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Is there a discrepancy between deBroglie's equation and the standard electromagnetic spectrum chart?

Physics Asked by suse on March 15, 2021

I learned that the wavelength of any particle, but particularly a quantized particle, is proportional to its momentum; that is to say, small particles have large wavelength properties and large particles have small wavelengths. That is why the wavelengths of classical particles like balls, humans, and football fields are barely perceptible but wavelengths of quantum particles, like electrons and photons, are measurable. If so, why on the standard electromagnetic spectra charts, do they show the wavelengths of humans as $1.0m$ and wavelengths of atomic nuclei as $10^{-12}m$? Aren’t the wavelengths of humans supposed to be small the wavelengths of tiny particles large?

One Answer

The term "wavelength" can be used to describe various physical phenomena as a function ,as far as your question goes, of (x,y,z,t), mathematically represented by sine or cosine functions:

sine

Wavelength is the length in the x axis between two repetitions of the wave. So in everyday terms, the dimension in (x,y,z) of an object can be described as its wavelength, assuming it would repeat in space like a sine wave.

Now we come to quantum mechanics that has given rise to the confusion.

The de Broglie wave was a proposal in the first days of describing quantum mechanical phenomena of interference effects in matter of very small particles, as electrons:

The de Broglie wavelength is the wavelength, λ, associated with a massive particle (i.e., a particle with mass, as opposed to a massless particle) and is related to its momentum, p, through the Planck constant, h

BUT this wavelength in space appears as a probability wave , it is the probability to find an electron at (x,y) that shows interference effects characteristic of a wave. A single electron is a point particle, leaving a footprint of a point on a screen, as seen in this double slit experiment where the interference is seen in the accumulation, a probability distribution.

dbls

That is why the wavelengths of classical particles like balls, humans, and football fields are barely perceptible but wavelengths of quantum particles, like electrons and photons, are measurable.

This is about probability waves.

why on the standard electromagnetic spectra charts, do they show the wavelengths of humans at 1.0 m and wavelengths of atomic nuclei at 10^-12 m

Electromagnetic waves, are classical waves, represented in (x,y,z,t) by sine and cosine functions as seen above, and transport energy that reflected on the human can be correlated with the size of a human ( though you have not given a link) .

The point is that in quantum mechanics one has probability waves and wavelengths, and in classical electromagnetism energy in motion waves.

Answered by anna v on March 15, 2021

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