The correct comparison of the energies of electromagnetic waves from the options given is:
Visible light has higher energy than infrared light because visible light has higher frequencies.
This statement is correct because the energy of electromagnetic waves is directly proportional to their frequency (E = hν, where E is energy, h is Planck's constant, and ν is frequency). Visible light has higher frequencies compared to infrared light, which means it also has higher energy.
The other statements are incorrect based on the relationships between energy, frequency, and wavelength:
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X-rays have lower energy than gamma rays because X-rays have higher frequencies. - This is incorrect; X-rays actually have higher frequencies than some gamma rays, so they can have lower energy, but the relationship is not straightforward based on frequency alone.
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X-rays have lower energy than gamma rays because X-rays have shorter wavelengths. - This is incorrect; typically, gamma rays have shorter wavelengths than X-rays and consequently higher energy.
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Visible light has higher energy than infrared light because visible light has longer wavelengths. - This is incorrect; it is the shorter wavelengths of visible light (compared to infrared) that give it higher energy, not the longer wavelengths.
Thus, the only correct statement regarding the comparison of energies is the one about visible light and infrared light.