De Broglie Relationship

Electrons have a physical feature called the De Broglie relation. Louis de Broglie, a French physicist, was the first to introduce it in 1924. The De Broglie relation says that an electron’s wavelength and momentum have a relationship, which is given by p = h/, where h is the Planck constant and is the wavelength. When an electron collides with another particle, such as a photon, this relationship can be used to calculate how much energy the electron has. The De Broglie relation is a mathematical formula that connects a particle’s momentum to its wavelength. We can use it to forecast or calculate some particle properties, such as their energy levels or momentum distribution function.

De Broglie Relationship

The De Broglie relation is a mathematical relationship between a particle’s wave function and its antiparticle’s wave function. The de Broglie relation is a mathematical relationship between a particle’s wave function and its antiparticle’s wave function. It was named after French physicist Louis-Victor de Broglie, who proposed it in 1924. De Broglie proposed an equation to link them, but it wasn’t until 1957 that scientists David Bohm, Eugene Wigner, and John von Neumann discovered that quantum mechanics can be represented in terms of probability waves. Many concepts relating to the spectrum of distinct atoms and the splitting of spectral lines in magnetic and electric fields were not explained by Bohr’s model. An attempt was made to build a more complete atomic model to solve the inadequacies of Bohr’s atomic model.

This is a model that explains how electrons behave in atoms. It was created in 1924 by Louis de Broglie. This model explains how waves and particles can both be described as a single thing at the same time. Wave-particle duality is another name for this. Electrons are portrayed as waves in this model, while protons are represented as particles. The De Broglie relation is a formula for calculating an electron’s wavelength as a function of its momentum or speed as it moves through space and time. The wavelength of a photon equals the frequency of light, according to the De Broglie relation. This indicates that light is both a wave and a particle.

By measuring how much momentum it takes for an electron to change wavelength, the De Broglie relation can be used to determine how much momentum an electron has. With this equation, you can figure out what wavelength an electron would have if it had more or less energy than it does now.

Relation between De Broglie wavelength and Kinetic Energy

De Broglie wavelength and kinetic energy have a relationship. A particle’s De Broglie wavelength is the distance it travels during its flight, while its kinetic energy is the force that propels it forward. When particles move in a straight line, their velocity is constant, and their de Broglie wavelength is equal to their velocity. The de Broglie wavelength of particles travelling at an angle to the straight line is smaller than their velocity. The kinetic energy of a De Broglie wavelength is greater the shorter it is because it has to travel less distance to attain its maximum speed. A De Broglie wavelength is the distance travelled by a particle in its orbit and is related to the particle’s momentum. The following is a derivation of kinetic energy from De Broglie wavelength:

E=hv

The first source of kinetic energy is:

E= 12mv2=p22m

p=2mE

where m is the mass of the particle, v is its velocity, and p is its momentum

De Broglie’s wavelength is given by,

λ=hp

λ=h2mE

Relation between Wavelength and Momentum

The momentum of a light wave is inversely proportional to its wavelength in this example. The De Broglie relation is the name for this relationship, and it may be demonstrated with a simple thought experiment. Consider two electrons flying at different speeds and in separate directions. They would transmit momentum to each other if they collided. This can be depicted by assigning different wavelengths to them, which are then linked by momentum and wavelength:

P=mv

λ=vf

M=mv

λ∝1M

λ=kM

λ=hM

This is the wavelength-to-momentum relationship for a moving particle.

Bohr’s Model

In 1915, Niels Bohr proposed the Bohr Model of the Atom. Some refer to Bohr’s Model as the Rutherford-Bohr Model because it is a revision of the earlier Rutherford Model. Quantum mechanics provides the basis for today’s atom model. The Bohr Model is important because it describes most of the acknowledged properties of atomic theory without all of the high-level maths that the contemporary version requires. Unlike previous theories, the Bohr Model explains the Rydberg formula for atomic hydrogen’s spectrum emission lines.

The Bohr Model is a planetary model in which negatively charged electrons orbit a small, positively charged nucleus, much like planets do around the sun (except that the orbits are not planar). The solar system’s gravitational pull is mathematically equivalent to the Coulomb (electrical) force that exists between positively charged nuclei and negatively charged electrons.

Momentum of Matter

According to De Broglie’s theory of matter waves, each particle of matter with linear momentum is also a wave. The magnitude of a particle’s linear momentum is inversely proportional to the wavelength of a matter wave associated with that particle. The particle’s speed is the same as the matter wave’s speed.

Conclusion

Bohr’s model does not explain several concepts relating to the spectrum of distinct atoms and the splitting of spectral lines under magnetic and electric fields. To overcome the inadequacies in Bohr’s atomic model, work on a more complete atomic model was begun.

E=mc2—1

E=hv–2

From 1 and 2m

mc2=hv–3

v=c

mv2=hv⟹λ=hmv