Work Function and Stopping Voltage

Every metal holds its electrons with a certain grip. The work function, written phi, is the minimum energy needed to rip the most loosely bound electron free and send it into the open. A photon hitting the metal hands over its whole energy, hf, in one shot. If hf is less than phi, nothing happens no matter how bright the light is: one photon, one electron, and that photon just wasn't strong enough. Each metal has its own phi, so each has its own cutoff frequency below which the photoelectric effect simply will not start.

Once hf exceeds phi, the leftover energy becomes the electron's kinetic energy: KE_max = hf - phi. The fastest electrons are the ones that needed the least energy to escape, barely overcoming phi. To measure that leftover energy without touching the electron, physicists run the ejected electrons into a reverse electric field. Turn up that reverse voltage until even the fastest electron can't cross it, and the current drops to zero. That voltage, the stopping voltage V_stop, satisfies eV_stop = KE_max, so a straightforward voltmeter reading gives you the electron's energy directly.

This sits right next to the photoelectric effect's big conceptual claim: light delivers energy in discrete photon packets, not as a continuous wave. The work function and stopping voltage are the two numbers that turn that claim into something measurable, bridging photon energy (hf) and particle kinetic energy, and they set up the later idea of threshold wavelength, where phi alone decides which colors of light can ever free an electron.