The Photon Momentum
If light is a particle, it should have momentum. Einstein showed that for a photon, momentum (\(p\)) is related to its wavelength (\(\lambda\)):
\[p = \frac{h}{\lambda}\]
This is a strange result: momentum (a particle property) is tied to wavelength (a wave property).
Worked Examples
Example 1: Radiation Pressure
Because photons have momentum, they exert pressure when they hit a surface. This is why "solar sails" work. A spacecraft can be pushed through the vacuum of space just by the momentum of sunlight hitting its mirrors.
The Bridge to Quantum Mechanics
The relation \(p = h/\lambda\) is the foundation of the Momentum Operator \(\hat{p} = -i\hbar \nabla\). When you differentiate a wave \(e^{ikx}\), you "pull down" the frequency \(k\). Since \(k = 2\pi/\lambda\), this derivative is literally "measuring" the photon's momentum as Einstein defined it. This simple formula is what allows us to translate between the geometric world of waves and the mechanical world of momentum.