# Difference between revisions of "Planck's constant"

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− | '''Planck's constant''' | + | '''Planck's constant''', denoted <math>h</math>, is a fundamental constant in [[physics]]. The current value of '''Planck's constant''' is <math>6.626070040(81) \times 10^{-34}</math> Joule-seconds (numbers in brackets represent uncertainty in the last two decimal places).<ref>http://physics.nist.gov/cgi-bin/cuu/Value?h</ref> |

− | + | ==History== | |

− | + | It was first used by [[Max Planck]] around 1900 to explain the radiation curves of black-bodies. He supposed that [[light]] could be modelled as a series of particles (now called [[photons]]), each with an [[energy]] proportional to its frequnecy, <math>\nu</math>. The constant of proportionality was Planck's constant. Mathematically this can be expressed as: | |

− | + | <math>E = h \nu</math> | |

− | [[ | + | |

+ | In 1924, Louis De Broglie proposed [[Wave-particle duality]], the idea that matter ([[proton]]s and [[electron]]s for example) had a wave-like nature.<ref>https://www.nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-bio.html</ref> Here too, is Planck's constant: | ||

+ | |||

+ | <math>\lambda = \frac{h}{p} </math> | ||

+ | |||

+ | where | ||

+ | :<math>\lambda</math> is the [[wavelength]] of the particle | ||

+ | :<math>p</math> is the [[momentum]] of the particle | ||

+ | |||

+ | The Planck constant also occurs in equations fundamental to [[quantum mechanics]], such as the [[Schrodinger equation]]. | ||

+ | |||

+ | ==Reduced Planck's Constant== | ||

+ | |||

+ | Planck's constant often occurs in equations with the mathematical constant <math>\pi</math>. As such, a factor of <math>\frac{1}{2 \pi}</math> may be taken into Planck's constant as | ||

+ | |||

+ | <math>\hbar = \frac{h}{2 \pi}</math> | ||

+ | |||

+ | The resulting constant is pronounced "h-bar". | ||

+ | |||

+ | ==See also== | ||

+ | *[[Quantum mechanics]] | ||

+ | *[[Photon]] | ||

+ | *[[Schrodinger equation]] | ||

+ | |||

+ | ==References== | ||

+ | {{Reflist}} | ||

+ | |||

+ | [[Category:Physics]] | ||

+ | [[Category:Quantum Mechanics]] |

## Latest revision as of 14:39, June 6, 2021

**Planck's constant**, denoted , is a fundamental constant in physics. The current value of **Planck's constant** is Joule-seconds (numbers in brackets represent uncertainty in the last two decimal places).^{[1]}

## History

It was first used by Max Planck around 1900 to explain the radiation curves of black-bodies. He supposed that light could be modelled as a series of particles (now called photons), each with an energy proportional to its frequnecy, . The constant of proportionality was Planck's constant. Mathematically this can be expressed as:

In 1924, Louis De Broglie proposed Wave-particle duality, the idea that matter (protons and electrons for example) had a wave-like nature.^{[2]} Here too, is Planck's constant:

where

- is the wavelength of the particle
- is the momentum of the particle

The Planck constant also occurs in equations fundamental to quantum mechanics, such as the Schrodinger equation.

## Reduced Planck's Constant

Planck's constant often occurs in equations with the mathematical constant . As such, a factor of may be taken into Planck's constant as

The resulting constant is pronounced "h-bar".