= Einstein photoelectric equation
{c}
{title2=$K_{\max}=h\nu-\Phi$}
= Einstein's photoelectric equation
{c}
{synonym}
For the ideal single-<photon> metal model, <conservation of energy> gives
$$
h\nu=\Phi+K_{\max},\qquad
K_{\max}=h\nu-\Phi,\qquad
\nu\geq\nu_0=\frac{\Phi}{h}.
$$
Here $h$ is the <Planck constant>, $\nu$ the incident <frequency>, $\Phi$ the <work function>, and $K_{\max}$ the largest emitted <kinetic energy> relative to the nearby <vacuum> level. An <Electron> at the highest occupied <energy> can reach this edge if it escapes without an additional loss. An <Electron> starting lower or losing <energy> within the metal emerges below it. The material takes recoil <momentum>; its recoil <energy> is neglected in this model.
For an original chosen example, take $\Phi=2.30\,\mathrm{eV}$ and $\nu=8.00\times10^{14}\,\mathrm{Hz}$. Using $h=6.62607015\times10^{-34}\,\mathrm{J\,s}$ and the <elementary charge> $e=1.602176634\times10^{-19}\,\mathrm C$ gives $h\nu=3.308534\,\mathrm{eV}$ and $K_{\max}=1.008534\,\mathrm{eV}$. The ideal <stopping potential> is therefore $1.008534\,\mathrm V$. At $4.00\times10^{14}\,\mathrm{Hz}$ the same model supplies only $1.654267\,\mathrm{eV}$ per <photon>, so this single-<photon> channel is closed. A negative result from $h\nu-\Phi$ means no emission through that channel, not an emitted <Electron> with negative <kinetic energy>.
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