# Debroglie hypothesis

Today we know that every particle exhibits both matter and wave nature. This is called **wave-particle duality**. The concept that matter behaves like wave is called **De Broglie Hypothesis**. This is named after Louis de Broglie , who proposed it in 1924.

## De Broglie Equation

De Broglie gave the following equation which can be used to calculate de Broglie wavelength, \(\lambda\), of any massed particle whose momentum is known.

\[\lambda = \frac{h}{p}\]

Where, \(h\) is the Plank's constant and \(p\) is the momentum of particle whose wavelength we need to find.

With some modifications the following equation can also be written for velocity(\(v\)) or kinetic energy(\(K\)) of the particle (of mass \(m\)).

\[\lambda = \frac{h}{mv} = \frac{h}{\sqrt{2mK}}\]

Notice that for heavy particles, the de Broglie wavelength is very very small, in fact negligible. Hence, we can conclude that though heavy particle do exhibit wave nature, however it can be neglected as its insignificant in all practical terms of use.

Calculate the de Broglie wavelength of a golf ball whose mass is 40 gram and velocity is 6 m/s.

We know,

\(\lambda = \frac{h}{mv} = \frac{6.63 \times 10^{-34}}{40 \times 10^{-3} \times 6} \text{m}=2.76 \times 10^{-33} \text{m}\)

## Explanation of Bohr's Quantisation Rule

One of the main limitations of Bohr's Atomic theory was that no justification was given for the principle of quantisation of angular momentum. It does not explains the assumption that why electron can rotate only in those orbits in which the angular momentum of the electron, \(mvr\) is a whole number multiple of \( \dfrac{h}{2\pi} \).

De Broglie successfully provided the explanation to Bohr's assumption by his hypothesis.

**Cite as:**Debroglie hypothesis.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/debroglie-hypothesis/