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I am currently writing up a lab report on the determination of Planck's constant using x-ray diffraction and atomic spectra.

In my introduction, I am talking about the history of Planck's constant, and I have a question:

When Constants are first come across, are they measured, determined or calculated?

As an example you could use Planck's constant was first ------ in the 19th century when explaining black body radiation at varying frequencies.

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Physical constants are determined by measurement. Of course they are not measured like one could measure the length of a rod with a ruler where the result can be directly read off from the ruler. An experiment has to be done based on known laws and in particular on the law the constant is involved. The measurement results have to be analyzed (called data analysis) and the constant to be determined to be computed from the measurement data. When a spring constant is measured, forces are applied on a spring whose elongation is measured. Typically a table is set up with entries for the force and the elongation. At the end the spring constant is determined by a (here linear) fit of these data. I guess, something similar was done by Max Planck. He had a couple of black-body radiation spectra available and it checked it against his new model of the black-body radiation and at the end fitted his model to the radiation data. And one of the fit parameters he chose was $\hbar$ (or $h$). In this way Planck's constant was found for the first time. Further experiments based on other physics were carried out for this purpose, but at the end the procedure is always the same, the underlying model is fitted to the measured data and the fit parameters extracted serve for determination of the constant. It is the same for the speed of light or gravitational constant determined by the Cavendish experiment etc.

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