The relationship between Planck's constant (h), the speed of light (c), and electric charge (e) is fundamental to quantum mechanics and is described by the equations of quantum electrodynamics (QED).
In QED, the fundamental interaction between light (electromagnetic radiation) and charged particles is described by the exchange of virtual photons. Planck's constant, denoted by h, is a fundamental constant of nature that relates the energy (E) of a quantum particle to its frequency (ν) through the equation E = hν. It sets the scale for the quantization of energy in quantum mechanics.
The speed of light, denoted by c, is a fundamental constant representing the maximum speed at which information or causality can propagate in the universe.
Electric charge, denoted by e, is a fundamental property of particles that determines their electromagnetic interactions. It is the charge associated with the elementary charge carried by the electron and proton.
In the context of QED, the relationship between Planck's constant, the speed of light, and electric charge is most prominently seen in the formulas for the energy and momentum of a photon. The energy of a photon can be expressed as E = hf, where f is the frequency of the photon. Additionally, the momentum of a photon can be given by p = hf/c, where p is the momentum and c is the speed of light.
These equations illustrate how Planck's constant, the speed of light, and electric charge interrelate in the quantum description of electromagnetic interactions. They provide a foundation for understanding phenomena such as the photoelectric effect, the quantization of energy levels in atoms, and the behavior of particles and electromagnetic waves at the quantum level.