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I recently learned about the "watering hole," a group of frequencies between 1.42 and 1.66 GHz. I also read that microwave ovens operate at 2.4 GHz.

If 21 to 18 cm (1.42 to 1.66 GHz) is the resonant frequency of hydrogen and hydroxyl, respectively, how do I arrive at the resonant frequency of water using those numbers? Is the resonant frequency 2.4 GHz (approx) based on the frequency microwave ovens use?

I guess what I am clearly trying to ask is: Is resonance of a molecule (like water) determined by constituent parts (as I am supposing) or are there other considerations?

And as I look at this question, why does hydrogen, something that is less massive, have a lower frequency resonance? Is it because there is less mass requiring less force to move it to resonance, are my facts incorrect, or is there something I'm going to learn with the answer to the first part of the question?

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    $\begingroup$ The microwave absorption of water is from the hydrogen bonds so is broad and flat rather than resonant lines. Microwave oven frequency is chosen for not being used for communications rather than a particular chemical match $\endgroup$
    – Martin Beckett
    Feb 9, 2018 at 2:42
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    $\begingroup$ @MartinBeckett To be fair, water absorption is probably a big part of why that band is not used for communication. $\endgroup$
    – The Photon
    Feb 9, 2018 at 3:42
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    $\begingroup$ I don't think we should ever expect to see any sharp resonant structures in the absorption spectrum of a liquid. Every molecule in the liquid is interacting with all its neighbors. Systems with a large number of degrees of freedom have a large number of weak resonances, not a single strong resonance. Any resonant frequency of the water molecule will be observed in the gaseous state only. $\endgroup$
    – user4552
    Feb 9, 2018 at 4:58
  • $\begingroup$ I just want to thank everyone for all the education that has been provided on this question. $\endgroup$
    – Everett
    Feb 9, 2018 at 8:05
  • $\begingroup$ @ThePhoton, it seems to have been a bit circular. The ISM band was fixed because some early microwaves used it, they chose the frequency because some adapted radar technology worked there. The frequency then became locked in because of the ISM band. None of it was really chosen ideally $\endgroup$
    – Martin Beckett
    Feb 13, 2018 at 1:45

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The microwave heating of water has nothing to do with resonances of the water molecule or any of its components. The heating is due to the permanent dipole moment of water, which is also responsible for its high dielectric constant. The electric microwave ac field lets the molecule rotate leading to frictional energy losses and thus heating.

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