De Broglie Wavelength

Key Stage 5

Meaning

The de Broglie wavelength is the wavelength associated with a particle (an object with mass) and is inversely proportional to its momentum, demonstrating the Wave-Particle Duality|wave-like nature]] of matter.

About de Broglie Wavelength

• The de Broglie wavelength suggests that particles such as electrons have wave properties.
• The de Broglie wavelength is confirmed by experiments such as electron diffraction through a crystal.
• The de Broglie wavelength is fundamental to the development of quantum mechanics.
• The de Broglie wavelength applies to all particles, including macroscopic objects, but the wavelength is significant only for very small particles like electrons.

Formula

The de Broglie Wavelength of an object is given by the formula:

• \(\lambda = \frac {h} {𝑝}\)

• \(\lambda = \frac {h} {mv}\)

Where:

𝜆 is the de Broglie wavelength,

ℎ is the Planck Constant,

𝑝 is the momentum of the object

m is the mass of the object

v is the velocity of the object

Examples

• Electrons showing diffraction patterns when passing through a thin crystal.
• The de Broglie wavelength of a moving car is extremely small and not observable.