Fibonacci numbers and the Pascal Triangle

 

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Planck constant and number PI

        


The German Max Planck (1858-1947) and Nobel Prize recipient in 1919, had introduced his constant in 1900 in a formula explaining the light radiation emitted from heated bodies. According to classical theory, comparable amounts of light energy should be produced at all frequencies. This is not only contrary to observation but also implies the absurd result that the total energy radiated by a heated body should be infinite. Planck postulated that energy can only be emitted or absorbed in discrete amounts, which he called quanta (the Latin word for "how much"). The energy quantum is related to the frequency of the light by a new fundamental constant, h. When a body is heated, its radiant energy in a particular frequency range is, according to classical theory, proportional to the temperature of the body. With Planck's hypothesis, however, the radiation can occur only in quantum amounts of energy. If the radiant energy is less than the quantum of energy, the amount of light in that frequency range will be reduced. Planck's formula correctly describes radiation from heated bodies. Planck's constant has the dimensions of action, which may be expressed as units of energy multiplied by time, units of momentum multiplied by length, or units of angular momentum.


The connection between Planck constant on one side and , Archimedes` constant PI on the other, is highly amusing:




where


A closely-related quantity is the reduced Planck constant (also known as Dirac's constant and denoted , pronounced "h-bar").

Using the best experimental values for r,R,m and (the value of c is fixed by definition) gives:


The value of Dirac`s constant is:


Planck`s constant is:



The value of Planck`s constant is:



The fine structure constant is:



Using the best experimental value for Rydberg constant , gives:



We have this value of the fine structure constant:






References


Planck, M. "Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum." Verhandl. Deutsch. phys. Ges. 2, 237, 1900.

Planck, M, "Über das Gesetz der Energieverteilung in Normalspektrum." Ann. Physik 4, 553, 1901.

P. A. M. Dirac, Nature 139, 323 (1937)

Dirac, P.A.M. Principles of Quantum Mechanics, 4th ed. Oxford, England: Oxford University Press, 1982.

B.W.Petley: The Fundemental Physical Constants and the Frontier of Measurement" Adam Hilger Ltd. Bristol UK, 1985.

Hans A.Bethe: "Intermediate Quantum Mechanics",W.A.Benjamin Inc,New York - Amsterdam (1964).

Srpska Akademija nauka i umetnosti: "Elektron-sto godina od otkrica", Zavod za udzbenike i nastavna sredstva, Beograd (1997)

Todorovic,Milan: "Atomska fizika".Elektrotehnicki fakultet, Beograd (1973).

Ivanovic,Dragisa: "Kvantna mehanika".Naucna knjiga, Beograd (1972).

The NIST reference on Planck constant

Planck constant From Wikipedia, the free encyclopedia

Bert Schreiber: The collected works of Bert Schreiber

        

        

  2001-2007 Radoslav Rasko Jovanovic   High School Lajkovac              created:  November, 2007.