light quanta

The equation explained

e V_s = h\nu - \Phi \implies V_s = \frac{h}{e}\nu - \frac{\Phi}{e}

In wordsThe energy a light quantum carries in, Planck's constant times the frequency, less the work an electron spends escaping the surface, is what is left to the electron's charge climbing through the stopping potential.OverviewThe same law as the display above, with the letters physics has used since:

h

for the quantum of action,

e

for the electron's charge,

\Phi

for the escape work.Full explanationNothing has changed but the letters. Where the paper writes

\frac{R}{N}\beta\nu

for the energy of one quantum, this writes

h\nu

; where it writes

\varepsilon

for the charge and

P

for the work of escape, this writes

e

and

\Phi

. Dividing through by the charge puts the law in the form an experiment reads off a graph: the stopping potential is a straight line in the frequency, of slope

\frac{h}{e}

and intercept

-\frac{\Phi}{e}

. The slope is the same for every substance, which is the part of the law that can be checked without knowing anything about the surface, and the intercept is the part that belongs to the substance alone.Every step

\frac{R}{N}\beta\nu = h\nu

The energy of one quantum, in the paper's letters and then in the modern one. The paper's

\frac{R}{N}\beta

is the number physics now writes

h

, and § 6 of the paper computes it as

6{,}5537\cdot 10^{-27}

erg s.

e V_s = h\nu - \Phi

The law of the display above with those letters put in: the quantum's energy, less the escape work, is the energy the electron still has, and the stopping potential is what just takes it away again.

V_s = \frac{h}{e}\nu - \frac{\Phi}{e}

Divide by the charge. In this form the law is a straight line in the frequency, and the two things an experiment can read from it, the slope and the intercept, are separated.Historian's marginThe modern letters are this edition's, not Einstein's. The paper of 1905 has no

h

in it: it writes the quantum's energy as

\frac{R}{N}\beta\nu

, built from the gas constant, Avogadro's number and Wien's constant, and it is Planck's 1900 radiation work that the constant comes from. Writing

h

here is a rename and nothing more, and it imports no later physics; the site's notation concordance records the substitution for § 8.AlsoOverviewFull explanationEvery stepHistorian's margin

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