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

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On a Heuristic Point of View Concerning the Generation and Transformation of LightShow the German source

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by A. EinsteinShow the German source

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§ 7. On Stokes’s rule.Show the German source

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Let monochromatic light be transformed by photoluminescence into light of a different frequency, and, in accordance with the result just obtained, let it be assumed that both the generating and the generated light consist of energy quanta of magnitude $(R/N) \beta \nu$, where $\nu$ denotes the frequency in question.Show the German source The transformation process is then to be interpreted as follows.Show the German source Each generating energy quantum of frequency $\nu_1$ is absorbed and — at least when the distribution density of the generating energy quanta is sufficiently small — by itself alone gives rise to the production of a light quantum of frequency $\nu_2$; possibly, in the absorption of the generating light quantum, light quanta of frequencies $\nu_3$, $\nu_4$, etc., as well as energy of other kinds (e.g., heat) may also arise at the same time.Show the German source Through what intermediate processes this final result comes about is immaterial.Show the German source If the photoluminescent substance is not to be regarded as a permanent source of energy, then by the energy principle the energy of a generated energy quantum cannot be greater than that of a generating light quantum; the following relation must therefore hold:Show the German source $$\frac{R}{N} \beta \nu_2 \leqq \frac{R}{N} \beta \nu_1$$$R$Gas constant$N$Avogadro's number$\beta$Spectral constant B${\nu }_2$Frequency of the emitted light${\nu }_1$Frequency of the absorbed lightExplain this equationShow the German source orShow the German source $$\nu_2 \leqq \nu_1 .$$${\nu }_2$Frequency of the emitted light${\nu }_1$Frequency of the absorbed lightExplain this equationShow the German source This is Stokes’s well-known rule.Show the German source

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It is especially to be emphasized that with weak illumination, other circumstances being equal, the quantity of light generated must according to our conception be proportional to the intensity of the exciting light, since each exciting energy quantum will cause an elementary process of the kind indicated above, independently of the action of the other exciting energy quanta.Show the German source In particular, there will be no lower limit for the intensity of the exciting light below which the light would be incapable of exciting light.Show the German source

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According to the conception of the phenomena set forth here, deviations from Stokes’s rule are conceivable in the following cases:
1. when the number of energy quanta per unit volume simultaneously undergoing transformation is so large that an energy quantum of the generated light can receive its energy from several generating energy quanta;
2. when the generating (or generated) light does not have the energetic character belonging to a “black radiation” within the range of validity of Wien’s law, that is, when, e.g., the exciting light is produced by a body of so high a temperature that Wien’s law no longer holds for the wavelength in question.Show the German source

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The last-mentioned possibility deserves particular interest.Show the German source For according to the conception developed here it is not ruled out that a “non-Wien radiation”, even at great dilution, behaves energetically differently from a “black radiation” within the range of validity of Wien’s law.Show the German source

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Bern, 17 March 1905.Show the German source

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(Received 18 March 1905.)Show the German source