De Broglie Wavelength

The nature of matter got ambiguous after the discovery of the quantum mechanics.

In 1924 physicist Louis de Broglie proposed that as light exhibits both wave like and particle like properties.

Matter too exhibits wave-like and particle-like properties. This nature was described as a dual behaviour of matter.

de Broglie considered that the relations for the energy and the wavelength true for photon also holds goods for these matters as well.

Let’s study the de Broglie wavelength

Light contains energy in discrete packets or particles called photons.

Consider a photon or a particle of light its energy is $E$.

But, frequency of light is defined as,

So, put the value of $f$ in the energy formula of photon then we get new $E$ as,

Here, we do the further simplifications in terms of $\lambda$

But, $E/C$ is the momentum $p$ then we get the new value of $\lambda$.

Momentum is defined as the product of mass $m$ and the velocity $v$ of a particle.

Then the equation of $\lambda$ becomes,

Now, the kinetic energy $K$ of a moving particle is.

Hence the value of $p$ is.

Now, put the value of $p$ in the equation of $\lambda$ then we get as above

Suppose a particle takes charge $q$ and accelerated through potential $V$ then the kinetic energy of a particle is as above.

Now put the value of $K$ in the equation of $\lambda$ then we get as above.

If we are putting the constant values of $h$, charge of electron $q$ and mass of electron $m$ then we get as above.

Hence this the simplified equation that we can to remember to calculate the de Broglie wavelength $\lambda$.

Revision

This is the formula of de Broglie wavelength.

To calculate the de Broglie wavelength $\lambda$ of an electron, we can use as above.

The End