What equation relates energy and frequency for a photon?

The relationship between energy and frequency for a photon is described by the equation E = hf, where E represents the energy of the photon, h is Planck’s constant (a fundamental constant in quantum mechanics approximately equal to (6.626 \times 10^{-34} , \text{Js})), and f is the frequency of the photon. This equation shows that the energy of a photon is directly proportional to its frequency, meaning that as the frequency increases, the energy of the photon also increases. This principle is a cornerstone of quantum mechanics and helps explain phenomena such as the photoelectric effect, which demonstrated that light can impart energy to electrons depending on its frequency.

The other choices do not pertain to the relationship between energy and frequency in the context of photons. For example, E = mc² expresses the equivalence of mass and energy, while E = mg relates energy to mass under the influence of gravity. E = kT describes the relationship between energy and temperature in thermodynamics but is not relevant to photons. These equations are important in their respective areas of physics but do not describe the specific energy-frequency relationship critical to understanding photon behavior.