De Broglie Wavelength
Quantum and Nuclear

# 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 λdB.

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

λdB = hp

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, 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.

metre, m

m

nm

## Mathematical expressions

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

• 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.