photoelectric effect

Meaning: Light arrives as photons, each with energy E = hf. One photon is absorbed by one electron in a metal. If the photon energy is at least the work function φ (the minimum energy needed to free an electron from the surface), the electron escapes with the leftover energy as kinetic energy. Below the threshold frequency f₀ = φ/h, no electrons are emitted at any intensity. Brighter light means more photons per second, so more electrons and a larger current, not faster electrons.

Equation: Kmax = hf − φ, where Kmax is the maximum kinetic energy of the ejected electrons (J), h is Planck's constant (6.63 × 10⁻³⁴ J·s), f is the light frequency (Hz), and φ is the work function (J).

On the MCAT: A passage graphs Kmax or stopping potential against frequency. The slope is h, the x-intercept is f₀, and the y-intercept is −φ. At fixed frequency, doubling the intensity doubles the current but leaves Kmax unchanged. A different metal shifts the intercepts but not the slope. Energies are often given in eV.

Common confusion: Students think that enough intensity of low-frequency light will eventually eject electrons. Energy is delivered one photon at a time, so intensity changes the number of photons, not the energy of each one. Also, Kmax is a maximum: ejected electrons have a range of kinetic energies.