understand that a photon has momentum and that the momentum is given by p = E / c

Energy and Momentum of a Photon 🎓

What is a Photon? 🔬

A photon is a tiny packet of light energy that travels at the speed of light, c = 3 × 10⁸ m/s. Think of it like a miniature “light bullet” that can move through space without any mass, but still carries energy and can push on objects when it hits them. ✨

Energy of a Photon 💡

The energy of a photon is related to its frequency (ν) or wavelength (λ) by Planck’s equation:

$E = hu = \dfrac{hc}{\lambda}$

Where h is Planck’s constant (6.626 × 10⁻³⁴ J·s). If you know the wavelength, you can find the energy, and vice‑versa. 📐

Momentum of a Photon 🚀

Even though a photon has no mass, it still carries momentum. Imagine a tiny snowball (the photon) rolling into a wall; the wall feels a small push. The momentum p of a photon is given by:

$p = \dfrac{E}{c}$

Because E = hc/λ, we can also write:

$p = \dfrac{h}{\lambda}$

So the shorter the wavelength, the larger the momentum. 🌈

Quick Example 📐

1. Take a green light photon with λ = 500 nm = 5.00 × 10⁻⁷ m.
2. Compute its momentum:

   $p = \dfrac{h}{\lambda} = \dfrac{6.626\times10^{-34}\,\text{J·s}}{5.00\times10^{-7}\,\text{m}} \approx 1.33\times10^{-27}\,\text{kg·m/s}$

3. Notice that this is a very tiny momentum, but it is real and measurable in experiments like the photoelectric effect.

Key Relationships in a Table 📊