Knowing More on De Broglie Wavelength of an Electron Derivation

The distance between one crest and another crest is known as wavelength in physics, and it is indicated by the symbol. The wave that repeats its features over a period of time, according to its definition. Before we get into detail about this topic, you need to know that an electron is a subatomic particle in the atom that is symbolized by the letter “e–.” The electrical charge on this electron is negative. These electrons are crucial in the passage of electricity into solid objects. Even electrons, according to French scientist Louis de Broglie, have wave qualities. In his thesis, he demonstrated that all matter/particles, including electrons, have wave qualities. De Broglie presented an equation to explain any matter/characteristics. particle’s

All particles, according to Louis de Broglie, have wave-like properties. They can exhibit wave-like characteristics. According to his assertion, the same theory is applicable to the electron.

A wavelength is assigned to an electron wave, and this wavelength is determined by the electron’s momentum. The electron’s momentum (p) is defined as the product of the electron’s mass (m) or velocity (v) .

∴Momentum of the electron (p) = m v

Then the wavelength λ is

∴ Wavelength λ = hp

The Planck constant, h, has a value of 6.62607015 x10-34 J.S

The de Broglie wavelength of the electron is defined by the formula. We can deduce from this that slow-moving electrons have a large wavelength while fast-moving electrons have a short or minimum wavelength.

De Broglie Wavelength of Electron Derivation

The De Broglie Wavelength of an Electron is derived from the relationship among mass and energy. Let’s start with the energy equation to get the de Broglie wavelength of an electron equation.

E = m c2

Here m = mass

E = energy

C = speed of light

Planck’s theory also claims that a quantum’s energy is proportional to its frequency & Planck’s constant.

E = h v

The de Broglie wavelength equation is obtained by combining the two energy equations.

m c2=h v

Real particles are incapable of traveling at the speed of light. As a result, replacing the velocity (v) with the speed of light (c).

m v2=h v

Substitute the ‘v’ by  v, then, m v2=  v h

∴ λ = h vm v2

The de Broglie wavelength of an electron is calculated using the equation above.

By replacing Planck’s constant (h), the mass of the electron (m), and the velocity of the electron (v) in the preceding equation, we can calculate the de Broglie wavelength of an electron at 100 EV. The de Broglie wavelength value is then calculated 1.227×10-10 m

According to de Broglie, any particle of matter in the universe possesses wave-like qualities. They may also possess the wavelength. The de Broglie wavelength equation can be used to determine these values. The wavelength of a particle can be calculated using the particle’s velocity and mass, as well as Planck’s constant. The wavelength is shortest for particles with a higher mass value than those with a lower mass value.

de broglie wavelength

. The de Broglie wavelength is a crucial notion in quantum mechanics. The de Broglie wavelength  is the wavelength (λ) that is related with an item in relation to its momentum and mass. The de Broglie wavelength of a particle is often inversely related to its fo

de broglie waves

Matter, it is thought, has a dual nature of wave-particles. The quality of a material item that changes in time or space while acting like waves, known as de Broglie waves, is named after the discoverer Louis de Broglie. It’s also known as matter-waves. It is very comparable to the empirically proved dual nature of light, which operates as both a particle and a wave.

Louis de Broglie, a physicist, proposed that particles could have both wave and particle qualities. The wave nature of electrons was also discovered experimentally, proving Louis de Broglie’s theory.

The wavelengths of the items we see in everyday life are incredibly little and undetectable, therefore we don’t perceive them as waves with in case of subatomic particles, wavelengths are clearly apparent.

de Broglie Wavelength for Electrons

The de Broglie waves occur as a closed-loop in the case of electrons moving in circles all around nuclei in atoms, so they can only exist as standing waves and fit equally around the loop. As a result of this need, electrons in atoms orbit the nucleus in specific configurations or states known as stationary orbits.

Applications of de Broglie Waves

1. Because matter’s wave characteristics can only be observed for very small objects, the de Broglie wavelength of a double-slit interference pattern is generated utilizing electrons as the source. De Broglie wavelength = 3.9 x 10-10 m for 10 eV electrons (which is the normal electron energy in an electron microscope).The gap between atoms is comparable to this. A crystal thus serves as an electron diffraction  grating. The crystal structure can be deduced from the diffraction pattern.
2. The wavelength used in a microscope restricts the size of the tiniest features that can be seen. 400 nm = 4 x 10-7 m is the shortest wavelength in visible light. Typical electron microscopes employ wavelengths 1000 times smaller than visible light which can be used to investigate a wide range of topics. Most electron microscopes have wavelengths that are 1000 times lower and can study extremely minute features. 

Conclusion:

In 1923, Louis-de-Broglie proposed the concept of De-Broglie waves, which were later tested and proven by Davisson and Germer in 1927. These waves describe the nature of the particle-related wave.Another version of the de Broglie wavelength formula exists for particles with mass but not photons, such as electrons, protons, and so on. The momentum of a particle at non-relativistic speeds is equal to its resting mass m multiplied by its velocity v.

The de Broglie wavelength is measured in meters. Because it is so small, it is measured in nanometres or Angstroms.