Planck's constant

The Planck constant (denoted h) is a natural constant named after Max Planck, one of the founders of quantum theory. A closely-related quantity is the reduced Planck constant (also known as Dirac's constant and denoted ħ, pronounced "h-bar").

Planck discovered in 1901 his constant in his study of black-body radiation. He found that the energy of this electromagnetic radiation consists of quanta of energy hν, where ν is the frequency of the radiation. These quanta are now called photons. The Planck constant is ubiquitous in quantum mechanics. For instance, it appears in the Schrödinger equation. Its small size is the main reason that quantum effects are only noticeable for microscopic particles such as electrons and nuclei.

Units, value and symbols

The Planck constant has dimensions of energy multiplied by time, which are also the dimensions of action. In SI units, the Planck constant is expressed in joule-seconds. The dimensions may also be written as momentum times distance (N·m·s), which are also the dimensions of angular momentum.

The value of the Planck constant is:

$h=\,\,\,6.626\ 068\ 96(33)\times 10^{-34}\ {\mbox{J}}\cdot {\mbox{s}}\,\,\,=\,\,\,4.135\ 667\ 33(10)\times 10^{-15}\ {\mbox{eV}}\cdot {\mbox{s}}.$

The two digits between the parentheses denote the standard uncertainty in the last two digits of the value.

The value of the Dirac constant is:

$\hbar \ \equiv {\frac {h}{2\pi }}=\,\,\,1.054\ 571\ 628(53)\times 10^{-34}\ {\mbox{J}}\cdot {\mbox{s}}\,\,\,=\,\,\,6.582\ 118\ 99(16)\times 10^{-16}\ {\mbox{eV}}\cdot {\mbox{s}}.$