Annus MirabilisEinstein in 1905
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light quanta

The equation explained

Rβν≧J.R \beta \nu \geqq J .
In wordsThe gas constant R times the constant β times the frequency, which is the energy of one gram-equivalent's worth of light quanta, is at least the work of ionization per gram-equivalent.OverviewIf one absorbed quantum ionizes one molecule, the work needed to ionize a molecule cannot be more than the energy of the quantum that does it. Counted by the gram-equivalent, that is this inequality.Full explanationSection 9 turns to the ionization of a gas by ultraviolet light. The paper says we shall have to assume that one absorbed light energy quantum is used to ionize one gas molecule. What follows first is a bound: the work of ionization of a molecule, which the paper is careful to call the theoretically necessary work, cannot be greater than the energy of an absorbed effective quantum. Multiplying both by the number of molecules in a gram-molecule turns the statement about one molecule into one about a gram-equivalent, where the quantum's energy becomes RβνR \beta \nu and the ionization work is what the paper writes JJ. The inequality is a bound and not an equation, because a quantum may carry more energy than ionization needs.Every stepRNβν\frac{R}{N} \beta \nuThe energy of one light quantum at the frequency ν\nu, from section 6.RNβν≧JN\frac{R}{N} \beta \nu \geqq \frac{J}{N}One quantum ionizes one molecule, so the quantum's energy is at least the work of ionizing one molecule, which is the work per gram-equivalent shared out over the molecules in it.Rβν≧J.R \beta \nu \geqq J .Multiply both sides by the number of molecules in a gram-molecule: the printed line.Also

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