In quantum theory, the relationship between energy and frequency is described by the equation E = hf, where E represents energy, h is Planck's constant (a fundamental constant in quantum mechanics), and f represents the frequency of the particle or wave.
This equation is derived from the wave-particle duality of quantum objects. According to quantum theory, particles such as photons and electrons exhibit both wave-like and particle-like properties. In the case of light, it can behave as both a particle (photon) and a wave (electromagnetic wave).
When considering the wave-like nature of light, the energy of a wave is related to its frequency. A higher frequency corresponds to a wave oscillating more rapidly, which means it has more energy associated with it. This relationship is intuitive if you think about, for example, ocean waves. Higher-frequency waves, such as those produced during a storm, have more energy than lower-frequency waves on a calm day.
The constant h in the equation, known as Planck's constant, is a fundamental constant in quantum physics. It relates the energy of a quantum object to the frequency of its associated wave. Planck's constant is a fixed value, approximately equal to 6.62607015 x 10^(-34) joule-seconds, and it provides the proportionality between energy and frequency in quantum theory.
So, in quantum theory, the energy of a quantum object is directly proportional to its frequency, and the constant of proportionality is Planck's constant.