7.3 Matter-Wave and Photon Momentum and Wavelength

Photons carry momentum

Even though light has no mass, a photon carries momentum given by p = h/λ = E/c, where h is Planck's constant, λ is wavelength, E is photon energy, and c is the speed of light. This momentum lets light exert pressure and explains phenomena like the Compton effect, where photons scatter off electrons and transfer momentum.

Matter has wave properties too

Louis de Broglie proposed that all matter has an associated wavelength: λ = h/p = h/(mv). This de Broglie wavelength is significant for tiny particles like electrons but immeasurably small for macroscopic objects. It explains why electrons show diffraction and interference patterns, confirming wave-particle duality.

Wave-particle duality unifies light and matter

Both light and matter exhibit wave-particle duality: they behave as waves (diffraction, interference) and as particles (discrete momentum, energy transfer in collisions). The same relationship, p = h/λ, links a particle's momentum to its wavelength for both photons and matter, showing these are two aspects of the same physical reality.

Key terms

Photon momentum formula

p = h/λ = E/c, where h is Planck's constant, λ is wavelength, E is energy, c is speed of light.

De Broglie wavelength

λ = h/(mv), the wavelength associated with any moving particle of momentum p = mv.

Wave-particle duality

The principle that both light and matter exhibit both wave-like (diffraction, interference) and particle-like (momentum, discrete energy) behavior.

Why macroscopic objects don't show observable wavelengths

Their momentum (mv) is so large that λ = h/p becomes far too small to detect.

Evidence for electron wave behavior

Electron diffraction through crystals produces interference patterns, confirming matter waves predicted by de Broglie.

Try an AP-style question

An electron's speed doubles (non-relativistic). What happens to its de Broglie wavelength?

1. It stays the same
2. It halves
3. It doubles
4. It quadruples