Planck's constant

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Planck's constant (h) defines the relationship of energy (of a photon) to frequency. It is 6.626176 x 10-34 joule-seconds (approx); [cgs] 6.626176 x 10-27 erg-seconds (approx).

The relationship is defined by: E = h\nu.\, ie the energy of a photon is equal to its frequency times Planck's constant.


Its actual existence, formulated by Max Planck was a founding pillar of Quantum mechanics.

Slash aitch[edit]

A related value called the reduced Planck constant, also known as slash aitch or h-bar from its symbol ({\hbar}), is equal to \frac{h}{2 \pi}. While playing around with the equations involved in quantum mechanics, scientists found that the Planck constant kept appearing when divided by 2{\pi} and introduced a new symbol to make their lives a little easier.

For example, in addition to a photon's frequency ν (cycles per second), physicists often do calculations involving its angular frequency ω (radians per second), which by definition is 2π times the frequency. Thus, the relationship between the energy of a photon and its angular frequency is E = \hbar\omega.

Planck units[edit]

The system of Planck units was designed to make the lives of quantum physicists easier still. In the Planck unit system, five basic constants of the universe -- the speed of light (c), the reduced Planck constant (ħ), Newton's gravitational constant (G), the Coulomb constant (ke), and the Boltzmann constant (kB) -- are all set equal to 1. The base units of length, time, mass, electric charge, etc., are then derived from these constants. For example, the Planck charge qP is defined as:

q_\text{P} = \sqrt{ \frac{\hbar c}{k_\text{e}}}

... which works out to approximately 11.706 times the charge on a proton.

Some of the Planck units, such as the Planck mass[1] and the Planck charge, seem not to have any fundamental meaning themselves and could very well end up being completely arbitrary; but others have special significance within the quantum world.

The Planck length is, theoretically, the shortest distance that can possibly be measured.[2] It is approx 1.6 x 10-35 m, about 1020 times smaller than the nucleus of an atom.

The Planck time is the time taken to travel the Planck length at the speed of light. It is approx 10-43 seconds. It is also the earliest time for which a valid description of the universe can ever be made.[3]

The Planck density is one planck mass per cubic Planck length. It is much, much denser than all but the tiniest black holes. One unit of Planck time after the Big Bang, the mass density of the universe is thought to have been one Planck density.

The Planck temperature unit is about 1.4 x 1032 Kelvin. It's about 9 x 1024 times hotter than the core of the sun, and is theoretically the highest temperature at which matter could exist at all. One unit of Planck time after the Big Bang, the temperature of the universe is thought to have been one Planck temperature.

External Links[edit]

References[edit]

  1. About 21.8 micrograms. Since c = 1 in the Planck unit system, the Planck mass is also the Planck unit of energy, which works out to around 2 x 109 Joules, roughly the energy released by detonating half a ton of TNT.
  2. According to Heisenberg's uncertainty principle, if you measure the position of a particle to an accuracy of one Planck length, the uncertainty in its momentum will be 3 kilogram-meters per second.
  3. This is believed to be true no matter what advances are made as time and space did not exist before this time. Then, science has been fooled before.