De Broglie Wavelength
Quantum and Nuclear

De Broglie wavelength

Glossary Definition for 16-19 IOP Glossary Project


All particles can show wave-like properties. The de Broglie wavelength of a particle indicates the length scale at which wave-like properties are important for that particle.

De Broglie wavelength is usually represented by the symbol λ or λdB.

For a particle with momentum p, the de Broglie wavelength is defined as:

λdB = hp

where h is the Planck constant.


If a particle is significantly larger than its own de Broglie wavelength, or if it is interacting with other objects on a scale significantly larger than its de Broglie wavelength, then its wave-like properties are not noticeable. For everyday objects at normal speeds, λdB is far too small for us to see any observable quantum effects. A car of 1,000 kg travelling at 30 m s–1, has a de Broglie wavelength λdB = 2 × 10–38 m, many orders of magnitude smaller than the sizes of atomic nuclei.

A typical electron in a metal has a de Broglie wavelength is of order ~ 10 nm. Therefore, we see quantum-mechanical effects in the properties of a metal when the width of the sample is around that value.

SI unit

metre, m

Expressed in SI base units


Other commonly-used unit(s)


Mathematical expressions

  • λdB = hp
  • where h is the Planck constant and p is the momentum of the particle.

Related entries

  • Wavelength

In context

We can infer the wave-like nature of matter by observing the diffraction pattern produced when electrons pass through a crystalline material. The pattern occurs when the de Broglie wavelength of the electrons is comparable with the spacing between the atoms of the crystals. For a material such as graphite, where the interatomic spacing is 0.1–0.2 nm, electrons need to be travelling at speeds of the order of ~ 106 m s–1 for this to be the case.

Limit Less Campaign

Support our manifesto for change

The IOP wants to support young people to fulfil their potential by doing physics. Please sign the manifesto today so that we can show our politicians there is widespread support for improving equity and inclusion across the education sector.

Sign today