Matter waves-wave nature of particle

The dual nature of radiation and matter tells that every object has two natures associated with it i.e,  a wave and particle. It is most commonly known as wave-particle duality. The wave nature of particles came from Maxwell’s equations of electromagnetism and the experiment of generation and detection of electromagnetic waves done by Hertz. J. J Thompson was the first to determine the speed and charge of cathode ray particles. The dual nature of radiation and matter was proved by de Broglie and later confirmed by many experiments such as the David and Germer experiments. This was one of the biggest experiments ever conducted on the nature of radiation and matter. The duality of nature has solved many theories and explained many concepts. 

According to the wave nature of particles, 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.

De Broglie’s Equation 

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 = hp 

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

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

Δx Δp ≤ h/2

Assume you determine the particle’s momentum precisely so that ‘delta p’ equals zero. The uncertainty in the particle’s position, ‘delta x,’ 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 

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 50o to produce the maximum intensity. A similar arrangement (seen below) was investigated, but with X-rays substituted by a variable-energy beam of electrons.

Conclusion 

After many experiments and observations by scientists like J.J. Thompon, de Broglie, Albert Einstein, this theory has become one of the biggest in science history. The wave nature of particles was discovered in the nineteenth century, which failed to explain particle nature thoroughly. Later on, Albert Einstein discovered that particles are nothing but a flow of energy packets called photons. The particle nature of radiation resolved some theories, such as the photoelectric and Compton effect. When David and Germer experimented on this, they were able to verify the dual nature of particle and quantum mechanics.