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Numerical value of the universal constant of Planck, $h$.
R. Ladenburg. Bericht uber die Bestimmung von Plancks elementarem Wirkungsquantum $h$. Jahrb. d. Rad. u. Elektr. 17, p. 93, 1920.
The constant $h$ is apparently destined to figure in all relations that quantitatively describe the interrelations of light and matter. Independently of the hypotheses that underlie the derivation of the corresponding formulas, the latter in most cases describe the phenomena with impeccable accuracy. The experimental possibilities for determining $h$ are likewise expanding from year to year. The author of the review being abstracted selects those cases in which $h$ can be determined most accurately, gives a brief exposition of the theory and methods of determination, and compiles a summary of the values of $h$ on the basis of the experimental material up to and including 1920. (Table 1).
Table 1.
| METHOD. | $h \cdot 10^{27}$ |
|---|---|
| I. Study of the black body: | |
| a) Isochromat method (Warburg and co-workers) | $6,540 \pm 0,02$ |
| b) Constant $\sigma$ of the Stefan–Boltzmann law for $c = 5,8 \cdot 10^{-5}$ (according to Gerlach) | $6,518 \pm 0,03$ |
| II. Einstein’s equation: | |
| a$_1$) Photoelectric measurements of Millikan with Na and Li. | $6,577$ |
| a$_2$) Photoelectric measurements of Hennigs and Kadesch with Mg, Al, Zn, Cu, Fe, Sn | $6,43$ |
| b$_1$) Resonance and ionization potentials, mean of 16 values | $6,58 \pm 0,03$ |
| b$_2$) Ionization potential of He and Hg according to Franck and Knipping | $6,54 \pm 0,03$ |
| c$_1$) Limit of the continuous X-ray spectrum according to Wagner | $6,520 \pm 0,02$ |
| c$_2$) The same according to Blake and Duane | $6,557 \pm 0,013$ |
| III. Theory of spectral series of Bohr. | |
| Values of the Rydberg constant from Paschen’s measurements. | $6,545 \pm 0,013$ |
The accuracy of the various methods presented in the table is different; therefore it makes no sense to derive an average value. The greatest accuracy (as estimated in advance) should be ascribed to the measurements of black-body radiation and to the spectral determinations of the Rydberg constant. Both methods give, for $h$, a concordant value
\[ h = 6,54 \cdot 10^{-27}\ \text{erg. sec.} \]
with an accuracy of about 2 per mille. If, for the magnitude of the electron charge, one adopts Millikan’s figure
\[ e = 4,774 \pm 0,004 \cdot 10^{-10} \]
then we obtain the following table of values of constants which often occur in many physico-chemical relations. (Table 2).
Table 2.
| $h = 6{,}54 \cdot 10^{-27}\ \mathrm{erg.\ sec.}$ | Planck’s constant. |
| $e = 4{,}774 \cdot 10^{-10}$ | Electron charge. |
| $m = 8{,}996 \cdot 10^{-27}$ | Rest mass of the electron. |
| $m_{\mathrm H} = 1{,}6490 \cdot 10^{-24}$ | Mass of the hydrogen atom. |
| $\dfrac{e}{m} = 1{,}769 \cdot 10^{7} \cdot 3 \cdot 10^{10} = 5{,}3 \cdot 10^{17}\ C.G.S.$ | |
| $\dfrac{e}{m_{\mathrm H}} = F = 9650 \cdot 3 \cdot 10^{10} = 28950\ C.G.S.$ | Faraday number. |
| $\dfrac{m_{\mathrm H}}{m} = 1833$ | |
| $\dfrac{m_{\mathrm{He}}}{m} = 1843$ | Ratio of the mass of [[unclear: particle/atom]] to the mass of the electron. |
| $N = \dfrac{1}{m_{\mathrm H}} = \dfrac{F}{e} = 6{,}064 \cdot 10^{23}$ | Number of molecules in a gram-molecule. |
| $M_{\mathrm H} = 1{,}0077$ | Atomic weight of hydrogen. |
| $M_{\mathrm{He}} = 4{,}002$ | Atomic weight of helium. |
| $R_0 = 8{,}315 \cdot 10^{7}$ | Gas constant. |
| $A = 4{,}185 \cdot 10^{7}$ | Mechanical equivalent. |
| $k = \dfrac{R_0}{N} = 1{,}3711 \cdot 10^{-16}\ \mathrm{erg.\ grad.}^{-1}$ | |
| $R_{\infty} = 109737{,}11$ | Rydberg constant, assuming an infinitely large mass of the atomic nucleus. |
| $R_{\mathrm H} = 109677{,}69$ | Rydberg constant for the hydrogen atom. |
| $R_{\mathrm{He}} = 109722{,}14$ | Rydberg constant for the helium atom. |
| $c_2 = \dfrac{c \cdot h}{k} = 1{,}430\ \mathrm{cm.\ grad.}$ | Planck’s-law constant. |
| $\sigma = \left(\dfrac{\pi \cdot k}{e}\right)^4 \dfrac{\left(\dfrac{e}{m}\right)\cdot R_{\infty}}{15\pi e} =$ $= 5{,}738 \cdot 10^{-5}\ \dfrac{\mathrm{erg.\ cm.}^{-2}\ \mathrm{sec.}^{-1}}{\mathrm{grad.}^{4}}$ |
Stefan–Boltzmann law constant. |
| $b = \dfrac{c \cdot h}{k \cdot 4{,}9651} = 0{,}2885\ \mathrm{cm.\ grad.}$ | Wien displacement-law constant. |
| $\alpha = \dfrac{2\pi e^2}{h \cdot c} = 7{,}299 \cdot 10^{-3}$ | Sommerfeld fine-structure constant of spectral lines. |
| $r_1 = \dfrac{e}{m} \cdot \dfrac{h^2}{4\pi^2 e^3} = 0{,}528 \cdot 10^{-8}\ \mathrm{cm.}$ | Radius of the first electron orbit in hydrogen according to Bohr. |
| $C_0 = \lg \dfrac{(2\pi)^{5/2} k^{5/2}}{N^{3/2}\cdot h^3 \cdot 1{,}013.01} = -1{,}587$ | Universal part of the chemical constant according to Nernst. |
S. Rosenblum.