Name: Dual Nature of Light and Matter
Uploaded: 2019-07-19
Duration: 7 min 31 s
Description: Light has a dual nature. It is both a wave and a particle. Explore this video about the wave and particle nature of light and the wavelength corresponding to...

Question

Derive de Broglie wave equation for material particles.

Accepted Answer

According to Plank's theory,the energy associated with a photon is given by

$E = hν$ where $ν =$ frequency and $h =$ Plank's constant

According to the Einstein theory of relativity, the same quantity is related to its mass and the velocity by the relation

$E = {mc}^{2}$

Thus, energy can be given in terms of frequency (a wave characteristic) as well in terms of mass (a particle property) as per the principle of dual nature of matter, the two forms can be unified, hence de-Broglie equated both these equations for the particle moving with velocity $v$ as

$m v^{2} = hν = \frac{hc}{λ}$ where $λ$ is the wavelength of the particle

From this

$\frac{h}{λ} = mv$

$\Rightarrow λ = \frac{h}{mv} = \frac{h}{P}$

Where $P$ is the momentum of particle and $h$ is the Plank's constant.

This equation relating the momentum of a particle with its wavelength is the de Broglie equation.

Derive de Broglie wave equation for material particles.

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