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I was trying to understand why gamma rays (like the x-ray machine at my dentist) have much higher energy compared to Radio AM waves with very high amplitude (hooked up to very high voltage), essentially was comparing energy coming from amplitude vs wave length.

I asked the above question in another forum and I was told gamma rays cannot even be generated the same way RF waves are generated with alternating current, they are 2 different things.

So now I have 2 questions instead:

  • What happens if a current is alternated at >= 3PHz (the frequency of x-rays) ? is such thing not possible?

  • If a regular AM radio transmitter is hooked up to a very high (close to infinite) power source, is it's wave still not as energetic as a gamma ray and cannot ionize atoms? why?

Dan
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5 Answers5

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The frequency of light belongs to the classical electromagnetic waves, perfectly modeled with Maxwell equations.

By going to smaller and smaller distances in the atoms and molecules we have arrived at the quantum mechanical level, and discovered experimentally that classical electromagnetic waves are built up of photons, elementary particles with energy equal to $h ν$ where $ν$ is the frequency of the classical wave a very large number of photons build up quantum mechanically.

To get an intuitive feeling please read this recent answer of mine .

Look at this table of wavelengths .

The gammas have energies of MeV, one has to go to the dimensions of a nucleus in order to reach such energies. The X rays of keV, which are attainable in the atomic dimensions. The corresponding wavelenths of the classical electromagnetic radiation that could be built up by such energies are tiny, pico-mm, in contrast with the large wavelengths for the classical waves, which are from centimeters to hundreds of meters.

What happens if a current is alternated at >= 3PHz (the frequency of x-rays) ? is such thing not possible?

It is not possible to manipulate particles at such small distances, to make the alternating current you envisage. It is in the domain of quantum mechanics where different equations hold to the ones describing charged particle behavior.

If a regular AM radio transmitter is hooked up to a very high (close to infinite) power source, is it's wave still not as energetic as a gamma ray and cannot ionize atoms? why?

Because radio wave photons have small energy .

anna v
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You cannot generate gamma rays in an electronic circuit. There are simply no circuit elements that are able to change/rectify/oscillate fast enough. Otherwise you would have to ask yourself why computers are still operating at a few Gigahertz if there was the possibility for anything substantially faster.

Moreover, gamma rays penetrate macroscopic matter almost undisturbed. So even if you were able to build an antenna small enough that it could theoretically send/receive gamma waves, the radiation would simply go right through the matter of that antenna. Moreover, those antennae would have to have a size of the order of picometers to femtometers, i.e. not far from or about the same size as an atomic nucleus, so no chance to build such a thing.

But, gamma rays are actually electromagnetic waves, just like ordinary radio waves are. And the wavelength of any electromagnetic wave is directly related to the energy of each photon it contains. The amplitude, by contrast, is related to the number of the photons.

So, radio waves also contain photons of a certain wavelength/energy, but usually so freaking many of them, that it does not make sense to count them, and we just use amplitude to measure their strength. As opposed to that, gamma rays come out of atomic nuclei only sparingly, so it makes sense to count them individually, and express the energy in terms of the individual quanta, i.e. photons. If we wanted to talk about the amplitude of a gamma wave, we would need so many of them, that the "shot noise" of the individual photons becomes negligible.

oliver
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I was trying to understand why gamma rays (like the x-ray machine at my dentist) have much higher energy compared to Radio AM waves with very high amplitude

When people talk about the "energy" associated with gamma rays, they are talking about the energy of each individual photon. When people talk about the power of a radio signal, they are talking about the sum of the energies of all of the photons. A college radio station near me increased its power from ten Watts to a thousand Watts. That's a hundredfold increase in power, but what it means in physics terms is that they now are puting out 100 times as many photons as before. The energy per photon did not change.

Every radio transmitter contains an electronic oscillator that is tuned to a specific frequency—the same frequency as the photons that the transmitter emits. And, the maximum frequency of an oscillator is limited by (among other things) the speed of light: The period of an oscillator ($1/\text{frequency}$) can be no smaller than the amount of time it would take a beam of light to cross from one side of the oscillator to the other. An electronic circuit that could oscillate at the frequency of gamma rays would have to be smaller than a single atom!

Not exactly practical.

If a regular AM radio transmitter is hooked up to a very high (close to infinite) power source, is it's wave still not as energetic as a gamma ray and cannot ionize atoms? why?

TLDR: That's not how radio transmitters work. I don't have time or space here to explain how they do work, but increasing the power of a radio transmission only increases the number of photons. It does not increase the energy of the individual photons.

Solomon Slow
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Actually, gamma radiation can be generated in an electric circuit if the voltage is high enough, for example, on the order of 1 MV. Experimental evidence of gamma radiation in a long spark is reported in https://homepages.cwi.nl/~ebert/2015-JPD-Pavlo.pdf (J. Phys. D: Appl. Phys. 48 (2015) 025205 (13pp)). They report photon energies above 200 keV, I believe this is technically gamma radiation. The mechanism of generation of gamma radiation in the spark is rather complicated.

akhmeteli
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Pretty much possible, but not in the direct sense of a simple electronic oscilator.

See Synchrotron light sources

(The article discusses "x-rays" based on the emission origin and application, but synchrotron sources are practical up to MeV range, or not-so-soft gamma rays).

You can look from another side: to radiate (or absorb) electromagnetic radiation efficiently, your antenna has to be of size comparable to your wavelength. Good luck constructing a half-wave dipole for anything shorter than milimeter-scale waves.

fraxinus
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