# Planck constant

**reduced Planck constantPlanck's constantreduced Planck's constanthħ\hbarPlanck's formulaℎℏconstant**

The Planck constant (denotedwikipedia

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### Physical constant

**constantconstantsuniversal constant**

, 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.

There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε 0, and the elementary charge e.

### Quantum mechanics

**quantum physicsquantum mechanicalquantum theory**

The Planck constant is of fundamental importance in quantum mechanics, and in physical measurement it is the basis for the definition of the kilogram.

where h is Planck's constant.

### Photon

**photonslight quantalight**

, 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.

In chemistry and optical engineering, photons are usually symbolized by hν, which is the photon energy, where h is Planck constant and the Greek letter ν (nu) is the photon's frequency.

### Electromagnetic radiation

**electromagnetic waveelectromagnetic waveselectromagnetic**

, that was proportional to the frequency of its associated electromagnetic wave.

This relationship is given by Planck's equation E = hν, where E is the energy per photon, ν is the frequency of the photon, and h is Planck's constant.

### Frequency

**frequenciesperiodperiodic**

, that was proportional to the frequency of its associated electromagnetic wave.

In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter \nu or ν (nu) (see e.g. Planck's formula).

### Black body

**blackbodyblack-bodyblack bodies**

At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories.

See the figure in the Introduction for the spectrum as a function of the frequency of the radiation, which is related to the energy of the radiation by the equation E=hf, with E = energy, h = Planck's constant, f = frequency.

### Atomic units

**atomic unita.u.atomic field**

Atomic unit systems are based (in part) on the Planck constant.

Reduced Planck's constant ;

### Stefan–Boltzmann law

**lawluminosity increases with the fourth power of temperatureproportional to the fourth power**

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy increases with temperature according to a definite rule, the Stefan–Boltzmann law (1879–84).

where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum.

### Mass–energy equivalence

**mass-energy equivalencemass-energymass–energy**

Since energy and mass are equivalent, the Planck constant also relates mass to frequency.

, where is Planck's constant and is the photon frequency.

### Quantum

**quantaquantizedquantal**

, 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.

As a result of his experiments, Planck deduced the numerical value of h, known as the Planck constant, and reported more precise values for the unit of electrical charge and the Avogadro–Loschmidt number, the number of real molecules in a mole, to the German Physical Society.

### Electronvolt

**eVkeVMeV**

In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.

In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1.

### Planck's law

**black-body radiationradiation lawblack-body spectrum**

To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator.

is the Planck constant, and

### Photoelectric effect

**photoelectricphotoelectronphotoemission**

They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.

The factor h is known as the Planck constant.

### Max Planck

**PlanckPlanck, M.Planck. M.**

In 1900, Max Planck empirically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment,

is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and

### Robert Andrews Millikan

**Robert MillikanRobert A. MillikanMillikan**

Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, when his predictions had been confirmed by the experimental work of Robert Andrews Millikan.

He used this same research to obtain an accurate value of Planck’s constant.

### Schrödinger equation

**wave mechanicsSchrödinger's equationSchrödinger**

The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.

is the reduced Planck constant, the symbol

### Energy

**energiesenergy transfertotal energy**

In 1900, Max Planck empirically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment,

In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: E = h\nu (where h is Planck's constant and \nu the frequency).

### Matter wave

**de Broglie wavelengthde Broglie relationmatter waves**

The de Broglie wavelength

, through the Planck constant,

### Albert Einstein

**EinsteinA. EinsteinEinstein, Albert**

was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself.

Einstein concluded that each wave of frequency f is associated with a collection of photons with energy hf each, where h is Planck's constant.

### Wavelength

**wavelengthsperiodsubwavelength**

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 Hz).

Louis de Broglie postulated that all particles with a specific value of momentum p have a wavelength λ = h/p, where h is Planck's constant.

### Wien approximation

**Wien's lawapproximationWien**

Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength).

h is Planck's constant.

### Rydberg formula

**formulaRydberg formula for any hydrogen-like elementRydberg series**

This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant R ∞ in terms of other fundamental constants.

Rydberg was trying: when he became aware of Balmer's formula for the hydrogen spectrum In this equation, m is an integer and h is a constant (not to be confused with the later Planck's constant).

### Niels Bohr

**BohrBohr, NielsN. Bohr**

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.

where m e is the electron's mass, e is its charge, h is Planck's constant and Z is the atom's atomic number (1 for hydrogen).

### Planck–Einstein relation

**E=hf'' (Planck–Einstein relation)energy of a photonenergy of a photon is proportional to its frequency**

The Planck–Einstein relation connects the particular photon energy

, is known as the Planck constant.

### Matrix mechanics

**matrix formulationmatrix theoryHeisenberg representation**

The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.

Before matrix mechanics, the old quantum theory described the motion of a particle by a classical orbit, with well defined position and momentum X(t), P(t), with the restriction that the time integral over one period T of the momentum times the velocity must be a positive integer multiple of Planck's constant