De-Broglie Principle and Hypothesis

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According to De Broglie’s theory of matter waves, each particle of matter with linear momentum is also a wave. The amount of a particle’s linear momentum is inversely proportional to the wavelength of a matter wave associated with that particle. The quantification of the electron’s angular momentum in Bohr’s model of the hydrogen atom is justified by De Broglie’s notion of the electron matter wave. The De Broglie hypothesis claims that all matter has wave-like qualities and that the wavelength of matter is proportional to its momentum.

De-broglie Principle And Hypothesis

The French physicist Louis de Broglie made a daring claim in his doctoral dissertation in 1923 (or 1924, depending on the source). De Broglie proposed that the wavelength of any matter could be determined from Einstein’s coupling of wavelength to momentum p, in the formula:

 λ=h/p

Here h is the planck’s constant

The de Broglie wavelength is the name given to this wavelength. Because it was uncertain whether Eshould be total energy, kinetic energy, or total relativistic energy with matter, he picked the momentum equation over the energy equation. They all have the same for photons, but not for matter.

However, using the kinetic energy E_K and assuming the momentum connection, a comparable de Broglie relationship for frequency f might be derived.

 f= E_K/h

Significance of the de Broglie Hypothesis

• The de Broglie hypothesis demonstrated that wave-particle duality was a fundamental principle shared by both radiation and matter, not just an aberrant behaviour of light. As a result, if the de Broglie wavelength is properly applied, wave equations can be used to describe material behaviour. This would be critical for quantum mechanics to advance. It is now an accepted part of atomic structure and particle physics theory.

• Though de Broglie’s hypothesis predicts wavelengths for any amount of matter, there are practical limitations on when it can be used. The de Broglie wavelength of a baseball thrown at a pitcher is around 20 orders of magnitude less than the diameter of a proton. The wave characteristics of a macroscopic item are so small that they are unobservable in any practical sense, yet they are fascinating to contemplate.

de Broglie Hypothesis

• At the sub-microscopic level, matter is thought to behave both like a particle and a wave, according to quantum mechanics. Matter’s particle behaviour is clear. When you think of a table, you imagine it as a solid, stationary object with a specific place. This is true at the macroscopic level. However, as we zoom in closer to the subatomic level, things become more convoluted, and matter does not always behave as we expect.

• Louis de Broglie, a French physicist, suggested this non-particle behaviour of matter in 1923. He proposed in his PhD thesis that particles contain wave-like qualities as well. He generated an equation to verify it using Einstein’s renowned mass-energy relation and the Planck equation, despite not having the means to test it at the time.

de broglie principle equation

De Broglie arrived at his equation through a sequence of substitutions based on well-known theories. De Broglie was the first to apply Einstein’s famous equation for the relationship between matter and energy:

 E=mc²……. (2)

Here E is the energy

 m is the mass

c is the speed of light

Using Planck’s theory, each quantum of a wave has a discrete quantity of energy that can be calculated using Planck’s equation:

 E=hν……… (1)

Here E is the energy

h is the planck’s constant

and ν is the frequency

De Broglie hypothesised that the two energies would be equivalent because particles and waves share the same characteristics:

 mc²= hν……… (3)

De Broglie proposed velocity (v) for the speed of light since real particles do not travel at the speed of light ( c ).

 mv²= hν…….. (4)

From above equation, De Broglie replaced v/λ for v in the equation and arrived at the final expression that connects wavelength and particle speed.

  mv²= hν/λ  ………. (5)

Hence

λ= hν/λ  = h/mv

The bulk of Wave-Particle Duality problems can be solved using the above equation and a variety of cancelling out units.

de broglie uncertainty principle quantum

• The wave-particle duality, and more specifically the de Broglie interval wave, can be used to derive Heisenberg’s uncertainty principle.

• The Heisenberg Uncertainty Principle is a fundamental principle of quantum physics that explains why a scientist cannot simultaneously measure many quantum variables. Until the advent of quantum physics, it was assumed that all variables of an object could be known with absolute precision at the same time. Newtonian physics set no boundaries on how better methods and techniques could reduce measurement error, therefore it was theoretically possible to characterise all information with sufficient care and accuracy. Heisenberg boldly proposed that this precision has a lower limit, making our understanding of a particle fundamentally unreliable.

Conclusion

According to the de-Broglie hypothesis, a moving material particle behaves like a wave at times and like a particle at other times. Every moving material particle is connected with a wave. The de-Broglie wave or matter-wave is an unseen wave associated with a moving particle that propagates in the form of wave packets with the group velocity. To see the wave nature of matter particles practically, the de-Broglie wavelength should be on the order of the particle size. The Heisenberg Uncertainty Principle is a fundamental principle of quantum physics that explains why a scientist cannot simultaneously measure many quantum variables.