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Because in theory, visible light contains more energy than the microwaves actually used to cook your food.

1) Does it have to do with resonance frequency of the $H_2O$ molecule?

2) How can microwaves be dangerous when they are about the same wavelength as Radio waves? (unless it has to do more with intensity)

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1) The frequency chosen in microwaves precisely corresponds to the vibrational states of water, fats and sugars according to "How stuff works" on microwaves.

http://home.howstuffworks.com/microwave1.htm

This frequency, has an energy, equal to, E = hf, where h is planck's constant. This energy is related to the vibrational states

http://en.wikipedia.org/wiki/Molecular_vibration

Since most foods have water, fat, or sugars in them, and they absorb this frequency and start vibrating, then they collide with other molecules and make them move too. When a group of molecules or atoms start moving around, then its "hot". That's what heat basically is.

Even if visible light is more energetic than microwaves, they do not correspond to the vibrational states of the molecules in the food, (water, fats, and sugars). Therefore, what happens is that the light is not effectively absorbed. It gets reflected, or passes right through.

If you have some EM wave that's extremely high in energy, it would probably ionize the molecules in your food, which would literally start breaking it apart. (Which you don't want)

2) Microwaves are dangerous to humans or living organisms because even if they are low in energy, corresponding to radio waves, there frequency corresponds to water, fats and sugars vibrational states. This is what we and living organisms are mostly made out of. Therefore, if you are inside a microwave, or if you put a live animal in a microwave, it will vibrate all the water, fats and sugar molecules. You will immediately feel really hot really fast, and all other molecules would start moving. You'll be so hot that the water content in your body would have enough energy to start boiling. And when your water content in your body starts boiling, your cells break down and you would probably die. This is why its dangerous.

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Microwaves don't heat matter through resonance, and the howstuffworks link doesn't claim that they do. –  Ben Crowell May 3 '13 at 5:10
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"Sometimes, microwave heating is explained as a resonance of water molecules, but this is incorrect:[11] such resonances occur only at above 1 terahertz (THz).[12]" Wikipedia

"The radio waves used by microwaves, as with any device that uses radio waves, produce a type of radiation. ... Microwaves produce non-ionizing radiation. Non-ionizing radiation doesn’t have the power to change your DNA and is not as dangerous as ionizing radiation. " LifeScript

"Microwaves... have an interesting property: They're absorbed by water, fats and sugars. Once absorbed, they're converted directly into atomic motion -- heat. These waves boast another interesting, related property, too: They're not absorbed by most plastics, glass or ceramics. Metal reflects microwaves, which is why metal pans don't work well in a microwave oven. It's also why the devices have metal walls -- for reflection." HowStuffWorks

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The first and third quotations appear to be inconsistent with each other; how do you reconcile them? Where do Wikipedia's citations go? What does the second quotation have to do with the question? –  Colin McFaul Jan 2 '13 at 4:47
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