With the development of the photoelectric effect, Crampton’s effect and Bohr’s model of the atom, the theory of light or actually rays generally consisting of particles or discrete quanta was gaining wider popularity.
However, Huygen’s well-established principle and the results of Young’s double-slit experiments made it absolutely clear that light is a wave and not a stream of particles.

The interference pattern observed when passing light through a double slit was definitely a result of the wave nature of light. This then led to the controversy over the nature of light. In 1704, Newton also proposed the particle nature of light through his material theory.

Neither theory was sufficient to explain all phenomena associated with light. As we know thinking to Thus scientists began to conclude that light has both wave and particle nature. In 1924, Louis de Broglie, a French physicist, proposed a theory. He suggested that all the particles in this universe are also related to the wave nature, that is, everything in this world, be it a tiny photon or a giant elephant, everything has an associated wave, it is different that the wave Characteristic or not he assigned a wavelength to each case with mass m and momentum p.

λ :h/p

Where, h is Planck’s constant and p = mv, v is the velocity of the body.

Thus, due to the large mass of an elephant, it has a very significant velocity and therefore a very small wavelength, which we are unable to perceive. However, smaller particles like electrons etc. have a very small mass and therefore have a very significant wavelength or wave nature. This theory of de Broglie also helps us to explain the discrete existence of orbitals in Bohr’s model of the atom. An electron will exist in an orbit if its length is an integral multiple of its natural wavelength, the orbit will not exist if it is unable to complete its wavelength.

Further developments by Davison and Germer of electron scattering from crystals and similar interference patterns obtained after bombarding a double slit with electrons reinforced de Broglie’s matter-wave theory or wave-particle duality theory.

The Compton Effect:

In the photoelectric effect, light strikes a metal in the form of a beam of particles called photons. The energy of a photon contributes to the work energy of an electron as well as providing kinetic energy to the emitted electron. These photons are particle like wave behavior of light. Sir Albert Einstein proposed that light is the collective effect of a large number of energy packets called photons where each photon has HF energy. where h is Planck’s constant and f is the frequency of light. This is the particle like wave behavior of light. The behavior of light waves or other electromagnetic waves such as particles can be explained by the Compton effect.

In this experiment, an X-ray beam of frequency fo and wavelength λo was directed at an electron. After the electron is hit by the incident X-ray, it turns out that both the electron and the incident X-ray are scattered at two different angles with respect to the axis of the incident X-ray. This collision obeys the same energy conservation principle as Newtonian particle collisions. It was found that after the collision the electron is accelerated in one direction and the incident X-ray is spread in another direction and it was also observed that the frequency and wavelength of the diffracted beam is different from that of the incident X-ray. Since the energy of the photon varies with frequency it can be concluded that the X-ray loses some energy during the collision and the frequency of the scattered beam is always lower than that of the incident X-ray. This lost energy of the X-ray photon forms part of the kinetic energy for the electron motion. This collision of X-rays or its photons and electrons is exactly like Newtonian particles like billboard balls.

The energy of photon is given by to:

From equation (1) it can be concluded that an electromagnetic wave with wavelength λ will contain a photon with momentum p.
From equation (2) it can be concluded that the particle with velocity p is associated with wavelength λ. This means that while a wave has particle-like properties, a particle in motion also exhibits wave-like behavior.

As we have already said, this conclusion was first derived by De Broglie and hence it is known as the De Broglie Hypothesis. you know about it As the wavelength of the moving particle is expressed.

λ :h/p

Where, p is the velocity, h is the Planck constant and the wavelength λ is called the de Broglie wavelength. De Broglie explained that as the electron orbits the nucleus it will have particle-like properties as well as wave-like behavior.

The Divisions and Germer Experiment:

The wave nature of the electron can be proven and established in many different ways, but the most famous experiment is the splitting and Germer experiment in 1927. In this experiment, they used a beam of high-speed electrons that normally hit the surface of a nickel block. They observed the pattern of scattered electrons after striking a nickel block. As we know that They used an electron density monitor for this purpose. Although it was expected that the electron would be scattered after striking at different angles with respect to the axis of the incident electron beam, but in the actual experiment it was found that the density of scattered electrons was higher at other angles. This angular distribution of scattered electrons is very similar to the scattering interference of light. So this experiment clearly shows the existence of wave-particle duality of electrons. The same principle can be applied to protons and neutrons.