The Photoelectric Effect: How One Equation Proved Light Is Particles

The experiment that broke classical light

Shine light on a clean metal surface and, under the right conditions, electrons pop off it -- the photoelectric effect, first observed by Heinrich Hertz in 1887 and studied systematically by Philipp Lenard around 1902. Classical wave theory made a clear prediction: a light wave carries energy proportional to its intensity (brightness), so a dim red light left shining long enough should eventually deliver enough cumulative energy to kick an electron loose, and a bright enough light of any colour should always do it. Neither prediction survived contact with the actual data.

What experiment actually showed

Two results refused to fit the wave picture. First, below a certain threshold frequency that depends on the metal, no electrons are ejected no matter how intense the light is -- turn a dim violet lamp into a blinding one and still nothing happens if the frequency itself is too low; there is no delay-then-emission, emission simply never starts. Second, above the threshold, electrons come out instantly (within nanoseconds, not the measurable buildup time a wave picture would predict for weak light), and their maximum kinetic energy depends only on the light's frequency, rising linearly with it -- increasing intensity at a fixed frequency ejects more electrons per second, but does not make each individual electron come out any faster.

Einstein's photon explanation (1905)

Einstein resolved this in his 1905 paper by proposing that light itself is quantised into discrete packets -- photons -- each carrying energy E = h*f, proportional to frequency alone, not intensity. A photoelectric event is then one photon handing its entire energy to one electron in a single collision. The electron uses part of that energy just escaping the metal's surface (a fixed energy cost called the work function, phi, specific to each metal) and keeps the rest as kinetic energy:

KE_max = h*f - phi

h      Planck's constant  (6.626e-34 J*s)
f      frequency of the incident light
phi    work function of the metal (minimum energy to free an electron)
KE_max maximum kinetic energy of an ejected electron

This single equation explains both puzzling observations at once. If h*f is less than phi, no single photon carries enough energy to free an electron, however many photons per second arrive -- hence the hard threshold frequency f0 = phi/h, independent of intensity. If h*f exceeds phi, each absorbed photon frees one electron essentially instantly, and the leftover energy h*f - phi becomes that electron's kinetic energy -- which is why KE_max rises linearly with frequency and is completely unaffected by intensity. Intensity only sets how many photons arrive per second, and therefore how many electrons are ejected per second (the photocurrent), never how energetic any single one of them is.

Why this convinced physicists light is a particle, too

Light had already been established beyond doubt as a wave by Young's double-slit interference a century earlier (see the wave-interference article on this site), and diffraction, polarisation and Maxwell's equations all reinforced that picture. The photoelectric effect forced physicists to accept that light also behaves as discrete quanta when it interacts with matter -- the origin of wave-particle duality. Robert Millikan spent roughly a decade (1905-1916) trying to experimentally disprove Einstein's simple linear equation, and instead ended up confirming it to high precision, measuring Planck's constant h from the slope of KE_max versus f independently of the value Planck had derived from blackbody radiation -- two completely different experiments agreeing on the same constant was powerful corroborating evidence. Einstein received the 1921 Nobel Prize in Physics specifically "for his discovery of the law of the photoelectric effect," not for relativity.

Reading the simulation's controls

Turning up the light's frequency slider moves f above or below phi/h for the selected metal, switching emission on or off and setting the ejected electrons' speed once it is on. Turning up intensity at a fixed frequency above threshold increases the rate of photon arrivals and therefore the number of electrons ejected per second (the current), visibly without changing how fast any individual electron leaves. Switching metals changes phi, shifting the threshold frequency -- easily ionised metals like caesium have a low work function and eject electrons even with visible light, while metals like platinum need ultraviolet light to clear their much higher work function.

Frequently asked questions

Try it live

Everything above runs in your browser — open Photoelectric Effect and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.