Question

) Kragh states that quantum theory “owes is origin” to the problem of blackbody radiation. What was this problem? What were some other problems plaguing classical physics at the end of the 19^th Century?

(b) Briefly explain the history of attempts to solve the blackbody problem: Wien’s 1894 proof, Wien’s 1896 law, Planck’s 1899 derivation of Wien’s law, and Planck’s own radiation law (along with the “quantum hypothesis” made in Dec. of 1900).

(c) How well these laws fit the empirical data was of course part of the evaluation of their “truthiness”. But other (dare we say philosophical?) motivations drove Planck’s work in particular. Explain the non-empirical considerations that guided Planck’s thinking about blackbodies, eventually leading to the birth of QM.

Answer 1

a) in classical theory, from equipartition theorem

for a blackbody radiation, there has to be energy radiated in each possible mode of fourier mode of equilibrium radiaion.

since there are infinite modes of radiaiton, hence this means infinite heat capacity (infinite energy at 0 temeprature), as well as unphysical mode of emmision which gave very high frequencies with increasing temperature of the blackbody

this all could not explain the experimetally observed phenomenon, and hecne quantum theorey evolved in order to explain black body radiation

other phenomenon that could not be expained with the classical mechanics that lead to evolution of quantum mechanics are photoelectric effect and gravitational lensing

b) weins 1894 proof : in 1894 wein rederived weins diplaement law, relating the maximum intensity wavelength to the temperature of the radiation of the blackbody

in 1896 : wein pointed out since that the black body spectrum corresponded to equilibrium radiation, it could be soved using principle of maximum entropy.

this formulation though could not verify experimental results at longer wavelengths and needed modificaiton

then finally plank made adjustments to the fomula wein gave in 1900 to give corrected formula for black body spectrum

c) plank, considered the infinite modes of release of energy to be vibrational mode of particels of the blackbody.Now, these resonateors, if infinite in number add up to infinite wasy in which energy can be released, hence he had to postulate that the energy could be released only in discrete packets each of the the same energy when released by the resonators vibrating at the same frequency