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.
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.
Light occupies a special position in our attempts to understand nature both classically and quantum mechanically. We recall that Newton, who made so many fundamental contributions to optics, championed a particle description of light and was not favorably disposed to the wave picture of light. However, the beautiful unification of electricity and magnetism achieved by Maxwell clearly showed that light was properly understood as the wave-like undulations of electric and magnetic fields propagating through space. The central role of light in marking the frontiers of physics continues on into the twentieth century with the ultraviolet catastrophe associated with black-body radiation on the one hand and the photoelectric effect on the other. Indeed, it was here that the era of quantum mechanics was initiated with Planck's introduction of the quantum of action that was necessary to explain the black-body radiation spectrum. The extension of these ideas led Einstein to explain the photoelectric effect, and to introduce the photon concept. It was, however, left to Dirac to combine the wave-and particlelike aspects of light so that the radiation field is capable of explaining all interference phenomena and yet shows the excitation of a specific atom located along a wave front absorbing one photon of energy. In this chapter, following Dirac, we associate each mode of the radiation field with a quantized simple harmonic oscillator, this is the essence of the quantum theory of radiation.
The theory of relativity is essentially the culmination of classical physics. Although revisions in our concepts of space and time are necessitated by both the special and general theories of relativity, the notion of causality, in which a cause precedes its effect, remains intact in the relativistic formulations of electrodynamics and mechanics and of gravitation. An upper limit is set on the speed of bodies, and of the propagation of energy, and physical quantities are often defined operationally, but once we adjust ourselves to these new rules, our representations of physical processes proceed pretty much as they did in classical physics. On the other hand, quantum theory seems to require a much more profound philosophical revision of our thought patterns. Even the viability of the usual meaning of a causal connection between one event and another is there called into question. SOME HISTORICAL BACKGROUND We begin with a brief and highly selective review of the experimental and theoretical problems that formed the conceptual backdrop to the emergence of quantum theory. We focus attention first on an important phenomenon – blackbody radiation – that was instrumental for the formulation of quantum mechanics. A blackbody is defined as a surface that absorbs all of the electromagnetic radiation that falls onto it. It is picturesquely so named since any light incident on such a body would be absorbed, making it appear black (at least at typical temperatures in our environment). A blackbody also emits radiation.
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?
The experimental foundations of quantum theory are presented in some detail in this chapter: on the one hand, the investigation of black-body radiation, which helps in developing an interdisciplinary view of physics, besides having historical interest; on the other hand, the energy and linear momentum of photons, atomic spectra, discrete energy levels, wave-like properties of electrons, interference phenomena and uncertainty relations. Black-body radiation Black-body radiation is not just a topic of historical interest. From a pedagogical point of view, it helps in developing an interdisciplinary view of physics, since it involves, among the other, branches of physics such as electrodynamics and thermodynamics, as well as a new constant of nature, the Planck constant, which is peculiar to quantum theory and quantum statistics. Moreover, looking at modern developments, the radiation that pervades the whole universe (Gamow 1946, Penzias and Wilson 1965, Smoot et al . 1992, Spergel et al . 2003) is a black-body radiation, and the expected emission of particles from black holes (space–time regions where gravity is so strong that no light ray can escape to infinity, and all nearby matter gets eaten up) is also (approximately) a black-body radiation (Hawking 1974, 1975). In this section, relying in part on Born (1969), we are aiming to derive the law of heat radiation, following Planck's method. We think of a box for which the walls are heated to a definite temperature T .
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.
Twentieth century physics began exactly in the year 1900 when the German physicist Max Planck proposed a possible solution to a problem that had been haunting physicists for years. The problem concerned the light emitted by any object that is heated to a certain temperature, and also the softer infrared radiation emitted, with less intensity, by colder objects. It had become well accepted that all this radiation had an electromagnetic origin, and the laws of Nature for these electromagnetic waves were already known. Also known were the laws for heat and cold, so-called ‘thermodynamics’. Or so it seemed. But if we use thermodynamic laws to compute the intensity of the radiation in question, the outcome does not make any sense at all. Such a calculation would tell us that an infinite amount of radiation should be emitted in the very far ultraviolet. Of course, this is not what happens. What does happen is that the intensity of the radiation shows a peak at a certain characteristic wavelength, and diminishes both at wavelengths longer and shorter than this. This characteristic wavelength is inversely proportional to the absolute temperature of the radiating object (absolute temperature is defined by a temperature scale that begins at 273°C below zero or 459.6 OF below zero). At 1000°C or 1800°F an object is ‘red hot’; at this point the object is radiating in the visible light region.