Showing that Plancks lucky guess formula works at all wavelengths

Short wavelengths

(eC/XT >> 1)

C

C

X 5(eC W - i) fi

X 5eC V XT

Planck fi

Wien

Long wavelengths (C/XT small)

And since ex = 1 + x + x2/2! + x3/3! +— ^ 1 + x for small x

Planck

Rayleigh J-ans

Planck first presented his formula as a 'comment' to the German Physical Society at its meeting on 19 October 1900. The title of his comment was simply 'On an Improvement of Wien's Radiation Law', and it was presented more as a guess than as a statement of physical significance. Nevertheless it seemed to be the correct formula. Heinrich Rubens (1865-1922) and Ferdinand Kurlbaum (1857-1927), two German physicists who had made a series of careful measurements on the blackbody spectrum, working through the night following the academy session, compared their experimental results with the formula, and reported complete agreement. As Planck himself later admitted, such experimental verification was crucial: '...without the intervention of Rubens the foundation of quantum theory would have perhaps taken place in a totally different manner, and perhaps even not at all in Germany.'

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