Einstein's Photoelectric Equation

Einstein's postulate. In 1905, Albert Einstein proposed that light of frequency $\nu$ is not delivered continuously at all, but arrives, and is absorbed, in discrete packets (later named photons), each packet carrying a fixed quantum of energy

where $h=6.63\times10^{-34}\ \text{J s}$ is Planck's constant, the same constant Planck had introduced five years earlier to explain black-body radiation. Einstein further proposed that in the photoelectric interaction, a single photon is absorbed, in its ENTIRETY, by a single electron in the metal -- there is no sharing of one photon's energy among several electrons, and no electron can gather energy from more than one photon at ordinary light intensities.

The equation. If the photon's energy $h\nu$ is greater than the work function $\phi_0$ (the minimum energy needed to free that electron from the metal), the electron is ejected, carrying away the EXCESS energy as kinetic energy. The electron that was least tightly bound to begin with ends up with the MAXIMUM possible kinetic energy $K_{max}$, giving Einstein's photoelectric equation:

Combined with the electrical relation $K_{max}=eV_0$ from Section 11.4, this becomes

which is exactly a straight line when $V_0$ is plotted against $\nu$ -- matching Section 11.4's second graph precisely, with slope $h/e$ (the SAME for every metal, since $h$ and $e$ are universal constants -- exactly why the lines for different metals come out parallel) and an intercept that gives $\phi_0$ (or, equivalently, a frequency-axis intercept that directly gives the threshold frequency $\nu_0=\phi_0/h$). …