Answer
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Work Step by Step
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1. The first type of radiation with a frequency of 107.1 MHz corresponds to FM radio waves. This is because the frequency range for FM radio is typically from 88 to 108 MHz.
2. The second type of radiation with a wavelength of 2.12x10^-10 m (or 0.212 nanometers) corresponds to X-rays. X-rays usually have wavelengths ranging from 0.01 to 10 nanometers.
3. The third type of radiation with photon energy of 3.97x10^19 J/photon would fall in the gamma-ray range. The energy of a gamma-ray photon is usually very high, greater than 10^18 J/photon.
In order of increasing photon energy: FM radio waves < X-rays < Gamma rays
And, in order of increasing frequency: FM radio waves < X-rays < Gamma rays
Please note that both orders are the same because in electromagnetic radiation, energy and frequency are directly proportional (via Planck's constant). As frequency increases, so does the energy, and vice versa.
