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, $u$, or wavelength, $\lambda$, by the famous equations:

• $E = hu$ (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 📊

Take‑Home Messages ✨

1. Energy of a photon: $E = hu = \dfrac{hc}{\lambda}$.
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.