## De Broglie wavelength

Glossary Definition for 16-19

#### Description

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 *λ*_{dB}.

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

* λ_{dB}* =

*h*

*p*

where *h* is the Planck constant.

#### Discussion

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, *λ*_{dB} 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 * λ_{dB}* = 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

m

#### Other commonly-used unit(s)

nm

#### Mathematical expressions

=*λ*_{dB}*h**p*
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 ~ 10^{6} m s^{–1} for this to be the case.