The Planck Constant (h) is a fundamental constant in physics that plays a central role in quantum mechanics. It relates the energy of a photon (a quantum of electromagnetic radiation) to its frequency. The value of the Planck constant is:

h=6.62607015×10⁻³⁴ Joule-seconds (Js)

Importance of the Planck Constant

1. Energy-Frequency Relationship: The Planck constant appears in the equation that links the energy (E) of a photon to its frequency (ν\nuν):
   • E=h⋅ν
2. This equation shows that the energy of a photon is directly proportional to its frequency, with h being the proportionality constant.
3. Quantum of Action: The Planck constant represents the smallest action (energy multiplied by time) that can occur in quantum systems. It is a key component in the quantization of energy levels in atoms and molecules.
4. Wave-Particle Duality: In the de Broglie wavelength formula, hhh is used to relate the wavelength of a particle to its momentum, bridging the concepts of wave and particle behavior.
5. Planck's Law of Blackbody Radiation: The Planck constant is central to Planck's law, which describes the spectral distribution of radiation emitted by a blackbody in thermal equilibrium.

Reduced Planck Constant (ħ)

Another related constant is the reduced Planck constant, also known as ħ (h-bar), which is defined as:

ℏ = h / (2π)

 ħ is frequently used in quantum mechanics, especially in the formulation of the Heisenberg uncertainty principle and the Schrödinger equation.

The Planck constant is one of the fundamental constants of nature and is crucial for understanding the quantum mechanical behavior of particles.

Planck described radiation emission as discrete packets, quantas, of energy.  Planck's constant (denoted h)  relates the wavelength to the frequency of an emission.  The constant defines the quantum of action in physics.  

Planck's constant is expressed in this equation in units of Joule seconds (J•s)

Planck's theory asserted that energy was transferred in units known as quanta in the ratio employed in Plank's Equation.  Plank's Equation is:

                  E = h • f

where:

• E is energy in Joules
• h is Planck's Constant
• f is the frequency

Note the following relations are also true:

`f = c/λ`

`f = E/h`

`E = (h⋅c) /λ` 

`λ = (h⋅c)/E`

`E = h * f`

where:

• E = energy of light
• f = frequency
• h = Planck's Constant
• c = Speed of Light in a vacuum 

Energy, Photon and Wavelength Calculators

• Quantum Energy (E=h⋅v): Computes radiant energy in the Planck-Einstein relationship (E = h•ν) based on Planck's constant and a frequency of radiation.
• Energy of a Photon (E=h⋅f): Computes the energy of a photon based on the frequency and Planck's Constant.
• Photon Energy from Wavelength (E=(h⋅c)/λ): Computes the energy of a photon based on Planck's constant (h), the speed of light (c) and the wavelength of the photon ( λ)
• Photon Wavelength form Energy (λ=(h⋅c)/E): Computes the wavelength of a photon based on Planck's constant (h), the speed of light (c) and the energy of the photon (E).
• DeBroglie Wavelength (λ=h/(m⋅v)): Computes the wavelength of a particle based on the Planck's Constant and momentum (p = m•v).
• Plank Constant (h):  Fundamental constant in physics that plays a central role in quantum mechanics which relates the energy of a photon to its frequency

Notes

In 2018 when analyzed by the CODATA Task Group on Fundamental Constants, the measurements produced a final value of h of 6.626070150 × 10-34 kg?m2/s, with an uncertainty of 10 parts per billion. If the SI is redefined as expected in November of 2018, this will be the exact value of Planck’s constant which will define other SI units including the kilogram.

See Uncertainty of Measurement Results, a discussion provided by NIST of the application of uncertainty to the documented constants. 

Interested in the physicist for whom this constant is named?  See Socratica's video on Max Plank.