use the electronvolt (eV) as a unit of energy

Energy and Momentum of a Photon

What is a Photon? 🔬

A photon is a tiny packet of light energy. Think of it as a “light‑ball” that travels at the speed of light, \$c = 3.0\times10^8\,\text{m/s}\$. Even though it has no mass, it carries both energy and momentum.

Energy of a Photon 💡

The energy of a photon is linked to its frequency, \$\nu\$, or wavelength, \$\lambda\$, by the famous equations:

  • \$E = h\nu\$ (where \$h = 6.626\times10^{-34}\,\text{J·s}\$ is Planck’s constant)
  • \$E = \dfrac{hc}{\lambda}\$

In physics we often use the electronvolt (eV) as a convenient unit of energy. One eV is the energy gained by an electron when it moves through a potential difference of one volt:

\$1\,\text{eV} = 1.602\times10^{-19}\,\text{J}\$

Because the photon energy is usually very small compared to everyday energies, the eV scale makes calculations easier. For example, visible light photons have energies around 2 eV, while X‑ray photons can reach 1 keV (1000 eV).

Momentum of a Photon 🌈

Even though a photon has no rest mass, it still carries momentum. The relationship between energy and momentum for a photon is:

\$E = pc\$

Rearranging gives the photon momentum:

\$p = \frac{E}{c} = \frac{h}{\lambda}\$

In particle‑physics units we often write the momentum in eV/\$c\$:

\$p \;(\text{eV}/c) = \frac{E \;(\text{eV})}{c} \;\approx\; E \;(\text{eV})\$

Numerically, a 500 nm photon (green light) has:

  • Energy: \$E \approx 2.48\,\text{eV}\$
  • Momentum: \$p \approx 1.33\times10^{-27}\,\text{kg·m/s}\$ or \$p \approx 2.48\,\text{eV}/c\$

Why Does Momentum Matter? 🌠

Photon momentum is responsible for radiation pressure – the tiny push that sunlight exerts on a sail or a dust particle in space. It also plays a key role in processes like the photoelectric effect, where photons transfer enough momentum to free electrons from a metal surface.

Quick Reference Table 📊

Wavelength (nm)Energy (eV)Momentum (eV/\$c\$)
4003.103.10
5002.482.48
7001.771.77
10124.0124.0
0.11240012400

Take‑Home Messages ✨

  1. Energy of a photon: \$E = h\nu = \dfrac{hc}{\lambda}\$.
  2. Momentum of a photon: \$p = \dfrac{E}{c} = \dfrac{h}{\lambda}\$.
  3. One electronvolt (eV) equals \$1.602\times10^{-19}\,\text{J}\$.
  4. For photons, energy in eV equals momentum in eV/\$c\$.
  5. Photon momentum explains radiation pressure and the photoelectric effect.