The classical mechanics did not account for the dual nature of particles and Heisenberg's uncertainty principle. So the new branch has been put forward named quantum mechanics.
De broglie relation
From the above formula de Broglie equation is given.The de Broglie equation relates a moving particle's wavelength with its momentum. The de Broglie wavelength is the wavelength, associated with a massive particle and is related to its momentum, p, through the Planck constant, h. In other words, you can say that matter also behaves like waves.
Significance of de Broglie wavelength
De Broglie equation says that every moving particle - microscopic or macroscopic - is associated with a wavelength. For microscopic objects, wave nature is observable. For larger objects, the wavelength is even smaller still, quickly becoming so small as to become unnoticeable. The wave particle duality of light was a big mystery for scientist. The light produce energy which traverses through space just like as the ripples spreading across the surface of a still pond after being disturbed by a dropped rock, it proves the wave like nature of light. While light can be considered as a steady stream of particles just like tiny droplets of water sprayed from a garden hose nozzle. There are various experiments which can be proves the wave nature of light. At the same time some experiments favors the particle nature.
de Broglie wavelength
If accelerating potential V is applied ti an electron beam, the energy acquired by the electron is expressed in electron-volt which is equal to charge on the electron in coulombs x potential in volts. This energy becomes the K.E of the electron. λ=mvh=(2meV)h λ=V1.226×10−9
Angular momentum from de Broglie wavelength
According to Bohr's model, electron revolves around the nucleus. According to de Broglie, the electron is not only the particle but also the wave. So, the circumference of the orbit is an integral multiple of wavelength. 2πr=nλ λ=mvh mvr=2πnh
Heisenberg uncertainty principle
The above formula is used for Heisenberg's Uncertainty Principle.The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. There is a minimum for the product of the uncertainties of these two measurements. There is likewise a minimum for the product of the uncertainties of the energy and time.
Significance of uncertainty principle
It is of significance only for microscopic particles. The energy of photon is insufficient to change the position and velocity of bigger bodies when it collides with them. In daily life, it has no significance.