work function

Meaning: Electrons in a metal are bound by attractive forces. The work function φ is the least energy that must be supplied to remove the most loosely bound electron from the surface. It is a property of the material, so different metals have different values. A photon gives its energy to one electron in an all-or-nothing event. If hf is less than φ, no electrons are emitted, however intense the light. If hf is greater than φ, the excess appears as the kinetic energy of the ejected electron.

Equation: Kmax = hf − φ, where Kmax is the maximum kinetic energy of the emitted electron (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). The threshold frequency is f₀ = φ/h. Work functions are often given in eV, where 1 eV = 1.60 × 10⁻¹⁹ J.

On the MCAT: Passages describe light shining on a metal and ask how Kmax or the current changes. Raising frequency above f₀ raises Kmax. Raising intensity at fixed frequency raises the number of electrons, so the current rises, but Kmax stays the same. On a graph of Kmax versus f, the slope is h, the x-intercept is f₀, and the y-intercept is −φ.

Common confusion: Students think brighter light can eject electrons when dim light of the same low frequency cannot. Intensity changes the number of photons, not the energy of each one. Only a higher frequency (shorter wavelength) helps.