De Broglie Concept

When an electromagnetic wave interacts with matter, it behaves like a particle of light, according to Compton’s formula. Louis de Broglie developed a novel speculative theory in 1924 that electrons and other matter particles might behave like waves. This concept is now known as de Broglie’s theory of matter waves. De Broglie’s hypothesis, along with Bohr’s early quantum theory, resulted in the creation of a new wave quantum mechanics theory to describe the physics of atoms and subatomic particles in 1926. Quantum physics has opened doors for technologies like laser and magnetic resonance imaging (MRI).

Definition of the De Broglie Equation

The de Broglie equation is an equation used to describe the wave qualities of matter, especially an electron’s wave nature:

λ=h/mv

where is the wavelength, h is Planck’s constant, and m is the mass of a particle travelling at a constant velocity v. De Broglie proposed that particles can have wave-like qualities.

 When matter waves were discovered in George Paget Thomson’s cathode ray diffraction experiment and the Davisson-Germer experiment, which especially applied to electrons, the de Broglie theory was confirmed. Since then, it has been demonstrated that the de Broglie equation applies to elementary particles, neutral atoms, and molecules.

De Broglie Equations

The de Broglie equations connect a particle’s wavelength to its momentum (p), and its frequency (f) to its kinetic energy (E) (exclusive of its rest energy and any potential energy):

λ=h/p and f=E/h

where h denotes Planck’s Constant The two equations may be expressed as follows:

p=ħk and E=ћω

Here ћ=h/2π is known as the reduced Planck’s constant

And k=2π/λ is known as the angular wavenumber, =2f represents the angular frequency.

De Broglie’s fundamental insight was that in a one-electron atom, an integer number (n) of wavelengths must fit inside a single circle formed by the Bohr orbit for a wave to maintain a stable amplitude and not decrease over time. He used the equation to connect this to the primary quantum number n:

nλ=2πr

This was pleasantly evocative of Bohr’s previously documented discovery concerning an electron’s angular momentum:

m_evr=2Πr

The de Broglie relation may be derived by inspecting the above and making small changes:

λ=h/m_ev=h/p

De Broglie offers an overview of the electronic structure of a hydrogen atom and explains how an electron in an orbit may interfere with itself in the same way as it can in a double-slit experiment.

Validation of De Broglie Hypothesis

Clinton Davisson and Lester H. Germer of Bell Labs shot slow-moving electrons at a crystalline nickel target in 1927. The angular dependence of the reflected electron intensity was tested and found to exhibit the same diffraction pattern that Bragg predicted for X-rays. Diffraction was assumed to be a feature solely of waves prior to the adoption of the de Broglie theory. As a result, the occurrence of any diffraction effects by matter confirmed matter’s wave-like nature. The observed diffraction pattern was expected when the de Broglie wavelength was introduced into the Bragg condition, experimentally verifying the de Broglie theory for electrons.

Experiments with Fresnel diffraction and specular reflection of neutral atoms validate the de Broglie hypothesis, i.e. the presence of atomic waves that undergo diffraction, interference, and allow quantum reflection via attractive potential tails. Laser cooling advancements have enabled the cooling of neutral atoms to temperatures close to absolute zero. Thermal de Broglie wavelengths are in micrometre range at these temperatures. The de Broglie wavelength of cold sodium atoms was specifically determined using atom Bragg diffraction and a Ramsey interferometry approach and was found to be compatible with the temperature reported by a separate method.

Recent tests have even confirmed the de Broglie relations for molecules and macromolecules, which are typically thought to be too massive to be affected by quantum mechanical processes. A team of researchers in Vienna exhibited diffraction for molecules as big as fullerenes in 1999. The researchers predicted a de Broglie wavelength of 2.5 pm for the most likely C60 velocity. Recent tests demonstrate the quantum nature of molecules with masses of up to 6910 amu. The de Broglie hypothesis is supposed to apply to any well-isolated item in general. Even macroscopic objects, like tennis balls, have a calculable de Broglie wavelength; yet, they are far too tiny to perceive empirically, and their wave-like nature is counterintuitive to ordinary perception.

Conclusion

The wavelength of a matter-wave associated with a particle is inversely proportional to the particle’s linear momentum. De Broglie’s concept of the electron matter wave justifies the quantisation of the electron’s angular momentum in Bohr’s model of the hydrogen atom. They demonstrate the existence of matter waves. Diffraction investigations with different particles reveal matter waves. De Broglie concluded that the bulk of particles is too heavy to perceive their wave properties. However, when the mass of an item is relatively little, the wave properties can be observed experimentally.