The photoelectric effect

Light ejecting electrons

The photoelectric effect occurs when light shining on a metal surface ejects electrons. Classical wave theory expected that a brighter light should deliver more energy to electrons and eventually knock them out, regardless of frequency. Experiments showed something very different.

Below a certain threshold frequency, no electrons are emitted, no matter how intense the light is. Above the threshold frequency, electrons are emitted almost immediately, even if the light is weak. Increasing intensity increases the number of emitted electrons, but it does not increase their maximum kinetic energy. Increasing frequency does.

These observations were difficult to reconcile with classical electromagnetic waves.

Einstein's photon hypothesis

Einstein proposed that light of frequency $f$ consists of localized energy packets, later called photons. Each photon has energy

$E=hf$

An electron in the metal absorbs energy from one photon. Some energy is required to escape the metal. This minimum energy is the work function $phi$. The remaining energy becomes the electron's maximum kinetic energy:

$K_{max}=hf-phi$

This is Einstein's photoelectric equation.

Threshold frequency

The threshold frequency $f_0$ occurs when the photon energy just equals the work function:

$hf_0=phi$

so

f_0=rac{phi}{h}

If $f<f_0$, then $hf<phi$, and no single photon has enough energy to free an electron. Increasing intensity increases the number of photons, but if each photon lacks enough energy, emission still does not occur in the simple one-photon photoelectric effect.

Stopping potential

Experimentally, the maximum kinetic energy can be measured using a stopping potential $V_s$. A reverse voltage is applied to stop the most energetic electrons. At the stopping voltage,

$eV_s=K_{max}$

Combining with Einstein's equation gives

$eV_s=hf-phi$

A graph of $V_s$ versus $f$ is a straight line. Its slope is $h/e$, and its intercept gives the work function.

Intensity versus frequency

In the photon picture, intensity is related to the number of photons arriving per unit time and area. Higher intensity at fixed frequency means more photons and therefore more emitted electrons, provided $f>f_0$.

Frequency determines energy per photon. This explains why weak ultraviolet light can eject electrons while intense red light may not.

Immediate emission

Classically, an electron might need time to absorb enough energy from a weak wave. Experiments instead show almost immediate emission above threshold. In the photon model, one electron absorbs one photon, so the energy transfer is discrete and rapid.

Broader significance

The photoelectric effect provided strong evidence for particle-like properties of light. Planck had quantized energy exchange in blackbody radiation; Einstein went further by treating light itself as quantized.

This did not eliminate wave behavior. Light still interferes and diffracts. The lesson is deeper: light has quantum behavior that cannot be reduced to purely classical waves or particles.

Applications

Photoelectric and related photoemission effects are used in photodetectors, solar cells, image sensors, vacuum phototubes, and surface analysis. Modern quantum theory extends Einstein's idea using electrons in solids, band structure, and quantum electrodynamics.

The big idea

The photoelectric effect showed that light energy is delivered in quanta. Einstein's equation $K_{max}=hf-phi$ explains threshold frequency, stopping potential, immediate emission, and the different roles of intensity and frequency. It is one of the clearest origins of the photon concept.