| Planck constant | |
|---|---|
| Name | Planck constant |
| Quantity | action, energy × time |
| SIunit | J·s |
Planck constant
The Planck constant is a fundamental physical constant that relates the energy of a quantum to the frequency of its associated wave. It is central to Quantum mechanics and underpins the quantization of energy, linking microscopic processes to observable phenomena in Atomic physics and Solid-state physics.
The Planck constant, commonly denoted by h and its reduced form ħ (h-bar), defines the scale at which classical descriptions break down and quantum effects dominate. It appears in the fundamental relation E = hν between energy E and frequency ν for photons, and in the quantization conditions used by Niels Bohr in early models of the hydrogen atom. The constant sets the quantum of action and determines the discrete spectra observed in black-body radiation and atomic transitions studied at institutions such as the Max Planck Society and the Cavendish Laboratory.
The constant was introduced by Max Planck in 1900 to derive Planck's law of black-body radiation, resolving the ultraviolet catastrophe predicted by classical Rayleigh–Jeans law. Planck's hypothesis—that electromagnetic energy is emitted in discrete quanta—was motivated by experimental data from measurements by Hermann von Helmholtz successors and by precise cavity radiator experiments performed in the late 19th century. Planck's work influenced pioneers including Albert Einstein (who applied quantization to the photoelectric effect), Arnold Sommerfeld, and Wolfgang Pauli, shaping the development of matrix mechanics and wave mechanics.
In theoretical formulations, h has units of action (joule-seconds, J·s) and appears in the canonical commutation relation [x,p] = iħ between position x and momentum p in canonical quantization. The reduced constant ħ = h/(2π) simplifies expressions in the Schrödinger equation, the Heisenberg uncertainty principle, and in angular momentum quantization where eigenvalues come in multiples of ħ. The Planck constant also defines derived scales such as the Planck length, Planck time, and Planck energy when combined with the gravitational constant G and the speed of light c, linking quantum theory to attempts at quantum gravity.
The relation E = hν explains the discrete energy transfer in the photoelectric effect, which was experimentally characterized by Heinrich Hertz and theoretically explained by Albert Einstein in 1905. Photons carry energy proportional to frequency and momentum p = h/λ, connecting h to Compton scattering and de Broglie matter waves. In atomic and molecular spectroscopy, transition energies are integer multiples of h times a frequency difference, underpinning technologies like lasers developed at laboratories such as Bell Labs and their successors. The Heisenberg uncertainty principle Δx·Δp ≥ ħ/2 establishes limits on simultaneous measurements and arises mathematically from the presence of ħ in commutation relations, with experimental tests carried out in facilities including CERN and university quantum optics groups.
Early determinations of h used black-body spectra and the photoelectric effect; later precision measurements exploited phenomena such as Josephson effect and Watt balance (also called Kibble balance) experiments. The Josephson constant K_J = 2e/h links h to measurements of voltage using superconducting junctions in standards laboratories like the National Institute of Standards and Technology (NIST) and the Physikalisch-Technische Bundesanstalt (PTB). The Kibble balance compares mechanical and electrical power to determine the Planck constant via electrical measurements traceable to the quantum Hall effect and the von Klitzing constant. Another route uses the Avogadro project with crystalline silicon spheres to relate h to the molar mass and N_A. Precision cryogenic and metrology techniques across national metrology institutes refined the value to parts in 10^8 before the SI redefinition.
In the 2019 redefinition of the SI, the Planck constant was assigned an exact numerical value, fixing the kilogram in terms of h and thus redefining mass via quantum electrical standards and the Kibble balance. This change connected h directly to other exact constants like the speed of light c and the elementary charge e (via Josephson and quantum Hall relations), and altered the status of the kilogram from an artifact to a constant-based definition. The fixed value influences precision measurements in quantum metrology, atomic clocks research at institutions such as NPL and NIST, and ongoing efforts in fundamental physics to test consistency among constants like the fine-structure constant α and the Rydberg constant.
Category:Physical constants Category:Quantum mechanics Category:Metrology