What assumption allowed Planck to account for the observed features of blackbody radiation?

Blackbody radiation is the electromagnetic radiation emitted by an object at a specific temperature. In the late 19th and early 20th century, physicists were trying to develop a model that could accurately predict the radiation intensity at different wavelengths and temperatures. The existing classical theories failed to explain the observed features of blackbody radiation, particularly the ultraviolet catastrophe where the predicted intensity for short wavelengths was infinitely large. The problem was finally solved by Max Planck in 1900.

Planck made a crucial assumption to solve the blackbody radiation problem. He proposed that the energy of electromagnetic radiation could only be emitted and absorbed in discrete packets, called quanta, rather than the continuous manner that was assumed in classical physics. This assumption, also known as the quantization of energy, was a major departure from the classical theories.

With this assumption, Planck derived his radiation law, which gives the radiation intensity at a specific wavelength and temperature. The formula for Planck's Radiation Law is: \[B(\lambda,T) = \frac{2\pi hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1}\] Here, \(B(\lambda,T)\) is the spectral radiance, \(\lambda\) is the wavelength, \(T\) is the temperature, \(h\) is the Planck's constant, \(c\) is the speed of light, and \(k\) is the Boltzmann constant.

Due to the quantization of energy assumption, Planck's Radiation Law was able to describe the observed features of blackbody radiation accurately. Specifically, it resolved the ultraviolet catastrophe by predicting that the intensity of radiation would approach zero at very short wavelengths. The law also correctly predicts the peak wavelength at which the radiation intensity is maximum, which shifts to shorter wavelengths with increasing temperature (known as Wien's displacement law). To summarize, the crucial assumption that allowed Planck to account for the observed features of blackbody radiation was the quantization of energy, in which he assumed that the energy of electromagnetic radiation could only be emitted and absorbed in discrete packets called quanta. This deviation from classical physics led to the successful development of Planck's Radiation Law, which accurately matches experimental observations and paved the way for the foundations of quantum mechanics.