Energy and momentum of a photon — common mistakes

Always check units carefully! Wavelength must be in metres, frequency in Hertz, and power in Watts (J/s). When converting between Joules and electronvolts, remember that 1 eV is a smaller unit of energy than 1 Joule, so you divide by the conversion factor to get eV from Joules.

A photon is unique because it has no rest mass and always travels at the speed of light in a vacuum. It's a fundamental packet of electromagnetic energy, unlike particles with mass such as electrons or protons.

A photon's speed in a vacuum is always the constant value 'c'. While light slows down in a medium, the photon's energy (determined by its frequency) remains constant. It's the wavelength that changes.

The different formulas (p=E/c, p=hf/c, p=h/λ) simply express the same physical quantity (momentum) using different known parameters of the photon (energy, frequency, or wavelength). They are all derived from each other and are useful in different problem contexts.

In classical physics, momentum is p=mv. However, in Einstein's theory of relativity, the full energy-momentum relation is E² = (pc)² + (m₀c²)². For a photon, the rest mass m₀ is zero, so the equation simplifies to E = pc, or p = E/c. This shows that a massless particle can indeed have momentum.