|The frequency at which microwave ovens operate is about 2.45 GHz, which is about the resonant frequency of the free water molecule. Can you calculate this resonant frequency or was it determined experimentally? — GW
While most microwave ovens operate at 2.45 GHz, that frequency is not a resonant frequency for the water molecule. In fact, using a frequency that water molecules responded to strongly (as in a resonance) would be a serious mistake—the microwaves would all be absorbed by water molecules at the surface of the food and the center of the food would remain raw. Instead, the 2.45 GHz frequency was chosen because it is absorbed weakly enough in liquid water (not free water molecules) that the waves maintain good strength even deep inside a typical piece of food. Higher frequencies would penetrate less well and cook less evenly. Lower frequencies would penetrate better, but would be absorbed so weakly that they wouldn't cook well. The 2.45 GHz frequency is a reasonable compromise between the two extremes.