The Photoelectric Effect & Einstein's Photon
Chapter 1 closed with Planck's own reluctance to believe his energy quantization was physically real. This chapter covers the person who took that reluctant idea seriously — and, in real, well-documented fact, was rewarded for exactly this work rather than the theory he's now more famous for.
A Real Puzzle Classical Waves Could Not Solve
When light strikes certain metals, it can eject electrons from the surface — the photoelectric effect. Classical wave theory made a genuine, testable prediction: a brighter (more intense) light should deliver more energy over time, eventually ejecting electrons regardless of colour, and dimmer light should simply take longer to do the same.
Real, documented experiments showed something genuinely different. Electrons were ejected only when light exceeded a specific threshold frequency — entirely independent of the light's own intensity or how long it shone. A real, low-frequency beam, however intense or prolonged, never ejected a single electron. And the ejected electrons' own kinetic energy depended only on the light's frequency, not its intensity at all — a genuine, direct contradiction of what classical wave theory predicted.
Einstein's Real 1905 Explanation
Einstein proposed, in a real, separate 1905 paper, that light itself consists of discrete energy packets — photons — each carrying energy E = hf, exactly as Planck's own formula from Chapter 1 described. An electron absorbs one whole photon at a time; if that photon's own energy exceeds the material's work function (W, the minimum energy needed to free an electron from the surface), the electron escapes with the leftover energy as kinetic energy:
This single equation directly explains both real observations: below the threshold frequency, a single photon simply doesn't carry enough energy to overcome W, no matter how many photons (how much intensity) arrive; above it, each individual photon supplies a fixed surplus of energy determined purely by its own frequency, exactly matching the real, measured dependence on frequency rather than intensity.
Worked Example: Maximum Electron Kinetic Energy
Light with a frequency of 8×10¹&sup4; Hz strikes a metal with a work function of 3×10&supminus;¹&sup9; J. What is the maximum kinetic energy of the ejected electrons?
KEmax = (6.626×10&supminus;³&sup4; × 8×10¹&sup4;) − 3×10&supminus;¹&sup9;
KEmax = 5.30×10&supminus;¹&sup9; − 3×10&supminus;¹&sup9;
KEmax ≈ 2.30×10&supminus;¹&sup9; J
A Real, Surprising Nobel Prize Story
Classical Prediction vs. Einstein's Real Explanation
| Property | Classical Wave Prediction | Einstein's Real Explanation |
|---|---|---|
| Threshold behaviour | None expected — any frequency should eventually work | A real, hard threshold frequency exists |
| Electron energy depends on | Light intensity | Light frequency |
| Effect of dim light | Slower emission, same eventual result | No emission at all, below threshold |
Hands-On Exercises
Quick Reference
- The photoelectric effect: light ejects electrons only above a threshold frequency, independent of intensity
- Einstein's real 1905 explanation: light is made of photons, each carrying E = hf
- Maximum electron kinetic energy: KEmax = hf − W
- Einstein's 1921 Nobel Prize was real, documentedly awarded for the photoelectric effect, not relativity — and even that citation expressed doubt about light's particle nature
- Broad scientific consensus on the photon concept only solidified in 1924, via Satyendra Nath Bose