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Below is a paragraph taken from the web site, physicsclassroom.com:

It is often useful to think of these electrons as being attached to the atoms by springs. The electrons and their attached springs have a tendency to vibrate at specific frequencies. Similar to a tuning fork or even a musical instrument, the electrons of atoms have a natural frequency at which they tend to vibrate. When a light wave with that same natural frequency impinges upon an atom, then the electrons of that atom will be set into vibrational motion. (This is merely another example of the resonance principle introduced in Unit 11 of The Physics Classroom Tutorial.) If a light wave of a given frequency strikes a material with electrons having the same vibrational frequencies, then those electrons will absorb the energy of the light wave and transform it into vibrational motion.

Can the above be right? Wouldn't the vibrational frequencies of the electrons in atoms be just non classical? How could there be a natural frequency of the electrons that matches a light wave with the same natural frequency if one is non classical (the electron) and the other is classical (the light wave)?

Perhaps they have this all wrong and resonance just refers to vibrational frequencies of molecules matching specific light wave frequencies. But that idea seems unlikely since molecules just vibrate within the infra-red range. For example, I've heard that the human body has a resonant frequency around 68 Hz. I've heard all objects have a resonant frequency.

What is meant by the resonant frequency of an object?

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  • $\begingroup$ The classical model of electrons bound by elastic forces can be used to derive the dependency of the refractive index of a dielectric material from the frequency of the em radiation going through it. It may happen that classical and semiclassical models give results that are not that far off from what you can get from an experiment. Doing everything quantumechanically might not be the aim of a website like physicsclassroom. $\endgroup$
    – Peltio
    Jun 24, 2015 at 20:49
  • $\begingroup$ Peltio -- But aren't orbitals inside an atom stationary; i.e. no real vibration (perhaps only that of a non classical type)? Just confused how those same orbitals could simultaneously have a classical vibration. $\endgroup$
    – adam3033
    Jun 24, 2015 at 21:19
  • $\begingroup$ @adam3033 - You need to keep in mind the old saying: All models are wrong, but some are more useful than others. The behavior of electrons as modeled by springs IS classical modeling. And for some purposes, such as the absorption of light by electrons, the classical model works pretty well. The quote which is giving you trouble is simply trying to provide an easy conceptual framework for the classical model. The concept of (sort of) stationary orbitals is very much non-classical. Don't try to mix the two - you'll just get a headache. $\endgroup$
    – WhatRoughBeast
    Jun 25, 2015 at 3:06
  • $\begingroup$ WhatRoughBeast -- Definitely see what you're saying. Would the best way to describe it, though, be that even though electrons absorb it, the electron, itself, isn't that classical vibration? Just absorbs? $\endgroup$
    – adam3033
    Jun 25, 2015 at 4:04

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Resonant frequency of an object: A frequency at which the object will best capture and retain energy from a driving force. Driving energy into an object or system with a force at the natural frequency of the object will maximize energy transfer.

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The resonant, frequency is the frequency at which an object tends to vibrate. Every rigid object in existence has a natural structural resonance frequency, a frequency at which it, metaphorically speaking, wants to shake more than any other. If you vibrate an object at its resonant frequency, it will gradually shake more and more wildly.

This frequency depends on the size, shape, and composition of the object. So an object will vibrate strongly when it is subjected to vibrations or regular impulses at a frequency equal to or very close to its resonant frequency.

Even mechanical resonance can produce vibrations strong enough to destroy the object in which they occur.

For particles, there are different opinions in physics currently. The most correct one i find to be that the frequency (and therefore wavelength) of particles like photon is given by it's internal oscillations speed.

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