light quanta
The equation explained
In wordsThe potential Π times the charge of a gram-equivalent, plus the work per gram-equivalent, is at most the gas constant R times the constant β times the frequency.OverviewDrop the assumption that some quanta give their whole energy to a single electron, and the equation weakens to an inequality: what the electron carries away can only be less than one quantum, never more.Full explanationThe paper says what the preceding equation assumed: that the energy of at least a part of the exciting light's quanta is given up completely, each to a single electron. It calls that assumption a natural one, and here it sets it aside. If an electron may take up only part of a quantum's energy, the fastest electron's energy is no longer fixed at one whole quantum less the work of leaving; it can fall short of it. So the two sides need no longer be equal, and what remains is that they cannot be exceeded. The relation is then one-sided, and the straight line of the preceding paragraphs becomes an upper bound rather than a prediction.Every stepThe relation of the preceding display, which assumed that a quantum gives its whole energy to one electron.Move the work per gram-equivalent to the left. In this form the left side is the whole energy the electron received and the right side is one quantum.Without the assumption an electron takes up only part of a quantum, so the energy it received is at most one quantum and may be less: the printed line.Also