Planck constant Definition and 11 Discussions

The Planck constant, or Planck's constant, is a fundamental physical constant denoted


{\displaystyle h}
, and is of fundamental importance in quantum mechanics. A photon's energy is equal to its frequency multiplied by the Planck constant. Due to mass–energy equivalence, the Planck constant also relates mass to frequency.
In metrology it is used, together with other constants, to define the kilogram, an SI unit. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value


{\displaystyle h}
= 6.62607015×10−34 J⋅Hz−1.At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but predictions of the frequency distribution of the radiation by then-existing theories diverged significantly at higher frequencies. In 1900, Max Planck empirically derived a formula for the observed spectrum. He assumed a hypothetical electrically charged oscillator in a cavity that contained black-body radiation could only change its energy in a minimal increment,


{\displaystyle E,}
that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant from the experimental measurements, and that constant is named in his honor. In 1905, Albert Einstein determined a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, and was eventually called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".
Confusion can arise when dealing with frequency or the Planck constant because the units of angular measure (cycle or radian) are omitted in SI.
In the language of quantity calculus, the expression for the value of the Planck constant, or a frequency, is the product of a numerical value and a unit of measurement. The symbol f (or ν), when used for the value of a frequency, implies cycles per second or hertz as the unit. When the symbol ω is used for the frequency's value it implies radians per second as the unit. The numerical values of these two ways of expressing the frequency have a ratio of 2π. Omitting the units of angular measure "cycle" and "radian" can lead to an error of 2π. A similar state of affairs occurs for the Planck constant. The symbol h is used to express the value of the Planck constant in J⋅s/cycle, and the symbol ħ ("h-bar") is used to express its value in J⋅s/rad. Both represent the value of the Planck constant, but, as discussed below, their numerical values have a ratio of 2π. In this article the word "value" as used in the tables means "numerical value", and the equations involving the Planck constant and/or frequency actually involve their numerical values using the appropriate implied units.

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  1. J

    B Reduced Planck Constant vs Dark Matter?

    Is the Reduced Planck Constant the minimum frequently/movement/spin matter can have to exist? So if a matter were to spin lower than 1.054 571 817... x 10-34 J s, it when cease to exist? Or would matter falling below the Reduced Planck Constant by classified as Dark Matter? I heard that Higgs...
  2. qnt200

    B Does the energy 6.626x10^-34J have any special meaning?

    We know that Planck's constant is 6.626x10-34Js. Does the energy of the same numerical value 6.626x10-34J have any special meaning. Is it perhaps the lowest possible energy or are energies less than that energy theoretically possible.
  3. F

    I The new definition of kg and the mass-energy equivalence

    Hi, today I stumbled upon a 2016 article in Scientific American about the (then) possibility of re-defining the kilogram through Planck's constant. The article is really a very quick review of the topic. At some point the author states the following "So for years, physicists have chased an...
  4. C

    Photoelectric effect : retarding potential with back current

    In the experiment of the determination of ##h## using the photoelectric effect produced by light emitted by led's there is the systematic problem of the "dark current" or "back current", i.e. the current caused by photoelectric effect on the anode of the system which is used in the expreriment...
  5. redtree

    I Planck's constant and quantization of energy

    Given: ##\textbf{E}=\hbar \textbf{k}## where ##\textbf{k} = [\vec{k}_1, \vec{k}_2,\vec{k}_3, i c \omega]## If ##\textbf{k}## can vary continuously, how does the equation imply that energy is quantized? For example, ##y = m x +b## where ##m = \hbar## does not imply quantized ##y##. For...
  6. Y

    B About the Lorentz invariance of Planck constant

    Is it proved experimentally that the Planck constant is invariant in the moving system? If that experiment exists, would you show me that in detail?
  7. Z

    Derivation of Wien's+Reyleigh-Jean's Laws from Planck's Law

    Homework Statement After reading the forum stickies I'm not entirely sure where to put this question since it involves using math to solve a question, but is informally stated and isn't a book problem, either-I just started reading Fong's Elementary Quantum Mechanics, and in the first few...
  8. W

    Why is the band offset of an LED equal to the band gap?

    I am doing an experiment where we have to use the threshold voltage of LEDs to determine Planck's constant given the following relation $$ eV_0 = E_g = \frac{hc}{\lambda} $$ where ## V_0 ## is the threshold voltage, ## \lambda ## is the wavelength of emitted light and ## E_g ## is the band...
  9. Logan Johnston

    How Is This Quantum Analogy Incorrect?

    Homework Statement "Sometimes the idea of the quantum is compared to the units we use for money. A dollar can be divided into smaller units, where the cent is the smallest possible unit. How is this analogy incorrect? Homework Equations E=nhf The Attempt at a Solution My thought is that...
  10. fricke

    Zero Planck constant

    What is the effect in quantum if Planck constant is zero? Here are some points that I could think of: if Planck constant is zero, the Heisenberg Uncertainty Principles will become zero, therefore either momentum or position of a particle can be known exactly. if Planck constant is zero, both...
  11. GM Jackson

    How does a black body emit as much energy as it absorbs?

    Homework Statement A black body absorbs all incident electromagnetic radiation, including visible light which has wavelengths from 380nm to 750nm. IR radiation has wavelengths that are so long they are measured in microns. That suggests that visible light has a higher frequency than IR, and...