Wave-Particle Duality of Electromagnetic Radiation

The photoelectric effect showed that light interacts with matter as if it were made of discrete energy packets -- photons. A further question then arose: if a photon carries energy like a particle, does it also carry MOMENTUM, another defining particle property? This was answered by Arthur Compton in 1923-24, in an experiment scattering a monochromatic beam of X-rays (of a single wavelength $\lambda$) off a graphite sheet and measuring the wavelength of the scattered rays as a function of scattering angle.

Compton found that the scattered X-rays showed intensity peaks at TWO wavelengths: one equal to the original incident wavelength $\lambda$, and a second, slightly LONGER wavelength $\lambda'=\lambda+\Delta\lambda$. This shift $\Delta\lambda$, called the COMPTON SHIFT, depends only on the scattering angle $\theta$ and not on the incident wavelength itself, following the relation

Compton explained this by treating the interaction as a PARTICLE COLLISION -- like two billiard balls -- between an incident X-ray photon and a nearly-free electron in the graphite. In this collision, both energy and momentum are conserved exactly as in ordinary particle mechanics; the scattered photon has LOWER energy (hence lower frequency, hence LONGER wavelength) than the incident photon, having handed some of its energy and momentum to the recoiling electron. This shift cannot be explained by the wave theory of light at all -- it vanishes only in the limit $h\to0$, which is precisely the classical (wave-only) limit, making Compton scattering a direct experimental test of the photon's particle-like momentum.

A photon's momentum follows from Einstein's relativistic relation for a massless particle travelling at the speed of light, $p=E/c$; combined with $E=h\nu$ and $c=\nu\lambda$, this gives $p=h\nu/c=h/\lambda$. All photons of a given frequency carry the same energy and the same momentum; photons are electrically neutral (undeflected by electric or magnetic fields), can be created or destroyed in interactions (so the NUMBER of photons is not conserved, even though energy and momentum are), always travel at exactly the speed of light (never at rest), and have zero rest mass in every frame of reference. …