Whose equation is this?
It was arguably the most revolutionary thing Einstein did in his career (Pais quotes Einstein calling it the only really revolutionary thing he did; relativity can be seen as simply putting existing physics on a more solid theoretical and philosophical foundation), and it was the one accomplishment specifically mentioned in his Nobel Prize citation, awarded “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.”
This is the step that puts the “quantum” in “quantum mechanics,” telling us that energy comes in discrete chunks, not a continuous range of values. It’s the theoretical explanation for the photoelectric effect, which in turn is the basis for all manner of light sensors– basically anything that converts a light signal into an electrical signal.
The Planck constant used in this equation (denoted h, also called Planck’s constant) is a physical constant that is the quantum of action, central in quantum mechanics. First recognized in 1900 by Max Planck, it was originally the proportionality constant between the minimal increment of energy, E, of a hypothetical electrically charged oscillator in a cavity that contained black body radiation, and the frequency, v, of its associated electromagnetic wave. In 1905, the value E, the minimal energy increment of a hypothetical oscillator, was theoretically associated by Einstein with a “quantum” or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called the photon.
The Planck–Einstein relation connects the particulate photon energy E with its associated wave frequency v:
This energy is extremely small in terms of ordinarily perceived everyday objects.
Since the frequency v, wavelength λ, and speed of light c are related by v = c / λ, the relation can also be expressed as