(a) Write the de Broglie equation. (b) Explain the significance of the equation.

Answer Details

(a) de Broglie equation:

where \(\lambda\) is the wavelength associated with a particle, \(h\) is Planck's constant, \(p = mv\) is the momentum, \(m\) the mass and \(v\) the velocity of the particle.

(b) Significance: the equation expresses the wave-particle duality of matter. It shows that every moving particle (such as an electron) has a wavelength and can therefore behave like a wave, exhibiting effects such as diffraction and interference. The wavelength is inversely proportional to momentum, so only very small (light, slow-enough) particles have wavelengths large enough for wave behaviour to be observable; ordinary large bodies have wavelengths far too small to detect. This idea underlies electron diffraction and the electron microscope.