Threshold frequency

Essential knowledge 15.5.A.2 names it directly: the emission of electrons via the photoelectric effect requires a minimum frequency of incident light, called the threshold frequency. Write it $f_0$.

Set the maximum kinetic energy to zero in the sheet equation $K_{\max} = hf - \phi$ and you have it:

The Modern Physics group of the AP Physics 2 sheet prints ten equations and this is not one of them. It is $K_{\max} = hf - \phi$ read at the point where the electron only just escapes, so derive it rather than recall it.

Brightness cannot buy you frequency. This is the whole reason the term exists. Statement 15.5.A.2.i says light at the threshold frequency or higher induces emission regardless of the number of photons that strike the material, and 15.5.A.2.ii says the energy of the emitted electrons does not depend on the number of incident photons. Red light below $f_0$ ejects nothing from a plate you could stand under all day, while one dim ultraviolet lamp above $f_0$ starts a current at once. A wave model predicts the opposite, which is what made this observation decisive.

In wavelength the inequality flips. Since $\lambda = c/f$, the threshold becomes a longest usable wavelength, $\lambda_0 = hc/\phi$, and light works when $\lambda \le \lambda_0$. With the printed $hc = 1240 \, \text{eV} \cdot \text{nm}$, a material of work function 2.0 eV has $\lambda_0 = 620$ nm and $f_0 = 4.8 \times 10^{14}$ Hz. Students who carry "bigger is better" across from frequency to wavelength lose the mark here.