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In the classical world, a radio antenna designed for operation at a certain wavelength must be close to the same size as the wavelength – typically within about one order of magnitude. Otherwise, the antenna will not work efficiently. Intuitively, one might imagine that low-energy photons are "too large" to be absorbed by a small antenna and will simply pass through. (Admittedly, this argument is rather misleading and shouldn't be taken too seriously.)

This limitation doesn't apply to atoms. A typical atomic orbital might have a characteristic length scale of a few ångströms, yet atoms often absorb and radiate photons with wavelengths as large as a few hundred nanometers. For their sizes, atomic "antennas" can be surprisingly efficient. For example, with careful experimental design, a single atom can block as much as 3% of an incident laser beam.

Comparing these two cases motivates me to wonder about what happens at intermediate scales. In a single atom, energy levels with large transition probabilities are normally separated by perhaps an eV (plus or minus a couple of orders of magnitude). Therefore, atomic spectra have their strongest absorption lines in this range. However, molecules of moderate size can have many energy levels separated by milli- or micro-eV. Is it possible that there are electrically small molecules that absorb and emit microwaves, or lower-frequency radio waves, with atom-like efficiency? If so, what would these molecules look like?

To take the question one step further: by analogy with chemiluminescence, would it be theoretically possible to engineer a chemical reaction that produces a large amount of low-frequency radio waves from a small flask?


I am aware that some polar molecules, such as trifluoroiodomethane, have rotational spectra that extend into the microwave range. Also, hyperfine transitions are very low-energy processes. However, as far as I know, the "antenna efficiency" of these systems is typically very low. (If this is wrong, I'd appreciate being corrected.)

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Yes, atoms and molecules can absorb or scatter radio waves if they are excited into very high quantum states (so called 'Rydberg States'; see https://en.wikipedia.org/wiki/Rydberg_atom ). These states are for instance created through recombination of ions and electrons in a plasma. The density of atoms in these states is very small but the absorption and resonance cross section is very large as it increases strongly with quantum number n (~n2.4 for absorption/ionization and ~n4 for resonance scattering). Given a long enough optical path length, radio waves could become totally absorbed or scattered this way. The spontaneous radio emission from such highly excited Rydberg states (with n>100) is also well known from astronomical observations (radio emission lines from HII-regions)

I published a paper about this some years ago in Radio Science which is available at https://www.researchgate.net/publication/253543274_Scattering_of_radio_waves_by_high_atomic_Rydberg_states (note that this paper is very long, going on 100 pages, it was therefore not fully published in print, but only a summery version, with the full version only published on microfiche at the time; the Researchgate version linked above is the full version).

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Atoms and molecules are indeed very small, and, when calculating their absorbtion of radiation, one usually assumes the electric/magnetic fields to be homogeneous (even for blue light the wave length of 400nm is much bigger than the size of an atom or a molecule).

There is however a crucial difference between the absorption of energy by atoms/molecules and what happens in the antenna. The atomic/molecular absorption is proportional to the light intensity, i.e., it is not sensitive to the phase of the radiation, while the frequency can be detected only via the absorption frequency, i.e., the separation between the energy levels. Thus, the major way of encoding information in optical communication is by switching light on/off, in a binary fashion. In radio language we can call it Amplitude modulation (AM).

Antenna, on the other hand, converts EM radiation into a current with the same frequency and phase as the radiation - it is the sensitivuty to the phase of the electromagnetic wave that is achieved by having a long antenna (the actual size is actually half wave length, rather than the whole wave length). This enables efficient information encoding via frequency and phase modulation.

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First of all, a radio wave is modulated EM radiation. At the atomic level, this means that the surface electrons on the antenna rod are accelerated back and forth.

The lower the desired frequency of the radio wave, the longer the rod must be. This prevents the electrons at the end of the rod from increasing the resistance of the entire rod too quickly.

Each electron moves only a little, hindered by its free path length, which is small. But in sum, many electrons accelerate synchronously in the same direction and emit a large number of polarised photons. Are these photons have wavelengths comparable with the length of the antenna? Not at all. The electrons emit radiation from IR to X-rays.*)

The reason why radio waves are penetrating the air is the next. The huge number of polarized photons override the stochastic process in gases. A single photon will be absorbed immediately by the molecules of the gas. The same happens at the receiver. The periodical arrival of polarized photons (with their aligned electric field component) induces an acceleration of surface electrons in the receiving conducting material. By this the receiving antenna can be very small comparing to the emitting antenna.

About the size of the atom and the absorption of photons. The double-slit experiment shows that the distance at which the edge affects the photon is very large compared to the wavelength of the photon. The effective cross-sections of both actors are large. This raises the question of how large the action radius of the interaction between electron and photon is. Such a function has a second component in addition to the distance, the energy content (respectively the wavelength or the frequency) of the photon.*

To take the question one step further: by analogy with chemiluminescence, would it be theoretically possible to engineer a chemical reaction that produces a large amount of low-frequency radio waves from a small flask?

Yes. Using modulated EM radiation this is possible. Using only light from a thermic source, no, this is impossible.


*)
This is the real reason why it s not recommended to stay in front of a radar. The modulated EM radiation of a radar is for example 2 gigahertz, while X-rays are in the range from 30 petahertz to 30 exahertz.

**)
Some time ago I asked on PSE what the original standard of comparison was for determining the wavelength or frequency of visible light. How did we determine that red has a wavelength of 650 nm?

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