What equation represents energy in relation to frequency?

The correct representation of energy in relation to frequency is given by the equation E = H * ν. In this context, E denotes the energy of a photon, H represents Planck's constant (approximately 6.626 x 10^-34 Js), and ν (nu) is the frequency of the electromagnetic radiation. This equation originates from quantum mechanics, which describes how energy is quantized and directly proportional to the frequency of light.

Understanding this relationship is crucial in fields like spectroscopy and quantum mechanics, where it shows that higher frequency light (such as ultraviolet light) carries more energy compared to lower frequency light (like infrared light). This concept is foundational in wave-particle duality, where electromagnetic waves exhibit both wave-like and particle-like properties, leading to the concept of photons as discrete packets of energy.

The other equations represent different fundamental concepts. For instance, E = m * c^2 ties energy to mass and the speed of light, focusing on relativistic physics. E = F * d addresses the work-energy principle related to mechanical systems, while E = P * t encapsulates the relationship between energy, power, and time, relating to electric circuits and mechanical systems rather than the interaction of energy and frequency.