The fact that matter is made up of waves is one of the most counter-intuitive facts in physics. In this lesson, you learned about both the particle and wave natures of light, as well as how they interact. You are aware of the Photoelectric effect resulting from Albert Einstein’s generosity.

In the photoelectric effect, electrons and photons exhibit the characteristics of a particle, similar to that of a billiard ball in a pool game. However, you are most likely familiar with the Diffraction experiment and the Interference Rings. It’s similar to how two waves on the surface of a pond interact with one another. In these instances, we can perceive the wave nature of light. It’s a mind-boggling puzzle. It even has something to do with our vision!

According to the wave nature of light, the gathering and focusing mechanisms of the eye lens are following it. However, the absorption of light by the rods and cones of the retina is consistent with the particle nature of light! While we were still trying to find out what was going on, Louis de Broglie came along and added to the confusion by introducing the de Broglie Relationship to the equation.

## Which Particles Behave Like Waves?

When it comes to classical mechanics, radiation is thought of as waves, while particles are hard billiard balls. It was discovered that radiation could act as waves and as particles, which was previously unknown. Radiation and moving particles can supply energy and momentum to various objects. In 1924, De Broglie proposed that matter should have a dual nature, using the symmetry of nature as justification for his theory. Particles do not have a fixed location in space. The dual nature of matter and light have set the groundwork for developing quantum theory.

## De Broglie’s Equation: Wave nature of matter

According to De Broglie’s hypothesis, there is symmetry in nature. If light and radiation act as particles and waves, then matter will also have particle and wave properties. The dual nature of matter was predicted by De Broglie.

λ=h /p = h /m v

Thanks to De Broglie’s relationship, we now have a wave theory of matter. ‘Lambda’ here denotes the particle’s wavelength, while ‘p’ here represents the particle’s momentum. The de Broglie connection is significant because it mathematically indicates that matter can act in the manner of a wave. In layman’s terms, the de Broglie equation states that every moving particle, whether microscopic or macroscopic, has its unique wavelength.

The wave aspect of the matter can be observed in macroscopic things, indicating that they are composed of waves. When it comes to more oversized items, the wavelength shrinks as the object grows in size, eventually becoming so tiny as to be imperceptible. This is why macroscopic objects in real life do not exhibit wave-like qualities. Even the cricket ball you throw has a wavelength that is too short for you to see. The Plank’s constant connects the wavelength and the momentum in the equation.

## Heisenberg’s Uncertainty Theory: Wave nature of matter

The Davisson-Germer experiment, which included diffracting electrons through a crystal, established the wave character of matter without any reasonable question. De Broglie was given the Nobel Prize in Physics in 1929 for his work on matter-wave theory, which was instrumental in establishing a whole new science of Quantum Physics. The Uncertainty Principle, developed by Heisenberg, was an elegant integration of the matter-wave theory. When it comes to electrons or any other particles, the Uncertainty Principle states that it is impossible to know both their momentum and their position properly at the same time. Whatever the case, there is always some degree of uncertainty in either the position (delta x) or the momentum (delta p).

## Heisenberg’s Uncertainty Equation: Wave nature of matter

Δx Δp ≤ h/4π

Assume you determine the particle’s momentum precisely so that ‘Δp’ equals zero. The uncertainty in the particle’s position, ‘Δx,’ must be infinite to meet the preceding equation. From de Broglie’s equation, we know that a particle with a defined momentum has a defined wavelength, denoted by the symbol ‘Lambda.’ A specific wavelength spans the entire expanse of space, all the way to infinity. According to Born’s Probability Interpretation, this indicates that the particle is not confined in space, so the position uncertainty becomes infinite.

However, in reality, wavelengths have a finite limit and are not infinite, implying that position and momentum uncertainty have a finite value. De Broglie and Heisenberg’s Uncertainty Principle equation are both apples from the same tree.

### Davisson-Germer Experiment On Wave Nature Of Matter

Davisson and Germer experimented on nickel crystals in 1927. The crystal structure is such that it behaves like a diffraction grating when illuminated by an X-ray beam with a wavelength of 1.65. The crystal’s interplanar spacing is equivalent to the X-ray wavelength. When the beam strikes the crystal, waves with a constant phase relation reflect separate planes. These reflected waves interfere at a scattering angle of 50 to produce the maximum intensity. A similar arrangement (seen below) was investigated, but with X-rays substituted by a variable-energy beam of electrons.

## Experimental Configuration

Davisson and Germer measured electron currents at various scattering angles for constant energy levels. They noticed a pattern similar to the X-ray diffraction pattern at 54 eV electron energy. It peaked at =50.

### Did You Know?

Any particle’s De Broglie wavelength is inversely proportional to its momentum. Due to the high masses of everyday things. As a result, wavelike phenomena are not observed on a large scale, and classical physics continues to function normally.

Electrons’ wave nature successfully explains the atomic structure. According to Bohr’s hypothesis, electrons can only rotate in defined orbits around the nucleus. The electron waves create a stationary wave with constant energy at these orbits. Energy is changed solely through the emission or absorption of photons during orbital transitions.

Due to the wave nature of matter, fascinating phenomena such as quantum tunnelling occur. Alpha decay of a heavy nucleus occurs as a result of the nuclei’s wave character.

Electron diffraction is used in crystallography to investigate various crystal structures.

### Conclusion

The concept of the wave character of matter is one of the most revolutionary ideas in modern physics. A particle is constrained to a specific location, but a wave is dispersed over space. It is possible to state that the nature of light is dependent on our ability to observe it in this manner. If we look at phenomena like interference, diffraction, or reflection, we can conclude that light is a wave. But, if we look at phenomena such as the photoelectric effect, we can conclude that light is a particle with a particle character. Light has a dual nature, and sometimes, it may behave as both a wave and particle nature of matter simultaneously. Aside from that, one of the most innovative concepts in Physics was introduced by Louis Victor de Broglie, who developed the de Broglie equation, which provided answers to numerous issues such as Does light possess a dual nature? What if more quantities had a dual nature? According to him, how might we get to that conclusion? Theoretically, particles show wave behaviour. Experiments such as the Davisson-Germer experiment provided conclusive evidence for this.