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From Current Literature
Values of Certain Fundamental Physical Constants According to Data as of December 1950
Du Mond and Cohen published*) the following brief summary of the results of their revision of the values of a number of fundamental physical constants according to data as of December 1950. As is known, since the publication of the results of the preceding revision of the values of the constants, carried out by the authors in January 1948, the values of some constants have undergone substantial refinement and change.
In processing the experimental data, the authors came to the conclusion that measurements of any given constant cannot be considered in isolation from measurements of other constants, but that the entire body of different measurements should be considered at once. The results of such a combined treatment of the experimental data are given in the table.
The experimental data themselves and the details of the authors’ treatment are not presented.
The value of each quantity is accompanied by a coefficient \(\Gamma\), indicating (in parts per million) the change that must be introduced into the given value when the value of the constant \(G^2\), entering into the equation
\[ \Delta \nu_H = \alpha^2 \left(\frac{\mu_p}{\mu_0}\right) R_\infty G^{-2}, \]
is changed by one part per million, if further development of theoretical knowledge requires a change in the present value of this constant \(G^2 = 0.004751364\). In the table, the physical scale of atomic weights is used exclusively.
) J. W. M. Du Mond and E. R. Cohen, Phys. Rev. 82*, 555 (1951).
Values of Certain Fundamental Physical Constants (December 1950)
| Symbol | Quantity | Value | |
|---|---|---|---|
| \(N\) | Avogadro number | \((6.02544 \pm 0.00011)\cdot 10^{23}\,(\text{g-mole})^{-1}\) (phys.) | \(-1.241\,\text{G}\) |
| \(c\) | Speed of light | \(299790.2 \pm 0.9\ \text{km/sec}\) | \(0.023\,\text{G}\) |
| \(e\) | Electron charge | \((4.80223 \pm 0.00007)\cdot 10^{-10}\) electrostatic units | \(1.291\,\text{G}\) |
| \(m\) | Rest mass of the electron | \((9.10721 \pm 0.00025)\cdot 10^{-28}\ \text{g}\) | \(1.077\,\text{G}\) |
| \(h\) | Planck constant | \((6.62377 \pm 0.00018)\cdot 10^{-27}\ \text{erg}\cdot\text{sec}\) | \(2.073\,\text{G}\) |
| \(\dfrac{\lambda_g}{\lambda_s}\) | Conversion factor for transition from X-units to mÅ | \(1.002020 \mp 0.000011\) | \(0.349\,\text{G}\) |
| \(F=\dfrac{Ne}{c}\) | Faraday number | \(9651.94 \pm 0.07\ \dfrac{\text{electromagn. units}}{\text{g-mole}}\) (phys.) | \(0.027\,\text{G}\) |
| \(\dfrac{h}{e}\) | — | \((1.379311 \pm 0.000018)\cdot 10^{-17}\ \dfrac{\text{erg}\cdot\text{sec}}{\text{electrostat. unit}}\) | \(0.782\,\text{G}\) |
| \(\dfrac{e}{mc}\) | Specific charge of the electron | \((1.758897 \pm 0.000032)\cdot 10^{7}\ \dfrac{\text{electromagn. units}}{\text{g}}\) | \(0.191\,\text{G}\) |
| \(\dfrac{h}{m}\) | — | \(7.27311 \pm 0.00009\ \dfrac{\text{cm}^{2}}{\text{sec}}\) or \(\dfrac{\text{erg}\cdot\text{sec}}{\text{g}}\) | \(0.966\,\text{G}\) |
| \(\alpha=\dfrac{2\pi e^{2}}{hc}\) | Fine-structure constant | \((7.29698 \pm 0.00005)\cdot 10^{-3}\) | \(0.486\,\text{G}\) |
| \(\alpha^{-1}\) | — | \(137.0429 \mp 0.0009\) | \(-0.486\,\text{G}\) |
| \(\lambda_{ce}\) | Compton wavelength for the electron | \((2.426067 \pm 0.000032)\cdot 10^{-10}\ \text{cm}\) | \(0.973\,\text{G}\) |
Continuation
| Symbol / formula | Quantity | Value | |
|---|---|---|---|
| $Nm$ | Atomic weight of the electron | $(5{,}48749 \pm 0{,}00010)\cdot 10^{-4}$ (phys.) | $-0{,}164\,\Gamma$ |
| $a_0=\dfrac{h^2}{4\pi^2me^3}$ | Radius of the first Bohr orbit | $(5{,}29151 \pm 0{,}00003)\cdot 10^{-9}\ \mathrm{cm}$ | $0{,}487\,\Gamma$ |
| $r_0=e^2m^{-1}c^{-2}$ | Classical radius of the electron | $(2{,}81751 \pm 0{,}00006)\cdot 10^{-13}\ \mathrm{cm}$ | $1{,}459\,\Gamma$ |
| $H$ | Atomic weight of hydrogen | $1{,}0081284 \pm 0{,}0000030$ (phys.) | — |
| $H^+=H-Nm$ | Atomic weight of the proton | $1{,}0075797 \pm 0{,}0000030$ (phys.) | $8{,}94\cdot 10^{-5}\,\Gamma$ |
| $\dfrac{H^+}{Nm}$ | Ratio of the proton mass to the electron mass | $1836{,}139 \pm 0{,}034$ | $0{,}164\,\Gamma$ |
| $R_\infty$ | Rydberg constant for infinite mass | $109737{,}323 \pm 0{,}010\ \mathrm{cm}^{-1}$ | — |
| $R_{\mathrm H}=\left(1-\dfrac{Nm}{H}\right)R_\infty$ | Rydberg constant for hydrogen | $109677{,}591 \pm 0{,}010\ \mathrm{cm}^{-1}$ | $8{,}94\cdot 10^{-5}\,\Gamma$ |
| $\mu=\dfrac{mH^+}{H}$ | Reduced mass of the electron in the hydrogen atom | $(9{,}10225 \pm 0{,}00024)\cdot 10^{-28}\ \mathrm{g}$ | $1{,}077\,\Gamma$ |
| $\sigma=\dfrac{2\pi^5R_0^4}{15c^2h^3N^4}$ | Stefan–Boltzmann constant | $(5{,}6699 \pm 0{,}0009)\cdot 10^{-5}\ \dfrac{\mathrm{erg}}{\mathrm{cm}^2\,\mathrm{sec}\cdot\mathrm{degree}}$ | $-1{,}301\,\Gamma$ |
| $c_1=8\pi hc$ | First radiation constant | $4{,}99071 \pm 0{,}00014)\cdot 10^{-15}\ \mathrm{erg}\cdot\mathrm{cm}$ | $2{,}096\,\Gamma$ |
| \(c_2=\dfrac{hc}{k_0}\) | Second radiation constant | \(1.43868 \pm 0.00006\ \mathrm{cm\cdot degree}\) | \(0.855\,\Gamma\) |
| \(\dfrac{c_2}{c}\) | Constant of atomic heat capacity | \((4.79894 \pm 0.00021)\cdot 10^{-11}\ \mathrm{sec\cdot degree}\) | \(0.832\,\Gamma\) |
| \(k=\dfrac{R_0}{N}\) | Boltzmann constant | \((1.38026 \pm 0.00006)\cdot 10^{-16}\ \mathrm{erg/degree}\) | \(1.241\,\Gamma\) |
| \(\lambda_{\max}T=\dfrac{R_0}{chN}=\dfrac{1}{4.965114\,k_0}=0.2014052\,c_2\) | Constant in Wien’s displacement law | \(0.289757 \pm 0.000012\ \mathrm{cm\cdot degree}\) | \(0.855\,\Gamma\) |
| \(\mu_0=\dfrac{he'}{4\pi m}\) | Bohr magneton | \((0.927120 \pm 0.000022)\cdot 10^{-20}\ \mathrm{erg\cdot gauss}\) | \(2.264\,\Gamma\) |
| \(\sqrt{\dfrac{3k}{N}}=\sqrt{\dfrac{3R_0}{N}}\) | Factor at the square root in the Curie constant for determining the magnetic moment per molecule | \((2.62148 \pm 0.00007)\cdot 10^{-20}\left(\dfrac{\mathrm{erg\cdot mole}}{\mathrm{degree}}\right)^{1/2}\) (phys.) | \(1.241\,\Gamma\) |
| \(E_0=\dfrac{c^2}{10^{14}F'}\) | Conversion factor for going from atomic mass units to MeV | \(931.152 \pm 0.008\ \dfrac{\mathrm{MeV}}{\text{atomic mass unit}}\) (phys.) | \(0.019\,\Gamma\) |
| \(E_g=\dfrac{c^3}{10^{14}e'}\) | Conversion factor for going from grams to MeV | \((5.61060 \pm 0.00009)\cdot 10^{26}\ \dfrac{\mathrm{MeV}}{\mathrm{g}}\) | \(-1.222\,\Gamma\) |
| \(E_e=\dfrac{c^2m}{10^{14}e'}\) | Energy corresponding to the mass of the electron (in MeV) | \(0.510969 \pm 0.000010\ \dfrac{\mathrm{MeV}}{\text{electron}}\) | \(9.145\,\Gamma\) |
| \(k_p=\dfrac{E_eH^+}{Nm}\) | Energy corresponding to the proton mass (in MeV) | \(938.210 \pm 0.008\ \dfrac{\mathrm{MeV}}{\text{proton}}\) | \(0.019\,G\) |
| \(\lambda_{cp}=\lambda_{ce}\dfrac{Nm}{H^+}\) | Compton wavelength for the proton | \((1.321287 \pm 0.000017)\cdot 10^{-13}\ \mathrm{cm}\) | \(0.809\,G\) |
| \(\lambda_0=\dfrac{hc^2}{10^8e}\) | Wavelength corresponding to \(1\ \mathrm{eV}\) | \((12396.44 \pm 0.17)\cdot 10^{-8}\ \mathrm{cm}\) | \(0.828\,G\) |
| \(\tilde{\nu}_0=\dfrac{10^8e}{hc^2}\) | Wave number corresponding to \(1\ \mathrm{eV}\) | \((8066.63 \pm 0.11)\ \mathrm{cm}^{-1}\) | \(-0.828\,G\) |
| \(\dfrac{e}{c}\cdot 10^8\) | Energy corresponding to \(1\ \mathrm{eV}\) | \((1.60184 \pm 0.000024)\cdot 10^{-12}\ \mathrm{erg}\) | \(2.268\,G\) |
| \(\dfrac{F'}{R_0}\cdot 10^8\) | Temperature corresponding to \(1\ \mathrm{eV}\) | \(11605.6 \pm 0.5\) absolute degrees | \(0.027\,G\) |
| \(n_0=\dfrac{N}{V_0}\) | Loschmidt number | \((2.68744 \pm 0.00007)\cdot 10^{19}\ \mathrm{cm}^{-3}\) | \(1.241\,G\) |
| \(\dfrac{S_0}{R_0}=\ln\dfrac{(2\pi K)^{3/2}(2.71828)^{5/2}}{h^3V^{5/2}}\) | Sackur--Tetrode constant | \(-5.57305 \pm 0.00007\) | \(0.225\,G\) |
| \(S_0\) | -- | \((4.634907 \pm 0.000036)\cdot 10^8\ \dfrac{\mathrm{erg}}{\mathrm{mole}\cdot\mathrm{degree}}\) (physical) | \(0.225\,G\) |