Work function

Also called phi

The work function of a material, written phi, is the minimum energy needed to free an electron from atoms in that material. It sets the threshold frequency for the photoelectric effect and is subtracted from the photon energy to leave kinetic energy.

The work function is a property of the material, not of the light, and it is usually quoted in electron volts. Essential knowledge 15.5.A.3.i defines it as the minimum energy required to emit an electron from atoms in the material.

It enters the sheet equation as the subtraction in Kmax=hfϕK_{\max} = hf - \phi. An absorbed photon spends at least ϕ\phi on getting the electron out; whatever is left over is kinetic energy. The result is a maximum rather than a single value precisely because 15.5.A.3.i makes ϕ\phi the minimum escape cost, and not every electron escapes that cheaply.

Set Kmax=0K_{\max} = 0 and you have the threshold frequency, the lowest frequency that can eject anything at all.

f0=ϕhf_0 = \frac{\phi}{h}

That rearrangement is not printed separately. It is the same sheet equation read at the point where the escaping electron just barely escapes. A material with a larger work function needs a higher threshold frequency and gives a smaller KmaxK_{\max} at any frequency above it.

The Topic 15.5 boundary statement is worth having in full: "Where applicable, work functions for materials will be provided on the exam; students are not expected to know values of work functions or variables of a material that influence the magnitude of its work function." So there is no table to memorize, and no explaining why one metal's ϕ\phi beats another's.

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