Compton Scattering and the Photon: Einstein, X-Rays, and the Evidence for Particle Light

Summary

The video traces the photon concept from Einstein's early ideas to Compton scattering, showing how photon momentum and energy-momentum conservation explain the observed wavelength shift in high‑energy X‑ray scattering experiments.

Introduction

This video traces the historical rise of the photon concept from Einstein’s early insights to modern tests, focusing on the momentum carried by light and its observable consequences in scattering experiments.

Background: Photons and Relativity

The lecture reviews the relativistic energy momentum relation, emphasizes that photons are massless particles with E = pc for high-energy quanta, and explains how the invariant E^2 - p^2 c^2 = m^2 c^4 leads to the conclusion that energy and momentum determine a particle’s mass in a relativistic framework. It also recalls that photons have energy E = hν and that the momentum of a photon is E/c = h/λ, linking wavelength to momentum.

Thomson vs Compton Scattering

The discussion contrasts classical Thomson scattering, where an electromagnetic wave drives a free electron and radiation is produced by acceleration, with Compton scattering, which treats the photon as a particle colliding with an electron, conserving energy and momentum, and producing a measurable change in photon wavelength. In the Compton picture the electron acquires kinetic energy and recoil momentum, causing the scattered photon to emerge with a longer wavelength.

The Experiment and Its Data

The original experiment used molybdenum X-ray photons with λ ≈ 0.0709 nm, corresponding to about 17.5 keV, directed at a carbon foil and detected at various angles. At θ = 90°, the data show two features: a peak at λ_final ≈ 0.0709 nm, indicating photons that pass with little interaction, and a shifted peak near λ_final ≈ 0.0731 nm, consistent with Compton scattering. The observed wavelength difference Δλ ≈ 0.0022 nm matches closely the theoretical Compton shift Δλ = λ_C (1 - cos θ), with λ_C ≈ 2.426 pm. For θ = 90°, Δλ ≈ λ_C, explaining the observed shift.

Interpretation and Significance

These results provided strong evidence that light behaves as particles with momentum, supporting Einstein’s photon concept and the burgeoning quantum theory. They contrasted with the wave-based Thomson scattering and illustrated energy and momentum transfer in a collision between photons and electrons. The two-peak structure observed in the spectrum, including the peak at the initial λ and the shifted peak, reflects the dual pathways for the incoming photons: unscattered and Compton-scattered, with the angle dependence explained by the Compton formula.

Conclusion

The Compton experiment bridged relativity and quantum theory, delivering a pivotal confirmation of the photon as a particle and shaping our understanding of light’s dual nature and momentum transfer in high-energy scattering.