The Photoelectric Effect

Light striking a metal surface can eject electrons, but only above a certain frequency. That threshold makes no sense if light is a smooth wave spreading energy evenly over time, because then enough dim light, given enough time, should eventually pile up enough energy to free an electron. It never does. The fix is to treat light as a stream of photons, each carrying energy E = hf, where h is Planck's constant and f is frequency. One photon meets one electron and hands over all its energy at once, or nothing happens. If hf is less than the work function of the metal, the minimum energy needed to pull an electron free, that photon simply cannot do the job, no matter how many identical photons arrive per second.

Above the threshold frequency, the leftover energy after escaping becomes the electron's kinetic energy: KE_max = hf - W, where W is the work function. Plot KE_max against frequency and you get a straight line: the slope is Planck's constant, the x-intercept is the threshold frequency, and the y-intercept (extended backward) is -W. This single graph ties the whole model together and gives a direct, measurable way to pull h out of a tabletop experiment.

This sits right next to the wave picture of light from earlier units: diffraction and interference still need waves, but ejection needs particles. Photons here also set up the next idea, matter waves, where particles like electrons turn out to have wave behavior too.