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What frequencies of em radiation can ionize air at atmospheric pressure? Does it depend on the power of the transmitter/generator or just the frequency? Do some frequencies or power densities make air more conductive but not ionize it into a plasma? I know that temperature can make air into a plasma. Is there any way to heat air using em radiation other than with light?

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    $\begingroup$ maybe this will help: physics.stackexchange.com/questions/163679/… Also please add whatever you googled on your own, and what exactly causes trouble in understanding for you $\endgroup$ – aaaaaa Feb 10 '17 at 22:36
  • $\begingroup$ You are asking a lot of questions. This forum works best when you ask an individual, "deep" question. As @aaaaaa says - show a bit more of your thinking - what do you know, what are you struggling with. The link provided has quite a helpful answer. $\endgroup$ – Floris Feb 10 '17 at 22:53
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Technically, one only needs photons with energies $\geq$13.6 eV to ionize a single monatomic hydrogen atom, which corresponds to ~3300 THz (i.e., ~3.3 billion MHz) or wavelengths of ~91 nm (i.e., ~$9.1 \times 10^{-8}$ m). Note that the energy of a photon is given by $E = h \ \nu$, where $h$ is Planck's constant and $\nu$ is the frequency. For electromagnetic radiation in vacuum, we also know that $c = \lambda \ \nu$, where $\lambda$ is the wavelength and $c$ is the speed of light. The index of refraction of air is close enough to 1.0 for the rough estimates I use below.

However, with air, assuming its Earth's atmosphere at STP, one would first dissociate the molecules before any ionization would occur. I wrote a detailed answer about the energies necessary to dissociate all of the molecules in Earth's atmosphere at https://physics.stackexchange.com/a/233126/59023.

You can easily scale these estimates down to a more practical lab setting. To dissociate $N_{2}$ (i.e., diatomic nitrogen) one needs ~945 kJ/mole or ~9.79 eV per $N_{2}$ bond (Note that 9.79 eV corresponds to a ~$2.36716 \times 10^{15}$ Hz or a ~126.7 nm photon). $N_{2}$ comprises ~78.08% of Earth's atmosphere by volume so it would occupy ~78.08% of a one meter cubed container. Thus, there would be ~$4.7 \times 10^{23}$ molecules of $N_{2}$ in a one meter cubed container or ~0.7808 moles. Thus, we would need ~737.86 kJ of energy to dissociate all of the $N_{2}$ molecules.

What frequencies of em radiation can ionize air?

It is generally stated that one needs at least UV light to ionize most atoms, thus why it is called ionizing radiation. The UV spectrum extends from ~10-400 nm or ~750-30000 THz, so you can see that both of the estimated wavelengths shown above fall in the UV spectrum range.

Does it depend on the power of the transmitter/generator or just the frequency?

I suppose the answer is yes, but not for the reasons your question seems to imply. The power of the transmitter would determine the number of photons per unit time generated while the frequency would determine the energy of each photon. If you only sent out one photon per second, my hand-wavy guess is that the recombination rate would swamp the ionization rate, thus you would not see a net charge. This is a good thing so we can live (i.e., the recombination rate is higher than the ionization rate from solar radiation).

Do some frequencies or power densities make air more conductive but not ionize it into a plasma?

I am not sure what you are asking. The air is an excellent insulator and really only conducts electricity when there is an arc, i.e., molecules are ionized along the path of the arc allowing electrons to flow, thus a current. This generally requires very large electric fields, like ~30 kV/cm (or ~76 kV/inch).

I know that temperature can make air into a plasma.

No, this is not really right. The temperature of a gas is a measure of the mean kinetic energy of the molecules in the center of momentum rest frame. If the gas is very tenuous, then there would be little-to-no particle-particle collisions. You can take a neutral particle and make it go as fast as you want without ionizing it (ignoring acceleration or the energy source) because its speed does not matter. In its rest frame, it does not know its moving unless it "looks" at something else.

High temperatures can lead to ionization if there is a sufficiently high particle-particle collision rate and if the kinetic energy of the collision exceeds the ionization energy of at least one of the atoms.

Is there any way to heat air using em radiation other than with light?

The short answer is yes. There are three basic energy transport methods: thermal conduction, radiation, and convection. A standard oven used for cooking food (i.e., not a microwave oven) uses a combination of thermal conduction and radiation (I think thermal conduction dominates here but have heard arguments for both sides).

Update
In the following question and answer Do conventional ovens heat by thermal conduction or radiation? I show that it is actually radiation that dominates in conventional ovens.

Regarding the last question, if the EM radiation can interact with the gas (e.g., similar to how microwave ovens vibrate/excite water molecules), one can deposit energy into the gas. If the gas is collisionally mediated, like Earth's atmosphere below ~10 km, then after enough energy is added through the radiation one could ionize the gas molecules.

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