Annus MirabilisEinstein in 1905
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Translation

On a Heuristic Point of View Concerning the Generation and Transformation of Light

Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt

by A. Einstein

§ 2. On Planck’s determination of the elementary quanta.

We shall show in what follows that the determination of the elementary quanta given by Mr. Planck is, to a certain extent, independent of the theory of “black radiation” he set up.

Planck’s formula[1)] for ϱν\varrho_\nu, which satisfies all experience so far, reads ϱν=αν3eβνT−1,\varrho_\nu = \frac{\alpha \nu^3}{e^{\frac{\beta \nu}{T}} - 1},Spectral energy densitySpectral constant AFrequency of the lightSpectral constant BTemperature of the radiationExplain this equation where α=6,10⋅10−56,\alpha = 6{,}10 \cdot 10^{-56},Spectral constant AExplain this equation β=4,866⋅10−11.\beta = 4{,}866 \cdot 10^{-11}.Spectral constant BExplain this equation For large values of T/νT/\nu, i.e., for large wavelengths and radiation densities, this formula goes over in the limit into the following: ϱν=αβν2T.\varrho_\nu = \frac{\alpha}{\beta} \nu^2 T.Spectral energy densitySpectral constant ASpectral constant BFrequency of the lightTemperature of the radiationExplain this equation One sees that this formula agrees with the one developed in § 1 from Maxwell’s theory and the electron theory. By equating the coefficients of the two formulas one obtains: RN8πL3=αβ\frac{R}{N} \frac{8 \pi}{L^3} = \frac{\alpha}{\beta}Gas constantAvogadro's numberSpeed of lightSpectral constant ASpectral constant BExplain this equation or N=βα8πRL3=6,17⋅1023,N = \frac{\beta}{\alpha} \frac{8 \pi R}{L^3} = 6{,}17 \cdot 10^{23},Avogadro's numberSpectral constant BSpectral constant AGas constantSpeed of lightExplain this equation i.e., an atom of hydrogen weighs 1/N1/N grams =1,62⋅10−24= 1{,}62 \cdot 10^{-24} g. This is exactly the value found by Mr. Planck, which agrees satisfactorily with the values for this quantity found by other means.

We therefore arrive at the conclusion: the greater the energy density and the wavelength of a radiation, the more useful do the theoretical foundations we have used prove to be; for small wavelengths and small radiation densities, however, they fail completely.

In what follows, “black radiation” will be considered in connection with experience, without taking as a basis any picture of the generation and propagation of the radiation.

Bern, 17 March 1905.

(Received 18 March 1905.)