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I wonder why microwave has more "energy" to heat things up than visible light does. Microwave has a much longer wavelength, therefore should supposedly has less energy than visible light.
But does wavelength and frequency really have to do with how fast a certain type of electromagnetic radiations give an object heat, or it is something to do with how a microwave oven is built?
Microwaves don't have more energy, they just resonate at the frequency that causes molecular bonds to rotate. This specifically applies to dielectric molecules, molecules like water that have electric dipoles.
From Wikipedia:
Water, fat, and other substances in the food absorb energy from the microwaves in a process called dielectric heating. Many molecules (such as those of water) are electric dipoles, meaning that they have a partial positive charge at one end and a partial negative charge at the other, and therefore rotate as they try to align themselves with the alternating electric field of the microwaves. Rotating molecules hit other molecules and put them into motion, thus dispersing energy. This energy, when dispersed as molecular vibration in solids and liquids (i.e., as both potential energy and kinetic energy of atoms), is heat. Sometimes, microwave heating is explained as a resonance of water molecules, but this is incorrect such resonances occur only at above 1 terahertz
For reference, energy is related to wavelength by the formula: $$E=\frac{hc}{\lambda}$$ and
$$\lambda=\frac{c}{f}$$
where
You can see by the first equation that as $\lambda$ gets smaller $E$ gets larger.
The key difference with microwaves is the amount of energy emitted
Microwaves don't have more "energy" than visible light per photon. But this is irrelevant in the case of a microwave oven.
There are two reasons for this but the first one one (as described in the existing answer) is actually a distraction: microwaves are relatively efficient at exciting molecular rotations and vibrations (especially of ions) so dumping their energy as heat in the object they are interacting with (usually your food).
But this is a distraction from a more significant point: microwave ovens push out a lot of microwave energy, usually a little under a kilowatt. This is about 10 times the energy radiated by a traditional incandescent (visible) lightbulb. If you could dump that much visible light into a small volume and your food absorbed it, it would cook. But you are more likely to end up with a very hot box and food that wasn't cooked efficiently. Many electric heaters (radiating red and near infra-red photons) push the same sort of power as a microwave, but they radiate it over a much larger area and don't cook you because the energy is dumped over a very much larger volume. Unless you stand too close.
Electric grills are basically just very powerful incandescent bulbs tuned to emit most of their radiation in the near infra red. They emit similar power to a microwave (~kW) but don't cook food as efficiently as infra red is mostly absorbed by the surface of the food they heat (microwave energy penetrates more deeply allowing food to warm from the inside. Interestingly very salty foods may not cook as well in a microwave as surface effects (where the radiation couples strongly with the dielectric fields caused by salty ions) absorb more of the microwave energy near the surface.
