c = speed of light. In other words equation (1) can be applied to particles and equation (2) is an equation for a wave of frequency ν. Schrödinger expressed de Broglie’s hypothesis concerning the wave behaviour of matter in a mathematical form that is adaptable to a variety of physical problems without additional arbitrary assumptions. It can also be applied to other particles, like electrons and protons. But in the end one cannot derive this relationship: it is a physical hypothesis, and has to be shown experimentally. So the two were not equated until de Broglie had a breakthrough! As you have noted, the de Broglie relation is trivially valid for the momentum of light; his arguments try to show that this relationship is the only possibility for a matter wave. The wavelength of a wave traveling at constant speed is given by λ = v/ f. In 1923, Louis De Broglie found that objects exhibit a wave nature and derived De Broglie equation to find 'λ' considering Plank's constant and Momentum (mv). This equation simply relates the wave character and the particle character of an object. It is represented by λ. Schrödinger’s wave mechanics. In that case, we can say that equation … m= mass. The formula relates the wavelength to the momentum of a wave/particle. This relationship is known as de Broglie relationship. On the basis of his observations, de Broglie derived a relationship between wavelength and momentum of matter.
This De Broglie equation is based on the fact that every object has a wavelength associated to it (or simply every particle has some wave character). The de Broglie equation relates a moving particle's wavelength with its momentum.
We know that light can be a wave as well as a particle. > Nature loves symmetry. Considering the particle nature, Einstein equation is given as, E= mc 2 —- (1) Where, E= energy. Louis de Broglie (1892-1987) developed a formula to relate this dual wave and particle behavior. This symmetric loving nature of Nature gave rise to de Broglie relation. Use this De Broglie Wavelength Calculator to find the wavelength of a particle.