# What really is Planck's constant and what are its origins?

In the physics texts I have read and other info online, they says Planck's constant is the quantum of action or that it is a constant of the ratio of the energy of a particle to its frequency. Im still not understanding exactly what it is?

From what I have read as well, Planck did a "fit" of data concerning others experiments and came up with this value, what data exactly did he fit to come up with this really small value, or maybe he did it some other way? Perhaps an answer concerning its origins will help me better understand my first question.

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What is the relativistic action of a massive particle? Take a look to this Question –  user16240 Nov 24 '12 at 6:19

In point particle classical mechanics the action $S$ is the time integral of the Lagrangian $L$

$$S=\int Ldt$$

You can check its dimensions are of $[ML^2T^{-2}][T]=[ML^2T^{-1}]$ this is, energy times time. The constant ratio is due to the energy $E$ and frequency $\nu$ relation for photons:

$$E=h\nu \Rightarrow h=\frac{E}{\nu}$$

The "fit" that you are talking about comes of the blackbody radiation spectrum. If we use as variables temperature $T$ and frecuency $\nu$ in classical physics we have two laws:

High frecuency law: Wien's law $$I(\nu,T)=\frac{2h\nu^3}{c^2}e^{-\frac{h\nu}{kT}}$$

Low frecuency law: Rayleigh-Jeans law $$I(\nu,T)=\frac{2h kT\nu^2}{c^2}$$

There is no intermediate frecuency law. Plack assumed that radiative energy is quantized via $E=h\nu$ and interpolated the energy fitting for an expresion of the type

$$I(\nu,T)=F(\nu,T)e^{g(\nu,T)}$$

that should satisfy both limits ($\nu \approx 0, h\nu >> kT$). Finally he obtained

$$I(\nu,T)=\frac{2h\nu^3}{c^2}\frac{1}{1-e^{\frac{h\nu}{kT}}}$$

However there is a much more nicer and physical derivation of Planck's law due to Einstein that you can find in Walter Greiner Quantum Mechanics an Introduction chapter 2

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