Case study 2.1 Quantum theory and black-body radiation. In 1899 Liimmer and Pringsheim investigated how the energy from a black-body radiator was distributed. The shape of the resulting spectral lines (Figure 2.9) was not easy to explain. According to the prevailing classical theory, which argued that radiation was emitted continuously, the energy radiated at each wavelength (EA) should vary with wavelength (X) (Figure 2.10).
Case study 2.1 Quantum theory and black-body radiation. In 1899 Liimmer and Pringsheim investigated how the energy from a black-body radiator was distributed. The shape of the resulting spectral lines (Figure 2.9) was not easy to explain. According to the prevailing classical theory, which argued that radiation was emitted continuously, the energy radiated at each wavelength (EA) should vary with wavelength (X) (Figure 2.10).
The quantum revolution began in 1900 with a novel solution to what might seem to be one of the minor puzzles of theoretical physics, the problem of black-body radiation: the problem of the interaction of those two sorts of entity which figure in the dualist ontology of late classical physics. The trouble for classical physics was that the facts about a black body's capacity to absorb and emit radiation defied thermodynamic explanation. The best that classical physics could do was to get the facts wrong and to generate paradox. So what was the problem of black-body radiation and why was it considered to be so puzzling? First, what is a black body? Some bodies absorb and emit radiation more readily than others. A mirror is a poor absorber of radiation in the form of light, a piece of coal is a good one. A good absorber of radiation in the form of light is ‘blacker’ than one that is not. One can extend the metaphor to radiation outside the visible range. Clearly, a body that is ‘blacker’ than another for one range of radiation frequencies need not be ‘blacker’ for all frequencies. A body's ‘blackness’ will, in general, depend on its chemical structure. But we can imagine a body whose blackness is maximal for all wavelengths. Such a body, if it exists, has a blackness which is independent of its chemical structure. We call it a black body. Two interesting questions are: first, are there bodies in Nature which are uniformly and maximally black for all wavelengths? and second, how does such a black body distribute the energy that it radiates as a function of the wavelength of the radiation it emits?
525. IN preceding chapters we saw how the classical system of mechanics failed to account for certain phenomena of physics, and it became clear that these could only be explained in terms of a new system of dynamics which must be supposed to supersede the old classical system when we have to deal with phenomena conditioned by the fine-scale structure of matter. The first instance of the failure of the classical mechanics was provided by the phenomenon of black-body radiation. On the assumption that black-body radiation represents a state of thermodynamical equilibrium, we found that the observed distribution of radiant energy in the spectrum of an ideal black body could be explained on the supposition that the energy of each part of the radiation-producing mechanism fell into “quanta.” Corresponding to a simple harmonic vibration of frequency v , there was supposed to be an energyquantum of amount hv , where h is Planck's universal constant of which the value has already been given. Calling this energy ∈ , it was found that the energy of vibration could be 0, ∈, 2∈, 3∈,… or any integral multiple of ∈ , but could not contain fractional parts of ∈ . The energy, after retaining one of these values for a certain time, had to be supposed to jump abruptly to some other value, which in turn was retained until another jump occurred.
This chapter deals with the important experimental studies on black-body radiation, Wein’s law, Rayleigh–Jeans law, Planck’s distribution law, etc. The black-body radiation studies reveal that the maximum wavelength of radiation 1 is inversely proportional to temperature T . The expression for Wein’s law has been deduced on the basis of thermodynamic considerations. The law gives a clue to understand that it holds true only at low temperatures and short wavelengths. The Rayleigh–Jeans law is based on the general theorem of elasticity and is in excellent quantitative agreement with experimental observations for large wavelengths and high temperatures, leading to ultraviolet ‘catastrophe’. Actually, Max Planck enunciated the correct form of the temperature–radiation law based on some assumptions and finally proposed Planck’s quantum theory. This chapter also explains the photoelectric effect and important conclusions drawn on the basis of experimental facts. Einstein applied the quantum theory to explain the photoelectric effect and to define threshold frequency. On the basis of plot of frequency of radiation versus voltage applied, a linear graph was obtained, which enabled finding the value of Planck’s constant h. The Compton effect has also been written in a lucid manner involving the mathematical formulation from which the Compton shift can easily be obtained. This chapter also details the atomic hydrogen spectrum including Bohr’s model of an atom, energy of electron revolving around the nucleus, radius of an orbit and expression for velocity of electron. It also mentions the drawbacks of Bohr’s theory. References, problems, and questions on this concept are provided at the end of the chapter.
A cold solid body does not produce any emissions, but with increasing temperature, it begins to become brighter and changes colour. A black body is a theoretical object, which absorbs 100% of the radiation that arrives on it. A black body heated to a sufficiently high temperature emits radiation. The study of the properties of black body radiation played a key role in the development of quantum physics. The history of the black body begins around 1860 when Kirchhoff defines what is meant by black body and formulates some general laws on its properties. Planck began to work on a cavity model where the walls were composed of resonators, that is, by electrically charged harmonic oscillators capable of exchanging energy with the electromagnetic radiation. In 1905, Einstein confirmed the idea of Planck explaining the photoelectric effect and showing that the radiation is not only emitted, but also absorbed in the form of packets or photons.
Modern physicists incorporate into their statistical analyses additional degrees of freedom, parameters that were unknown to the nineteenth-century scientists. The true black body intensity distribution is continuous, but the model of discrete radiators provides a good approximation for the observed wavelengths of light and stimulated a paradigm shift in the thinking of physicists about microphysics. Niels Bohr model was a source of consternation to the contemporary physics community. As with thermodynamics, quantum theory is extraordinarily useful and has been applied with tremendous ingenuity by solid-state physicists, engineers, and others who are able to harness its guidance for technological innovation. The disconcerting quantum jumps were explained away by re-envisioning the localized planetary electron as a distributed cloud surrounding the atomic nucleus. The technique of Fourier analysis was Werner Heisenberg’s path to the development of a quantum theory, which he ultimately expressed in the mathematical form of matrices.
One of the first inklings of a problem in physics at the end of the 19th century was the nature of the radiation emission spectrum from a black body. This could not be explained in terms of established and irrefutable methods of statistical mechanics. It was Planck’s idea to divide up the energy spectrum of a series of harmonic oscillators each with a different state of energy but whose energy steps depended upon the frequency of the oscillation that marked the beginning of quantum physics. As a result, Planck introduced a fundamental constant of nature, Planck’s constant.