From Hertz to Quantum Light: Photoelectric Effect and Photons Explained

Overview of the Episode

The talk traces the photoelectric effect from Hertz’s 1887 experiments to Einstein's photon hypothesis and Planck's constant, culminating in Millikan’s precise verification in 1915. It highlights four defining properties observed in photoelectric experiments, explains the photon energy vs work function relationship, and presents a hands-on numerical example with ultraviolet light to illustrate how photon energy, the work function, and electron kinetic energy determine the emitted electrons’ behavior. The narrative also touches the cautious shift from wave-only interpretations to quantum physics, and how these ideas shaped the foundations of quantum mechanics.

Introduction and Historical Context

The lecture begins by revisiting the photoelectric effect, first demonstrated by Heinrich Hertz in 1887. Hertz irradiated polished metal plates with high-energy light and observed that electrons were ejected, producing a photoelectric current. Four key properties emerged from these early experiments: a threshold or critical frequency below which no current appears, a threshold that depends on the metal and surface conditions, a current magnitude that scales with light intensity, and a surprising independence of the emitted electrons’ energy from light intensity. The energy of the emitted electrons increased with the light frequency, a detail that could not be reconciled with a purely wave description of light.

From Waves to Photons

The speaker explains how Einstein, in 1905, proposed that light comes in bundles of energy called quanta, later named photons. Each photon has energy E = hν, where h is Planck's constant. This idea provided a natural explanation for Hertz’s observations: electrons are emitted only when photons carry enough energy to overcome the work function φ of the metal, allowing an electron to escape. The relation between photon energy, work function, and electron kinetic energy becomes Ekinetic ≈ hν − φ. Planck’s constant is central to this framework and connects to the black body spectrum that Planck himself introduced to fit experimental data.

Millikan’s Confirmation and the Quantum Picture

Although Einstein’s photon concept was compelling, it faced skepticism because of the dominance of Maxwellian wave theory and concerns about determinism. The turning point came with Robert Millikan’s experiment in 1915, which measured the kinetic energy of photoelectrons with exceptional precision (better than 1%). Millikan’s results confirmed Einstein’s prediction that the electron’s kinetic energy increases linearly with the frequency of the incident light, not its intensity. This work solidified the photon picture and established the photon energy–frequency relationship as a cornerstone of quantum theory. The discussion emphasizes how these findings laid the groundwork for the quantum description of light and matter, marking a crucial shift in physics toward probabilistic and wave-particle dual descriptions.

Practical Calculation: 290 nm Ultraviolet Light

The lecturer walks through a back-of-the-envelope calculation to illustrate the concepts. For UV light with wavelength λ = 290 nm incident on a metal with work function φ = 4.05 eV, the photon energy is given by Eγ = hc/λ. Using the practical approximation hc ≈ 200 MeV fm and converting to electron-volts, Eγ comes out to about 4.28 eV. The kinetic energy of the emitted electron is then KE ≈ Eγ − φ ≈ 0.23 eV. Since the electron rest mass energy is 511 keV, this KE is non-relativistic, and the velocity can be estimated from KE = (1/2)mv², yielding a velocity around 2.8 × 10^5 m/s, roughly 284 kilometers per second. The calculation is presented as an example of how, with simple constants, one can obtain reasonable estimates without a calculator, illustrating the interplay of photon energy, work function, and electron dynamics.

Why This Matters for Quantum Foundations

Beyond the numbers, the talk discusses the broader significance: the photoelectric effect provided direct evidence for quantized light and helped usher in quantum mechanics. It also illustrates the tension between a deterministic, wave-only view and a probabilistic, particle-based description. The narrative closes by reflecting on how this historical episode shaped the modern understanding of light as both wave and particle, and how the constants introduced by Planck and used by Einstein connect to the birth of quantum theory. The audience is left with a clear sense of the experimental and theoretical milestones that transformed our understanding of light and matter.