The photon

The photoelectric effect shows that light, when it interacts with matter, acts as if it were made of packets of energy hν.

Einstein showed that the quantum also carries momentum hν/c. A definite energy together with a definite momentum is a strong sign of a particle, and the particle was later named the photon. Compton's experiment on X-rays scattered by electrons, in 1924, confirmed this particle-like behaviour.

Einstein received the Nobel Prize in Physics in 1921 for his work in theoretical physics and on the photoelectric effect; Millikan received it in 1923 for his work on the elementary charge and on the photoelectric effect.

The photon picture: (i) in its interaction with matter, radiation behaves as if made of photons; (ii) each photon has energy E = hν, momentum p = hν/c and speed c.

(iii) All photons of a given frequency ν, or wavelength λ, have the same energy E = hν = hc/λ and the same momentum p = hν/c = h/λ, whatever the intensity. Brighter light only means more photons crossing a given area per second.

(iv) Photons carry no charge, so electric and magnetic fields do not deflect them. (v) In a collision between a photon and a particle, total energy and total momentum are conserved, but the number of photons need not be: a photon may be absorbed or a new one created.

Example 11.1: a laser emits 2.0 × 10⁻³ W of light at 6.0 × 10¹⁴ Hz. Each photon has E = hν = 6.63 × 10⁻³⁴ × 6.0 × 10¹⁴ = 3.98 × 10⁻¹⁹ J, and the number emitted per second is N = P/E = 2.0 × 10⁻³/3.98 × 10⁻¹⁹ = 5.0 × 10¹⁵.

Exercise 11.1: a 30 kV electron can give at most 30 keV to an X-ray photon, so νmax = eV/h = (30 × 10³ × 1.6 × 10⁻¹⁹)/(6.63 × 10⁻³⁴) = 7.24 × 10¹⁸ Hz, and λmin = c/νmax = 0.0414 nm.