Final answer:
The correct statement is that C. the photon energy is larger for the 1.5 micrometer light than for the 3.0 micrometer light because photon energy is inversely proportional to wavelength.
Step-by-step explanation:
When comparing two light photons, one with a wavelength of 1.5 micrometers and the other with a wavelength of 3 micrometers, it's important to understand that the energy of a photon is inversely proportional to its wavelength. In other words, as the wavelength increases, the photon's energy decreases. Given this relationship, the correct statement is (C) The photon energy is larger for the 1.5 micrometer light than for the 3.0 micrometer light. This is because the 1.5 micrometer photon has a shorter wavelength and therefore, according to the principles of quantum mechanics and wave-particle duality, it carries more energy compared to the photon with a longer wavelength of 3 micrometers.
Remember that photon energy decreases with longer wavelengths, and higher frequency translates to higher energy. Hence, for the visible spectrum, violet photons have more energy than red photons, and the same concept applies to wavelengths outside the visible range as well.