Planck’s quantum theory of radiation

Further work on similar types of cells has been carried out, in which not only is use made of the Nernst Theorem but likewise of the Einstein theory of atomic heat of solids (as modified by Nernst and Lmdemann) This will be taken up after we have discussed Planck s Quantum Theory of radiation and Einstein s application of it to the heat capacity of solids (Vol. Ill)... 

The photoelectric effect conld not be explained by the wave theory of light. Einstein, however, made an extraordinary assumption. He snggested that a beam of light is really a stream of particles. These particles of light are now called photons. Using Planck s quantum theory of radiation as a starting point, Einstein deduced that... 

Planck s quantum theory of radiation has the following postulates ... 

With the solution of the hydrogen atom, the list of analytically solvable systems to be considered here is complete. Planck s quantum theory of light described black-body radiation, and now the simplicity of the spectrum of the hydrogen (and hydrogen-like ions) is adequately explained by quantum mechanics. We will find in the next chapter that although an exact analytic understanding of the behavior... 

In 1905, while an examiner at the Swiss Patent Office, Einstein in his spare time devised a theory to explain photoemission. His theory adopted Planck s quantum theory of a blackbody radiator and assumed that radiation itself was quantized. When a quantum of energy (hv) falls on a metal surface, its entire energy may be used to eject an electron from an atom. Because of the interaction of the ejected electron with surrounding atoms (their electronic distributions), a certain minimum energy is required for the electron to escape from the surface. The minimum energy to escape (< ) depends on the metal and is called the work function. The maximum kinetic energy of an emitted photoelectron is given by Einstein s equation... 

Solvay s desire to submit his work on the fundamental principles what he called gravito-materialitique to the attention of Europe s leading physicists prompted Nernst to envision an international conference on the current problems of kinetic theory of matter and the quantum theory of radiation. The idea struck an immediate responsive chord in Solvay s mind, and he charged Nernst to explore it further with Planck, Lorentz, Einstein, and the other prominent physicists. Nernst was quick to pursue the idea immediately on his return from Brussels to Berlin. 

This is reminiscent of Planck s formula for the energy of a photon. It comes as no surprise then that the quantum theory of radiation has the structure of an assembly of oscillators, with each oscillator representing a mode of electromagnetic waves of a specified frequency. 

The new era in physics started in 1900 with a young German physicist named Max Planck. While analyzing the data on radiation emitted by solids heated to various temperatures, Planck discovered that atoms and molecules emit energy only in certain discrete quantities, or quanta. Physicists had always assumed that energy is continuous and that any amount of energy could be released in a radiation process. Planck s quantum theory turned physics upside down. Indeed, the flurry of research that ensued altered our concept of nature forever. 

Planck constant /plank/ Symbol h A fundamental constant the ratio of the energy (W) carried by a photon to its frequency (v). A basic relationship in the quantum theory of radiation is W = hv. The value of h is 6.626 196 x 10" J s. The Planck constant appears in many relationships in which some observable measurement is quantized (i.e. can take only specific discrete values rather than any of a range of values). The constant is named for the German physicist Max Planck (1858-1947). 

Planck s Quantum Theory To explain the dependence of radiation emitted by objects on wavelength, Planck proposed that atoms and molecules could emit (or absorb) energy in discrete quantities called quanta. Planck s theory revolutionized physics. 

Plots of equation 9.23 are shown in Figure 9.15. Note that they are the same as the plots of blackbody radiation, but understand that Planck s equation predicts the intensity of blackbody radiation at all wavelengths and all temperatures. Thus, by predicting the intensities of blackbody radiation, Planck s quantum theory correctly models a phenomenon that classical science could not. 

Planck s quantum theory answered one of the great unknowns of earlier science, that of blackbody radiation. There were still several unanswered... 

This expression proved to be in perfect agreement with experiment when li was given a certain finite value, and the classical Rayleigh-Jeans law was obtained only in the limit as h O. Thus the turn of the century ushered in Planck s law and with it the birth of the quantum theory of radiation. 

The year 1913 marks a major climax in the history of science. The application of Planck s quantum hypothesis to blackbody radiation, and later by Einstein to the photoelectric effect, had met with disbelief and in some quarters even with scorn. Bohr s application to the theory of the hydrogen atom compelled belief and worked a revolution in thought. In the following ten years this new knowledge was quickly assimilated and applied with spectacular success to the interpretation of spectra and chemical periodicity. 

The early years of the twentieth century saw giant advances in man s understanding of nature which must be mentioned in any synopsis of the scientific history of this era. Thus, in 1901, M. Planck (NLP 1918 ) published his first paper on the black-body radiation law which ushered in the era of quantum mechanics. In 1905, A. Einstein (NLP 1918 ) published his Anna Mirabilis Papers on the photo effect, on Brownian motion, and on the theory of special relativity and the equivalence of matter and energy. 

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