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jaketodd
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Why is the de Broglie wavelength sometimes larger than the particle it describes?
Thanks,
Jake
Thanks,
Jake
jaketodd said:Why is the de Broglie wavelength sometimes larger than the particle it describes?
Thanks,
Jake
Jacques_L said:Please let us know what a "size of a particle" could be.
Radiocrystallographists use the width of X diffraction rays to evaluate the size of the diffracting crystallites. So clays give broad diffration peaks on a Debye-Scherrer diffractograms, though silts give fine peaks. I could confuse in justice an international crook by such facts. To give precise spots or peaks, the Bragg law demands large crystallites, and monochromatic waves, so with long and broad spindle of each incident quanton, photon or neutron or electron.
For instance, we obtained broad spots by diffracting electrons on a carbide inclusion in a Laue diffractogram, in a Siemens electronic microscope. The monochromaticicty of the electrons was not so perfect, and maybe the carbide inclusion was not a so perfect crystal.
When you write or say "size of a particle", you surrepticiously mean that it is or can be a corpuscle. But where are the experiments that could support such a postulate ?
A little more has to be known : the broglian period, frequency and when moving the broglian wavelength, suffice when an electron interferes with itself - in an Aharanov-Bohm experiment, for instance.
But when an electron interferes whith electromagnetic fields, a photon for instance in a Compton diffusion, then the intervening period is the Dirac-Schrödinger, [itex]\frac{h}{2mc^2}[/itex], half of the broglian one. So is the wavelength, too.
SpectraCat said:This is the second time you have mentioned "Compton diffusion" ... the context seems to suggest you mean "Compton scattering" .. is that correct? I think in French, the word for scattering might be "diffusion", however in English, diffusion has a different meaning in the context of physics.
Jacques_L said:Thank you for correcting my english. You are right.
Thanks for the welcome.SpectraCat said:Also, I should have done this before: Welcome to PF!
The De Broglie wavelength, named after French physicist Louis de Broglie, is the wavelength associated with a moving particle. It is a fundamental concept in quantum mechanics and is expressed as λ = h/mv, where λ is the De Broglie wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.
The De Broglie wavelength is a key concept in the wave-particle duality theory, which states that particles (such as electrons) can exhibit both wave-like and particle-like behavior. The De Broglie wavelength relates the particle's momentum (p) to its wavelength (λ) through the equation λ = h/p. This duality is a fundamental principle in quantum mechanics and has been experimentally verified.
The De Broglie wavelength plays a crucial role in understanding the behavior of atomic and subatomic particles. It explains why electrons can exhibit wave-like properties, such as diffraction and interference, which are typically associated with waves. It also helps to explain the stability of atoms and the periodic table, as the De Broglie wavelength determines the allowed energy levels of electrons in an atom.
The De Broglie wavelength is typically too small to be directly measured in experiments. However, it can be indirectly measured using diffraction and interference techniques, where the particle's wavelength can be inferred from the resulting interference pattern. For example, in the double-slit experiment, the distance between the slits and the distance between the slits and the screen can be used to calculate the De Broglie wavelength of a particle passing through the slits.
The De Broglie wavelength is closely related to Heisenberg's uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is because the De Broglie wavelength is inversely proportional to the particle's momentum, meaning that the more precisely we know the momentum of a particle, the less we know about its position. This uncertainty is a fundamental property of quantum systems and has far-reaching implications in understanding the behavior of particles.