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Encyclopedia > Planck's constant
A commemoration plaque for Max Planck on his discovery of Planck's constant, in front of Humboldt University, Berlin. English translation: "Max Planck, discoverer of the elementary quantum of action h, taught in this house from 1889 to 1928."

Planck's constant (denoted h) is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is 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 $hbar$, pronounced "h-bar"). Planck's constant is also used in measuring energy emitted by light photons, such as in the equation E=hν, where E is energy, h is Planck's constant, and ν (Greek letter nu) is frequency. Image File history File links Download high resolution version (1168x1760, 265 KB) A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... Image File history File links Download high resolution version (1168x1760, 265 KB) A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... Max Karl Ernst Ludwig Planck (April 23, 1858 â€“ October 4, 1947) was a German physicist. ... Alternative meaning: Humboldt State University, located in Arcata, California Humboldt-Universität zu Berlin The Humboldt University of Berlin (German Humboldt-Universität zu Berlin) is the successor to Berlins oldest university, the Friedrich Wilhelm University (Friedrich-Wilhelms-Universität), founded in 1810 by the liberal Prussian educational reformer... Berlin is the capital city and one of the sixteen states of the Federal Republic of Germany. ... // ... In physics, a quantum refers to an indivisible, and perhaps, elementary entity. ... Fig. ... Max Karl Ernst Ludwig Planck (April 23, 1858 â€“ October 4, 1947) was a German physicist. ... Because of technical limitations, some web browsers may not display some special characters in this article. ... For other uses, see Nu. ...

Planck's constant and the reduced Planck's constant are used to describe quantization, a phenomenon occurring in subatomic particles such as electrons and photons in which certain physical properties occur in fixed amounts rather than assuming a continuous range of possible values. In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ... The Electron is a fundamental subatomic particle that carries an electric charge. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, microwaves, radio waves, and visible light are all forms of light. ...

The value of Planck's constant is:

$h = 6.626 0693 (11) times10^{-34} mathrm{J}cdotmathrm{s}$
$= 4.135 667 43(35) times10^{-15} mathrm{eV}cdotmathrm{s}$

## Units, value and symbols GA_googleFillSlot("encyclopedia_square");

Planck's constant has dimensions of energy multiplied by time, which are also the dimensions of action. In SI units Planck's constant is expressed in Joule-seconds. The dimensions may also be written as momentum times distance (Nms), which are also the dimensions of angular momentum. Often the unit of choice is eV•s, because of the small energies that are often encountered in quantum physics. Two distinct views exist on the meaning of time. ... In physics, the action is an integral quantity that is used to determine the evolution of a physical system between two defined states using the calculus of variations. ... Cover of brochure The International System of Units. ... A joule-second is a unit of power over time called action or a unit of angular momentum. ... In classical mechanics, momentum (pl. ... Distance is a numerical description of how far apart things lie. ... The newton (symbol: N) is the SI unit of force. ... The metre, or meter (U.S.), is a measure of length. ... Look up second in Wiktionary, the free dictionary. ... Gyroscope. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...

The value of Planck's constant is:

$h =,,, 6.626 0693 (11) times10^{-34} mbox{J}cdotmbox{s} ,,, = ,,, 4.135 667 43(35) times10^{-15} mbox{eV}cdotmbox{s}$

The two digits between the parentheses denote the uncertainty (standard deviation) in the last two digits of the value. Various brackets in Arial // In writing Brackets are punctuation marks, used in pairs to set apart or interject text within other text. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is defined as the square root of the variance. ...

The value of Dirac's constant is:

$hbar stackrel{mathrm{def}}{=} frac{h}{2pi} = ,,, 1.054 571 68(18)times10^{-34} mbox{J}cdotmbox{s} ,,, = ,,, 6.582 119 15(56) times10^{-16} mbox{eV}cdotmbox{s}$

The figures cited here are the 2002 CODATA-recommended values for the constants and their uncertainties. The 2002 CODATA results were made available in December 2003 and represent the best-known, internationally-accepted values for these constants, based on all data available as of 31 December 2002. New CODATA figures are scheduled to be published approximately every four years. CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ... December 31 is the 365th day of the year (366th in leap years) in the Gregorian Calendar. ... For album titles with the same name, see 2002 (album). ...

Unicode reserves codepoints U+210E () for Planck's constant, and U+210F () for Dirac's constant. Because of technical limitations, some web browsers may not display some special characters in this article. ...

## Origins of Planck's constant

Planck's constant, $h$, was proposed in reference to the problem of black-body radiation. The underlying assumption to Planck's law of black body radiation was that the electromagnetic radiation emitted by a black body could be modeled as a set of harmonic oscillators with quantized energy of the form: As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... Black body spectrum as a function of wavelength In physics, the spectral intensity of electromagnetic radiation from a black body at temperature T is given by the Plancks law of black body radiation: where: I(Î½) is the amount of energy per unit time per unit surface area per unit... The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. ...

$E = h nu = h omega /(2 pi) = hbar omega$

$E$ is the quantized energy of the photons of radiation having frequency (Hz) of $nu$ (nu) or angular frequency (radian/sec) of $omega$ (omega). The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, microwaves, radio waves, and visible light are all forms of light. ... Sine waves of various frequencies; the bottom waves have higher frequencies than those above. ... The hertz (symbol: Hz) is the SI unit of frequency. ... For other uses, see Nu. ... It has been suggested that this article or section be merged into Angular velocity. ... The radian is a unit of plane angle. ... Note: This article contains special characters. ...

This model proved extremely accurate, but it provided an intellectual stumbling block for theoreticians who did not understand where the quantization of energy arose — Planck himself only considered it "a purely formal assumption". This line of questioning helped lead to the formation of quantum mechanics. Fig. ...

In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental corner-stones to the entire theory lies in the commutator relationship between the position operator $hat{x}$ and the momentum operator $hat{p}$: In mathematics, the commutator gives an indication of how poorly a certain binary operation fails to be commutative. ...

$[hat{p_i}, hat{x_j}] = -i hbar delta_{ij}$

where δij is the Kronecker delta. For more information, see the mathematical formulation of quantum mechanics. In mathematics, the Kronecker delta or Kroneckers delta, named after Leopold Kronecker (1823-1891), is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ...

## Usage

Planck's constant is used to describe quantization. For instance, the energy (E) carried by a beam of light with constant frequency (ν) can only take on the values Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength [citation needed]. The elementary particle that defines light is the photon. ... Sine waves of various frequencies; the bottom waves have higher frequencies than those above. ...

$E = n h nu ,,quad ninmathbb{N}$

It is sometimes more convenient to use the angular frequency $omega=2pi,nu$, which gives It has been suggested that this article or section be merged into Angular velocity. ...

$E = n hbar omega ,,quad ninmathbb{N}$

Many such "quantization conditions" exist. A particularly interesting condition governs the quantization of angular momentum. Let J be the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction. These quantities can only take on the values Gyroscope. ...

$begin{matrix} J^2 = j(j+1) hbar^2, & j = 0, 1/2, 1, 3/2, ldots J_z = m hbar, qquadquad & m = -j, -j+1, ldots, jend{matrix}$

Thus, $hbar$ may be said to be the "quantum of angular momentum".

Planck's constant also occurs in statements of Heisenberg's uncertainty principle. The uncertainty (more precisely: the standard deviation) in any position measurement, Δx, and the uncertainty in a momentum measurement along the same direction, Δp, obeys Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics, and acknowledged to be one of the most important physicists of the twentieth century. ... In quantum physics, the Heisenberg uncertainty principle or the Heisenberg indeterminacy principle â€” the latter name given to it by Niels Bohr â€” states that when measuring conjugate quantities, which are pairs of observables of a single elementary particle, increasing the accuracy of the measurement of one quantity increases the uncertainty of... // Relation between uncertainty, probability and risk In his seminal work Risk, Uncertainty, and Profit, Frank Knight (1921) established the important distinction between risk and uncertainty: â€¦ Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is defined as the square root of the variance. ...

$Delta x Delta p ge begin{matrix}frac{1}{2}end{matrix} hbar$

There are a number of other such pairs of physically measurable values which obey a similar rule.

## Dirac's constant

Dirac's constant or the "reduced Planck's constant", $hbar = frac{h}{2 pi}$, differs only from Planck's constant by a factor of . The SI unit of measurement of Planck's constant is joule per hertz, or joule per (turn per second), while the unit of measurement of Dirac's constant is joule per (radian per second). The two constants are merely conversion factors between energy units and frequency units. Cover of brochure The International System of Units. ... The hertz (symbol: Hz) is the SI unit of frequency. ... The word turn can mean: Look up turn in Wiktionary, the free dictionary. ... The radian is a unit of plane angle. ...

Electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... In physics, the SchrÃ¶dinger equation, proposed by the Austrian physicist Erwin SchrÃ¶dinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ... The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance Ïƒ takes on the quantized values where e is the elementary charge and h is Plancks constant. ...

## References

• NIST link to CODATA value
• Barrow, John D. (2002). The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe (in English). Pantheon Books. ISBN 0-375-42221-8.

CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ... John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ...

Results from FactBites:

 NationMaster - Encyclopedia: Planck pressure (710 words) Planck units are only one system of natural units among other systems, but might be considered unique in that these units are not based on properties of any prototype, object, or particle but are based only on properties of free space. Planck's tenure at Münich was interrupted by illness in 1875. Planck's suggestion was that the heat energy radiated by a fl body be thought of as a stream of "energy bundles," the magnitude of which is a function of the wavelength of the radiation.
 Kids.Net.Au - Encyclopedia > Plancks constant (164 words) Planck's constant, denoted h, named after the physicist Max Planck, is a physical constant which appears in all quantum mechanical equations. Js Planck's constant can be seen as a conversion factor between frequency and energy, especially for photons. The constant $\hbar$ is sometimes referred to as Dirac's constant after Paul Dirac.
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