Einstein's Photon Theory
The photoelectric effect left classical wave theory with three separate, unexplained failures. In 1905, Einstein swept away all three at once with a single radical proposal: that light itself is not a continuous wave at all, but a stream of discrete energy packets.
The problem Einstein inherited
The previous lesson set out the photoelectric effect and the three ways classical wave theory fails to explain it: emission depends only on frequency, not intensity; there is a sharp threshold frequency below which no emission ever occurs, however intense the light; and emission (when it happens) is instantaneous, with no measurable time delay even at very low intensity. A continuous wave model of light cannot account for any of these three observations — and yet all three were measured, repeatedly and reliably, in real experiments.
What was needed was not a patch to the wave model, but a genuinely different picture of what light is. That is exactly what Einstein supplied in 1905, building on an idea Max Planck had introduced five years earlier purely as a mathematical trick to fix the black-body radiation spectrum: that energy is exchanged only in discrete quanta, of size $E=hf$. Planck did not believe light itself was made of particles — he treated the quantisation as a property of the oscillators emitting the radiation, not of the radiation itself. Einstein's move was to take the idea further and more literally than Planck ever intended.
Einstein's proposal: light as photons
Einstein proposed that electromagnetic radiation itself, not merely the process of emitting or absorbing it, is made of discrete packets of energy — photons. Each photon of light of frequency $f$ carries a fixed quantity of energy,
This is the crucial departure from the wave picture. In classical electromagnetism, the energy carried by a light wave is spread continuously across its wavefront, and a dim beam simply carries a smaller amount of that continuously distributed energy. In Einstein's picture, a dim beam instead carries fewer photons per second, each one still carrying the full energy $hf$ set by the light's frequency — intensity controls the number of photons arriving, not the energy of any individual one.
Every explanation below traces back to a single mechanism: when light hits the metal surface, one photon transfers its entire energy $hf$ to one electron, in one interaction, all at once. Because the interaction is one-to-one and complete, everything about a photon's energy — whether it's enough to free an electron, and how much kinetic energy is left over if so — is decided by the frequency of that single photon, never by how many other photons happen to be arriving alongside it.
How this resolves all three classical failures
With light modelled as photons rather than a continuous wave, each of the three experimental observations that defeated classical theory follows immediately.
Emission depends on frequency, not intensity
A photon interacts with a single electron and gives it the whole of its energy $hf$ in that one event. The electron's maximum kinetic energy after leaving the surface is therefore set entirely by how much energy that one photon delivered, minus the energy needed to escape the metal — a quantity fixed by the light's frequency alone. Increasing the light's intensity increases the number of photons arriving per second, and so the number of electrons emitted per second, but it does nothing to the energy carried by any individual photon. That is why $KE_{max}$ tracks frequency and is completely indifferent to intensity.
There is a threshold frequency
Freeing an electron from the metal surface costs a fixed minimum amount of energy — the metal's work function. If a single photon's energy $hf$ is below that amount, it simply does not carry enough energy to free an electron, no matter how many such photons arrive per second: each one still interacts with only one electron, and none of them individually has enough energy to do the job. Raising the intensity only increases the rate of these individually-too-weak interactions; it can never make up the shortfall by combining several photons' energy on one electron. Only once the frequency itself rises high enough that a single photon's energy exceeds the work function does emission become possible at all — the threshold frequency.
Emission is instantaneous
Classical theory pictured energy soaking gradually into the metal from a continuous wave, building up at a point on the surface until enough had accumulated to free an electron — which predicts a measurable delay, especially for a dim beam. The photon picture removes that build-up entirely: a single photon delivers its full energy to a single electron in one discrete interaction, not gradually over time. As soon as a photon of sufficient energy arrives and interacts, emission happens — there is nothing to wait for.
The full statement of the three classical failures, and the underlying photoelectric equation $hf = \phi + KE_{max}$ linking photon energy, work function and maximum kinetic energy, are covered in the previous lesson, The Photoelectric Effect, and in more depth still in the core Electromagnetic Radiation and Quantum Phenomena topic.
What this means for the nature of light
Einstein's photon theory did more than solve one troublesome experiment — it forced a fundamental rethink of what electromagnetic radiation actually is. Phenomena like diffraction and interference (Young's double-slit experiment being the classic case) only make sense if light spreads and combines like a wave; the photoelectric effect only makes sense if light delivers energy in discrete, particle-like lumps. Rather than being one or the other, light has to be understood as having both a wave character and a particle character, each showing up depending on the situation. This is the first solid experimental foothold for what later became known as wave-particle duality — a principle this module returns to and extends to matter itself in the lessons that follow.
It is worth pausing on how strange this must have looked at the time. A century before Einstein, Thomas Young's double-slit experiment had produced a clean, convincing interference pattern from light, apparently settling once and for all that light is a wave. Einstein's photon proposal did not overturn that evidence — interference and diffraction are still real, and still only explicable by treating light as a wave — but it insisted that the same light also had to be treated as a stream of particles in other circumstances. Unsurprisingly, this met real resistance: it seemed to contradict a century of settled, well-confirmed wave physics. Einstein's photon theory was only widely accepted once further evidence (including the Compton effect, showing photons colliding with electrons like particles) made the particle character of light impossible to ignore.
Key takeaways
- Einstein (1905) proposed that light itself is made of discrete photons, each carrying energy $E=hf$, extending Planck's 1900 quantisation of energy exchange to radiation itself.
- A photon interacts with a single electron in one complete event, transferring its full energy at once — intensity controls how many photons arrive per second, not the energy of any individual photon.
- This explains why $KE_{max}$ depends on frequency, not intensity: one photon's energy, fixed by frequency, determines the outcome of one interaction.
- This explains the threshold frequency: a photon below a certain frequency simply lacks enough energy to free an electron, regardless of how many such photons arrive.
- This explains instantaneous emission: energy is delivered in one discrete interaction, not built up gradually, so there is no time delay to wait out.
- The photon theory established that light must be understood as having both wave character (diffraction, interference) and particle character (photoelectric emission) — the first solid evidence for wave-particle duality.
- Despite Young's double-slit experiment having seemingly settled "light is a wave" a century earlier, Einstein's proposal met real resistance, since it appeared to contradict well-established wave physics.