De Broglie’s theory

Introduction

Louis de Broglie is best known in the world of physics for  his work on quantum theory, and for predicting the wave nature of electrons. He was given the Nobel Prize award for Physics in 1929. He defined himself as “far more in the mindset of a pure theorist than of an experimenter or engineer, particularly fond of the broad and philosophical outlook.”                                                                                                                 

De Broglie’s Electron wave theory 

De Broglie established his groundbreaking theory of electron waves in this thesis (1924), which he had previously published in scholarly journals. The idea that matter on the atomic scale might possess wave-like qualities stems from an Einstein suggestion made 20 years prior. Einstein proposed that light with small wavelengths may behave like particles formed as if it were formed of particles under certain conditions, which was confirmed in 1923. However, when de Broglie expanded the concept of a dual nature of light to matter, it was only beginning to acquire scientific recognition.

De Broglie’s solution addressed a problem posed by calculations of electron mobility within the atom. Experiments had established that the electron must move around a nucleus and that, for reasons unknown at the time, its motion is constrained. De Broglie’s concept of an electron possessing wave-like qualities explained the confined motion. A wave that is constrained inside the bounds imposed by the nuclear charge is restricted in shape and consequently in motion because any wave shape that does not fit within the atomic boundaries interferes with itself and cancels it out. When de Broglie proposed this hypothesis in 1923, there was no scientific proof that the electron, whose corpuscular properties were widely established, might behave as radiant energy under certain conditions. Thus, De Broglie’s suggestion, his sole significant contribution to physics, was a triumph of intuition.

Although de Broglie’s initial papers on “matter waves” received little attention from other physicists, a copy of his doctoral thesis was forwarded to Einstein, who responded enthusiastically.

Einstein emphasised the significance of de Broglie’s findings both publicly and implicitly by expanding on them. Thus, Austrian physicist Erwin Schrödinger learned of hypothetical waves and built a mathematical theory, wave mechanics, based on the concept. Wave mechanics has since become an indispensable instrument in physics. However, Clinton Davisson and Lester Germer in the United States and George Thomson in Scotland did not discover the electron’s wave character until 1927.

Matter Waves By de Broglie

The Compton Scattering

When Albert Einstein came up with his theory of special relativity, it was first published in 1905. This meant that even though photons don’t have any mass, they still have momentum, the sum of an object’s mass times its speed.

Special relativity shows that energy and mass are linked through E2=p2c2+m2c4, where E stands for energy, p stands for momentum, c stands for the speed of light, and m stands for an object’s mass. The energy of an object with no mass, like a photon, will be E2=p2c2 or E=pc if it does not have any mass. An experiment done by Arthur Compton in 1922 proved that photons do have the speed Einstein predicted in 1922.

X-rays were fired at aluminium foil by Compton to see how it was made. They moved some of their angular momenta when X-rays hit them from the outside of the aluminium atoms. Electrons had enough energy to leave the atom. The X-ray photon lost the same energy so that the electrons could leave. Compton scattering is the name given to this process now that it has been done.

People talk about this process called inverse Compton scattering when a photon gets more energy when it hits an electron. When looking at X-ray astronomy, both the Compton scattering process itself and the process in which inverse Compton scattering takes place are essential.

Electron wave 

De Broglie used Einstein’s equations to show that electrons can behave like waves, the same way that particles do, in 1924.

De-broglie’s Equation says –

λ = h/mv,

Wavelength of photons

Einstein’s equation for figuring out a photon’s energy and the Planck relation is used to figure out the wavelength of a photon. Special relativity says that the energy of photons is E = pc, and E = h/v is the energy of photons.

Using c = λν,

Wavelength of a particle

De Broglie said that particles also have a wavelength and that the same equation can be used to figure out how long they are. Here, the particle’s momentum equals mv, where m is the particle’s mass, and v is its velocity.

When De Broglie looked at the way electrons move around the nucleus, he found that they have to move in a limited way at both ends. If you look at each orbit, there are only a certain number of wavelengths that fit around each one,

In this case, the orbit is thought to be circular. When you have a circle with radius R, its circumference is 2r. This is also known as the “shell number.” This means that each electron has a fixed amount of angular momentum. This is in line with Niels Bohr’s theory of the atom.

Bohr had already shown that the angular momentum of each electron (L) is equal to the shell number times a certain number.

There is less space in the orbit of an electron when it moves from high energy to low energy. This means that fewer full wavelengths can fit, which means the energy and frequency are less. It is always the same because E = hv. The energy at the lowest possible level is always more than zero because there must be enough space for all the wavelengths in each shell to fit inside them.

Conclusion

According to De Broglie’s theory of matter waves, each particle of matter with linear momentum is also a wave. The wavelength of a matter wave linked with a particle is inversely proportional to the particle’s linear momentum. The particle’s speed is equal to the speed of the matter-wave. The quantization of the electron’s angular momentum in Bohr’s model of the hydrogen atom is justified by De Broglie’s concept of the electron matter-wave. In the Davisson- Germer experiment, electrons are dispersed off a crystal nickel surface. Electron matter-wave diffraction patterns are noticed. They are confirmation of matter waves. Diffraction investigations with various particles reveal matter waves.