Photons

Light behaves as a wave in interference and diffraction. But in some experiments it behaves like a stream of particles. Each particle of light is a photon, a packet of energy.

Photon energy: E = hν = hc / λ, with Planck's constant h = 6.63 × 10⁻³⁴ J s.

Photon energies are tiny, so we use the electron volt: 1 eV = 1.6 × 10⁻¹⁹ J. A handy shortcut: hc ≈ 1240 eV nm, so E (in eV) = 1240 / λ (in nm).

Example: red light of 620 nm has photons of 1240/620 = 2 eV.

Facts about photons:

• All photons of one frequency have the same energy.
• They travel at c in vacuum.
• They have zero rest mass: a photon is never at rest.
• They carry momentum p = h/λ = hν/c. For 620 nm, p ≈ 1.1 × 10⁻²⁷ kg m/s.
• In collisions, energy and momentum are conserved, but the number of photons need not be.

Brighter light of the same colour means more photons per second, not more energetic ones. The power of a beam is P = N × E, where N is the number of photons per second.

Example: a 1 W beam of 620 nm light carries N = 1 / (2 × 1.6 × 10⁻¹⁹) ≈ 3 × 10¹⁸ photons per second. That huge number is why light seems smooth to us.

X-rays: electrons accelerated through a voltage V, then stopped by a metal target, can give up all their energy eV to one photon. So the highest frequency is ν_max = eV/h, and the shortest wavelength λ_min = hc/eV. With 10 kV, λ_min = 1240/10 000 nm ≈ 0.12 nm.