$ \\ 
\multicolumn{1}{l}{Deuteron-electron mass ratio} & $m_{d}/m_{e}$ & $%
3670.483014$ \\ 
\multicolumn{1}{l}{Deuteron-proton mass ratio} & $m_{d}/m_{p}$ & $%
1.999007496 $ \\ 
\multicolumn{1}{l}{Deuteron molar mass} & $M\left( d\right) $, $M_{d}$ & $%
2.013553214\times 10^{-3}\unit{kg}\unit{mol}^{-1}$ \\ 
\multicolumn{1}{l}{Deuteron magnetic moment} & $\mu _{d}$ & $%
0.43307375\times 10^{-26}\unit{J}\unit{T}^{-1}$ \\ 
\multicolumn{1}{l}{\ in Bohr magnetons} & $\mu _{d}/\mu _{B}$ & $%
0.4669754479\times 10^{-3}$ \\ 
\multicolumn{1}{l}{\ in nuclear magnetons} & $\mu _{d}/\mu _{N}$ & $%
0.857438230$ \\ 
\multicolumn{1}{l}{Deuteron-electron magnetic moment ratio} & $\mu _{d}/\mu
_{e}$ & $0.4664345460\times 10^{-3}$ \\ 
\multicolumn{1}{l}{Deuteron-proton magnetic moment ratio} & $\mu _{d}/\mu
_{p}$ & $0.3070122035$%
\end{tabular}

\vspace{1pt}

\subsubsection{Physico-Chemical Constants\label{PhysicoChemical}}

\begin{tabular}{cll}
\hspace{2.85in} & \hspace{0.6in} &  \\ 
\multicolumn{1}{l}{Avogadro's number} & $N_{A}$ & $6.0221367\times 10^{23}%
\unit{mol}^{-1}$ \\ 
\multicolumn{1}{l}{Avogadro constant} &  & $10^{23}\unit{mol}^{-1}$ \\ 
\multicolumn{1}{l}{Atomic mass constant 
\CustomNote[*]{Note}{$\frac{1}{12}m(^{12}C)$}} & $m_{u}$ & $1.6605402\times
10^{-27}\unit{kg}$ \\ 
\multicolumn{1}{l}{\ in electron volts 
\CustomNote[*]{Note}{$m_{u}c^{2}/\{e\}$}} &  & $931.49432\unit{MeV}$ \\ 
\multicolumn{1}{l}{Faraday constant} & $F$ & $96485.309\unit{C}\unit{mol}%
^{-1}$ \\ 
\multicolumn{1}{l}{Molar Planck constant} & $N_{A}h$ & $3.99031323\times
10^{-10}\unit{J}\unit{s}\unit{mol}^{-1}$ \\ 
\multicolumn{1}{l}{} & $N_{A}hc$ & $0.11962658\unit{J}\unit{m}\unit{mol}%
^{-1} $ \\ 
\multicolumn{1}{l}{Molar gas constant} & $R$ & $8.314510\unit{J}\unit{mol}%
^{-1}\unit{K}^{-1}$ \\ 
\multicolumn{1}{l}{Boltzmann constant} & $k$ & $1.380658\times 10^{-23}\unit{%
J}\unit{K}^{-1}$ \\ 
\multicolumn{1}{l}{\ in electron volts} &  & $8.617385\times 10^{-5}\unit{eV}%
\unit{K}^{-1}$ \\ 
\multicolumn{1}{l}{\ in hertz} &  & $2.083674\times 10^{10}\unit{Hz}\unit{K}%
^{-1}$ \\ 
\multicolumn{1}{l}{\ in wavenumbers} &  & $69.50387\unit{m}^{-1}\unit{K}%
^{-1} $ \\ 
\multicolumn{1}{l}{Molar volume (ideal gas) 
\CustomNote[*]{Note}{$T=273.15\unit{K}$, $p=101325\unit{Pa}$}} & $V_{m}$ & $%
22.41410\unit{L}\unit{mol}^{-1}$ \\ 
\multicolumn{1}{l}{\ Loschmidt constant 101325 Pa 
\CustomNote[*]{Note}{$T=273.15\unit{K}$, $p=101325\unit{Pa}$}} & $n_{0}$ & $%
2.686763\times 10^{25}\unit{m}^{-3}$ \\ 
\multicolumn{1}{l}{100 kPa 
\CustomNote[*]{Note}{%
\ $T=273.15\unit{K}$, $p=100\unit{kPa}$}} & $V_{m}$ & $22.71108\unit{L}\unit{%
mol}^{-1}$ \\ 
\multicolumn{1}{l}{Sackur-Tetrode constant 100 kPa%
\CustomNote[*]{Note}{$p_{0}=100\unit{kPa}$}} & $S_{0}/R$ & $-1.151693$ \\ 
\multicolumn{1}{l}{Sackur-Tetrode constant 101325 Pa 
\CustomNote[*]{Note}{$p_{0}=101325\unit{Pa}$}} &  & $-1.164856$ \\ 
\multicolumn{1}{l}{Stefan-Boltzmann constant} & $\sigma $ & $5.67051\times
10^{-8}\unit{W}\unit{m}^{-2}\unit{K}^{-4}$ \\ 
\multicolumn{1}{l}{First radiation constant} & $c_{1}$ & $3.7417749\times
10^{-16}\unit{W}\unit{m}^{2}$ \\ 
\multicolumn{1}{l}{Second radiation constant} & $c_{2}$ & $0.01438769\unit{m}%
\unit{K}$ \\ 
\multicolumn{1}{l}{Wien displacement law constant} & $b$ & $2.897756\times
10^{-3}\unit{m}\unit{K}$ \\ 
\multicolumn{1}{l}{Coulomb force constant} & $k_{0}$ & $8.98755\times 10^{9}%
\unit{N}\unit{m}^{2}\unit{C}^{-2}$ \\ 
\multicolumn{1}{l}{Permeability constant} & $\mu _{0}/4\pi $ & $10^{-7}\unit{%
T}\unit{m}\unit{A}^{-1}$%
\end{tabular}

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