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Planck's constant

What is Planck's constant?

Planck's constant, symbolized as h, is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency. In the International System of Units (SI), the constant value is 6.62607015×10−34 joule-hertz−1 (or Joule-seconds). It is also referred to as the Planck constant.

Essential for understanding the motions of atoms and subatomic particles, Planck's constant explains how quantum mechanics and modern electronics -- including computer chips, solar panels and lasers -- function. As Planck's constant helped develop the theory of quantum mechanics, it is crucial to scientists' understanding of stellar evolution, or changes in stars over time.

Planck's constant explained

In classical mechanics and everyday life, we would expect that energy is available at any value; that you can have energy from zero to infinity and every value in between -- this is a continuum. However, theoretical physicist Max Planck discovered that this is not true and that energy comes in discrete steps or packets. This showed the quantum nature of energy and led to quantum mechanics.

To illustrate the difference, imagine you wanted sugar for your coffee at a restaurant. You may expect that it comes in a shaker or dispenser, so you can add as much or as little as you like. This is like a continuum where it can be any value. Instead, it comes as a sugar cubes or sugar packets. You can add none, one or more packets, but not anything in between. It is the same with the amount of energy in a photon. It must be in a multiple of a specific value -- Planck's constant.

How was Planck's constant discovered?

Planck's constant was discovered by Max Planck in the beginning of the 20th century. He was working to find a formula to describe the radiant energy emitted as black-body radiation. Black-body radiation is the energy emitted by all objects depending on its heat; for example, a warm object emitting infrared radiation, or a glowing hot iron emitting light and heat.

Planck's constant is important to understanding atoms, subatomic particles, quantum mechanics and electronics.
Planck's constant is essential for understanding the motions of atoms and subatomic particles, as well as how quantum mechanics and modern electronics operate.

At the time, existing formulas did not describe accurately the observed results for all temperatures. Although Planck developed an accurate formula for all values, his equation was not mathematically unique. To keep it accurate, he had to define that the energy would only be in whole increments of a value. He was able to calculate this increment value from observational data. This value became Planck's constant.

By defining that the energy had to be emitted in discrete packets, he had unknowingly postulated the existence of photons and ushered in the understanding of the quantum nature of energy and electromagnetic radiation.

What is reduced Planck's constant?

Intrinsic to Planck's constant is frequency measured in hertz. One full cycle, a hertz, is 360 degrees or2π radians a second. Dividing Planck's constant by 2π removes frequency from the value and allows the resulting value to be used with radians. This value is called the reduced Planck's constant and is symbolized as ħ (pronounced "h-bar"). Its value is 1.054571817×10−34 joule seconds.

The reduced Planck's constant is more commonly used in modern physics.

What are other Planck units?

Max Planck proposed a system of units (length, mass, time and temperature) based only on fundamental universal constants. Because these values are the same throughout time and the universe, they could theoretically be used across societies and even with extraterrestrial life. In practicality, though, these values are mainly of use to theoretical physicists to simplify equations.

At the Planck scale, even quantum theory begins to break down, pushing scientists to even more exotic theories, such as a so-called unified theory of everything or superstring theory. The theory of everything refers to a way of connecting all known phenomena to explain the behavior of all matter and energy. In superstring theory, in which nine dimensions of space and one dimension of time exist, basic particles in the universe are made up of vibrating, one-dimensional mathematical objects, or strings.

The Planck units are based on four physical constants:

  • the speed of light in vacuum, c;
  • the gravitational constant, G;
  • the reduced Planck's constant, ħ; and
  • the Boltzmann constant, kB.

Planck length is LP = √(ℏG/c3) ≈ 1.616255×10−35 m -- A Planck length is very small. At distances this small, the Heisenberg uncertainty principle takes over and conventional physics breaks down.

Planck mass is MP = √(ℏc/G) ≈ 2.176434×10−8 kg -- A Planck mass is roughly equal to a speck of dust.

Planck time tP = √(ℏG/c5) ≈ 5.391247×10−44 s -- A Planck time is the amount of time it takes a photon to travel one Planck length. It is so short that the Heisenberg uncertainty principle renders shorter times meaningless. The current understanding of physics cannot accurately describe the nature of the universe for one Planck time after the Big Bang.

Planck temperature TP = √(ℏc5/GKB2) ≈ 1.416784×1032 -- A Planck temperature is incredibly hot and is the point at which the wavelength of the light reaches the Planck length. The current understanding of physics cannot accurately describe temperatures higher than it, as at this temperature, black holes would be created by the heat energy.

See also: Table of physical constants

This was last updated in August 2022

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