Results · §7 · fluorescence and its conditions

Page 144

Stokes's rule

If each exciting quantum of frequency $\nu_1$ is absorbed and on its own gives rise to a light quantum of frequency $\nu_2$ , the energy principle requires $\frac{R}{N}\beta\nu_2 \leqq \frac{R}{N}\beta\nu_1$ , that is $\nu_2 \leqq \nu_1$ , which is the known rule of Stokes.

As printed

Wenn die photolumineszierende Substanz nicht als eine beständige Quelle von Energie anzusehen ist, so kann nach dem Energieprinzip die Energie eines erzeugten Energiequants nicht größer sein als die eines erzeugenden Lichtquants; es muß also die Bezeichnung gelten: $\frac{R}{N} \beta \nu_2 \leqq \frac{R}{N} \beta \nu_1$ Gas constantAvogadro's numberSpectral constant BFrequency of the emitted lightFrequency of the absorbed lightExplain this equation oder $\nu_2 \leqq \nu_1 .$ Frequency of the emitted lightFrequency of the absorbed lightExplain this equation Dies ist die bekannte Stokessche Regel.

Text on page 144 of the German source, § 7, paragraph 1

In modern notation

h\,\nu_2 \le h\,\nu_1

Premise: The photoluminescent substance is not to be regarded as a permanent source of energy; only then does the energy principle bound the produced quantum.
Premise: Each exciting quantum acts on its own, at least when the exciting quanta are sparse enough; the absorption may also produce quanta of other frequencies and energy of another kind, such as heat.
Conditional: The paper names when deviations are conceivable: when so many quanta are being transformed at once that one produced quantum can take its energy from several, and when the exciting or produced light is not of the kind Wien's law describes, for instance light from a body so hot that Wien's law fails at the wavelength in question.

Decoder

$\nu_1$: The frequency of the exciting light, absorbed by the photoluminescent substance.
$\nu_2$: The frequency of the light the substance produces.
$\frac{R}{N}\beta\nu$: The energy of one quantum of light of frequency $\nu$ , taken from § 6 for both the exciting and the produced light.

Try it

LQ-07: Choose the exciting frequency: can the frequency of the emitted light exceed it while each quantum acts on its own? Choose the preset “Stokes's Rule (§7 as printed)” there.

LQ-07: Let two quanta act together: which of the paper's two conceivable deviations is this? Choose the preset “Deviation Case 1 (k = 2 multi-quantum)” there.

Where this stops: The limit on frequency holds under these conditions; it does not forbid higher-frequency emission in general. The budget does not predict actual material rates or spectra. A dense field need not satisfy the independent-quantum assumptions used in the analogy. Read the argument

Argument: A consequence of the quantum picture and the energy principle
Model: Holds when each exciting quantum acts on its own and the substance supplies no energy
Evidence: Accounts for a rule already known from experiment
History: The rule was known before 1905, and the paper calls it known; its derivation from energy quanta is introduced here

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§7 · fluorescence and its conditions

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