Result

De Broglie wavelength

λ = \frac{h}{p}

Statement

The wavelength associated with a particle of momentum p.

Symbols and units

$λ$	de Broglie wavelength	m
$h$	Planck constant	6.626×10⁻³⁴ J·s
$p$	momentum	kg·m/s

When it applies

Any particle with momentum p, though the wave nature is significant only when λ is comparable to relevant length scales.

Don't use when

The wave description only becomes practically relevant when λ is comparable to the length scales in the problem — for macroscopic objects the wavelength is so small that classical mechanics is indistinguishable from the quantum prediction.

Derivation

Proposed by analogy with the photon momentum relation p = h/λ, extended to any moving particle regardless of whether it has mass.

λ = \frac{h}{p}

Watch out for

Every moving object has a de Broglie wavelength in principle, but for everyday masses and speeds it is unobservably small. An electron accelerated through a modest voltage has a wavelength comparable to the spacing between atoms in a crystal — exactly why electron diffraction confirmed matter waves exist.