Planck constant

The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to the Planck constant times its frequency. The Planck constant is of fundamental importance in quantum mechanics.

6.626070150 × 10−34 J⋅s = ( kg⋅m2⋅s−2)(s) = kg⋅m2⋅/s

At the end of the 19th-century physicists were unable to explain the spectrum of black body radiation, which had been measured with some accuracy. In 1900, Max Planck derived a formula for the spectrum that agreed with the measurements. He did this by assuming a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, and that constant is named in his honor. In 1905, the value E was associated by Albert 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 a photon.

Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, including the kilogram as traditionally defined by a metal cylinder called the International Prototype of the Kilogram (IPK), to replace the IPK as the standard of mass. The new definition was approved by the BIPM on 16 November 2018.

The new value of the Planck constant by the ISO standard is set to 6.626 070 150 x 10-34 J⋅s

How the planck constant is applied in everyday life needs the avogadro number

The Planck constant is related to the quantization of light and matter. It can be seen as a subatomic-scale constant. In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency. Atomic unit systems are based (in part) on the Planck constant.

The Planck constant is one of the smallest constants used in physics. This reflects the fact that on a scale adapted to humans, where energies are typically of the order of kilojoules and times are typically of the order of seconds or minutes, the Planck constant (the quantum of action) is very small.

Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of 540 THz (540×1012 Hz). Each photon has an energy E = hf = 3.58×10−19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 6.022×1023 mol−1. The result is that green light of wavelength 555 nm has an energy of 216 kJ/mol, a typical energy of everyday life.