The photoelectric effect
Classical physics says brighter light should always knock electrons out, given enough time. It doesn't. Pick a metal, tune the light's frequency, and watch. Below one exact frequency — nothing comes out, no matter how intense the beam. Above it, electrons fly out instantly, and their energy depends only on colour, never on brightness.
What the simulator is showing
Threshold frequency
Below ν₀, absolutely no electrons are emitted — no matter how bright (intense) the light is. Classical wave theory couldn't explain this at all; photon theory explains it immediately: each photon either has enough energy on its own, or it doesn't.
Work function
φ is the minimum energy needed to free an electron from a given metal's surface. Every metal has its own φ — caesium's is low, copper's is high — so every metal has its own threshold frequency ν₀ = φ/h.
Stopping potential is intensity-independent
Brighter light emits more electrons (more photocurrent) — but it does not make each electron more energetic. Kmax and V₀ depend only on frequency, never on intensity.
Einstein's photoelectric equation
Kmax = hν − φ. A straight line against ν, with slope h/e and x-intercept ν₀ — this is literally how Millikan experimentally measured Planck's constant.
Part of the Dual Nature of Radiation and Matter chapter — read the notes, grab the formula sheet and take the quiz. One of Priodemy for School, free with every EduSuite school.
The experiment that broke the wave theory
What classical physics predicted, and got wrong
If light were purely a wave, its energy would depend on intensity. Shine a dim beam for long enough and an electron should gradually absorb enough energy to escape, whatever the colour. Brighter light should eject faster electrons. Neither prediction survives contact with the experiment, and that failure is the whole reason this topic exists.
What actually happens is that below a certain threshold frequency no electrons are emitted at all — not fewer, not slower, none — no matter how bright the source or how long you wait. Above the threshold, emission begins immediately, with no delay for energy to accumulate. Increasing the intensity produces more electrons but not faster ones. Increasing the frequency is what raises their energy.
Einstein's explanation
Einstein proposed that light arrives as discrete packets, each carrying energy E = hf. One photon interacts with one electron, all or nothing. To escape the metal, an electron must be given at least the work function φ, the energy binding it to the surface. Anything left over becomes kinetic energy:
hf = φ + KEmax
Every observation follows. A single photon below the threshold simply lacks the energy to free an electron, and two low-energy photons cannot team up, so no amount of intensity helps. Above the threshold the surplus appears instantly as kinetic energy, which is why there is no time lag. Brighter light means more photons, hence more electrons, but each photon still carries the same energy — so the maximum kinetic energy is unchanged.
Stopping potential and the graph
The stopping potential V₀ is the reverse voltage that just prevents the fastest electrons from reaching the collector, so eV₀ = KEmax. Plotting V₀ against frequency gives a straight line of gradient h/e, with an intercept on the frequency axis at the threshold. Millikan measured this line precisely and obtained a value for Planck's constant from an optical experiment — which is how the photon picture was confirmed. Change the metal here and watch the line shift sideways while its gradient stays identical: the work function differs, but h does not.
Mistakes that cost marks
Saying intensity affects electron energy. Intensity controls the number of photoelectrons, frequency controls their energy. Reversing this is the single most penalised error in the chapter.
Forgetting that KEmax is a maximum. Electrons deeper in the metal lose energy on the way out, so emitted electrons have a spread of energies. The equation describes only the most energetic ones.
Unit mismatches. Work functions are quoted in electronvolts, while h is in joule-seconds. Convert with 1 eV = 1.6 × 10⁻¹⁹ J before combining them, or the answer will be out by a factor of about 10¹⁹.