Planck constant

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 building from 1889 to 1928."]]

The **Planck constant** ('''Planck's constant**) says how much the energy of a photon increases when the frequency of its electromagnetic wave increases by 1 (In SI Units). It is named after the physicist Max Planck.  The Planck constant is a **fundamental physical constant**. It is written as ***h*'''.

The Planck constant has dimensions of physical action: energy multiplied by time, or momentum multiplied by distance. In SI units, the Planck constant is expressed in joule seconds (J⋅s) or (N⋅m⋅s) or (kg⋅m2⋅s&minus;1).
The symbols are defined here.

In SI Units the Planck constant is exactly  J·s (by definition). Scientists have used this quantity to calculate measurements like the Planck length and the Planck time.

## Background
|}
[[File:NewtonDualPrismExperiment.jpg|thumb|200px|Illustration taken from Newton's original letter to the Royal Society (1 January 1671 [Julian calendar]).  S represents sunlight.  The light between the planes BC and DE are in colour. These colours are recombined to form sunlight on the plane GH]]

Between 1670 and 1900 scientists discussed the nature of light. Some scientists believed that light consisted of many millions of tiny particles. Other scientists believed that light was a wave.

### Light: waves or particles? 
In 1678, Christiaan Huygens wrote the book *Traité de la lumiere* ("Treatise on light"). He believed that light was made up of waves. He said that light could not be made up of particles because light from two beams do not bounce off each other.
In 1672, Isaac Newton wrote the book *Opticks*. He believed that light was made up of red, yellow and blue particles which he called corpusles. Newton explained this by his "two prism experiment". The first prism broke light up into different colours. The second prism merged these colours back into white light.

During the 18th century, Newton's theory was given the most attention. In 1803, Thomas Young described the "double-slit experiment". The wavelength of radio waves varies from 10&nbsp;m to 1500&nbsp;m and the wavelength of microwaves is about 2&nbsp;cm. In a vacuum, all electromagnetic waves travel at the speed of light. The frequency of the electromagnetic wave is given by:

:\nu = \frac{c}{\lambda}.

The symbols are defined here.

### Black body radiators 
All warm things give off thermal radiation, which is electromagnetic radiation.  For most things on Earth this radiation is in the infra-red range, but something very hot (1000&nbsp;°C or more), gives off visible radiation, that is, light.  In the late 1800's many scientists studied the wavelengths of electromagnetic radiation from black-body radiators at different temperatures.

#### Rayleigh-Jeans Law 
Lord Rayleigh first published the basics of the Rayleigh-Jeans law in 1900. The theory was based on the Kinetic theory of gasses. Sir James Jeans published a more complete theory in 1905. The law relates the quantity and wavelength of electromagnetic energy given off by a black body radiator at different temperatures. The equation describing this is:  
:B_\lambda(T) = \frac{2 c k T}{\lambda^4}.

For long-wavelength radiation, the results predicted by this equation corresponded well with practical results obtained in a laboratory. However, for short wavelengths (ultraviolet light) the difference between theory and practice were so large that it earned the nickname "the ultra-violet catastrophe".

#### Planck's Law 
in 1895 Wien published the results of his studies into the radiation from a black body. His formula was:
 
:B_\lambda(T) = \frac{2 h c^2} {\lambda^5} e^{-\frac{hc}{\lambda kT}}.

This formula worked well for short wavelength electromagnetic radiation, but did not work well with long wavelengths.

In 1900 Max Planck published the results of his studies. He tried to develop an expression for black-body radiation expressed in terms of wavelength by assuming that radiation consisted of small quanta and then to see what happened if the quanta were made infinitely small. (This is a standard mathematical approach). The expression was:
 
:B_\lambda(T) = \frac{2 h c^2}{\lambda^5}~\frac{1}{e^\frac{hc}{\lambda kT}-1}.

If the wavelength of light is allowed to become very large, then it can be shown that the Raleigh-Jeans and the Planck relationships are almost identical.

He calculated *h* and *k* and found that
:h =  erg·sec.
:k =  erg·deg-1.

The values are close to the modern day accepted values of  and  respectively. The Planck law agrees well with the experimental data, but its full significance was only appreciated several years later.

### Quantum theory of light 
, Einstein and Jeans are standing. Planck is second from the left. Einstein is second from the right. Jeans is fifth from the right. Wien is seated, third from the right]]

It turns out that electrons are dislodged by the photoelectric effect if light reaches  a threshold frequency. Below this no electrons can be emitted from the metal. In 1905 Albert Einstein published a paper explaining the effect. Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy. Einstein said that the effect was due to a photon striking an electron. This demonstrated the particle nature of light.

Einstein also found that electromagnetic radiation with a long wavelength had no effect. Einstein said that this was because the "particles" did not have enough energy to disturb the electrons.

Planck suggested]] 
In the electric circuit shown on the right, the voltage drop across the light emitting diode (LED) depends on the material of the LED. For silicon diodes the drop is 0.6&nbsp;V. However for LEDs it is between 1.8&nbsp;V and 2.7&nbsp;V. This information enables a user to calculate the Planck constant.

### Value of Theoretical Planck constant 
The Planck constant can also be mathematically derived:

h=\frac{\mu_0\pi}{12c^3}{[{q_0}{[0.9163a_0]}^2]^2}{f_{1r}}^5\cdot{s}=6.63\times10^{-34}  J\cdot s

Here, \mu_0 is the permeability of free space, c is the speed of light, q_0 is the electric charge of electron, a_0 is the Bohr's radius, and f_{1r} is the frequency of revolution of the electron in a hydrogen atom (f_{1r}=3.29\times10^{15}  rev/s). When these constant values are substituted to the theoretical Planck constant, the theoretical Planck constant value is exactly equal to the experimental value.

The Planck's constant elementary formula in terms of proton-to-electron mass ratio, the charge of electron, speed of light and vacuum permittivity is derived in. It is expressed as follows:

h =  \frac{ e^2}{c \, \varepsilon_0} \sqrt{\pi \, \sqrt{\frac{2}{3}}\, \, \frac{m_p }{m_e}} 

where e is the elementary charge of an electron, m_p the mass of a proton, m_ethe mass of an electron, \varepsilon_0  the vacuum permittivity, and c the speed of light.

## Related pages 
* Wave–particle duality

## Notes 
## References