Question

h) What was Planck's intention to deduce Planck's law and how did he do it?

Answer 1

At the end of the 19th-century, physicists were unable to explain why the observed spectrum of black body radiation diverged significantly at higher frequencies from that predicted by existing theories. The ultraviolet catastrophe was the prediction of late 19th century classical physics that an ideal black body at thermal equilibrium will emit radiation in all frequency ranges, emitting more energy as the frequency increases. By calculating the total amount of radiated energy it can be shown that a blackbody would release an infinite amount of energy, contradicting the principles of conservation of energy. In 1900, Max Planck empirically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave.

Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by ${\displaystyle B_{\nu }(\nu ,T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{\frac {h\nu }{k_{\mathrm {B} }T}}-1}}}$

Max Planck developed the law in 1900 with only empirically determined constants, and later showed that, expressed as an energy distribution, it is the unique stable distribution for radiation in thermodynamic equilibrium.