Classical mechanics blackbodies

Blackbody radiation was explained by Max Planck in 1901, but only by overthrowing the very foundations of classical mechanics. Planck reasoned that the very high-frequency oscillators must not be excited by the thermal energy of the hot body to the same degree as the lower frequency oscillators. This was a challenge to explain because classical mechanics allows an oscillator to have any energy. Planck s argument involved two steps, which are explained as follows. 

We have introduced you to the concepts and methods of quantum mechanics this branch of physics was developed to explain the behavior of matter on the nanometer length scale. The results of a number of key experiments demanded the creation of a new physical theory classical mechanics and electrodynamics failed completely to account for these new observations. The pivotal experiments and observations included the spectrum and temperature dependence of blackbody radiation, the very existence of stable atoms and their discrete line spectra, the... 

Planck (1901) was the first to discard classical mechanics to explain blackbody radiation when he proposed that an oscillator could only acquire and lose energy in discrete units, called quanta. The magnitude of the quantum of energy was not fixed, but depended on the change in the oscillator energy E according to the equation... 

FIGURE 9.12 The experimentally determined behavior of blackbodies. This plot shows the intensity of light at different wavelengths for different temperatures of the blackbody. Explaining these curves theoretically was a major problem for classical mechanics. 

QM grew out of studies of blackbody radiation and of the photoelectric effect. Besides QM, radioactivity and relativity contributed to the transition from classical to modem physics. The classical Rutherford nuclear atom, the Bohr atom, and the Schrodinger wave-mechanical atom are discussed. Hybridization, wavefunctions, Slater determinants and other basic concepts are explained. For obtaining eigenvectors and eigenvalues from the secular equations the elegant and simple matrix diagonalization method is explained and used. All the necessary mathematics is explained. 

Describe blackbody radiation, and discuss how related paradoxes of classical physics were resolved by quantum mechanics (Section 4.2, Problems 9 and 10). 

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