wave-Particle duality(part-2) planck's work
ON THE NATURE OF LIGHT
Corpuscular theories of light, which treated light as though it were composed of particles, have been batting around since the days of Newton and Laplace. But light has an irritating tendency to exhibit distinctively non-particle-like behavior, such as diffraction and interference, which corpuscular theories could not explain. Once Maxwell introduced his wave theory of electromagnetic radiation (in 1870) and it became clear that this theory could beautifully explain such phenomena, most physicists abandoned corpuscular theories of light.
According to Maxwell, all electromagnetic radiation-light included-consists of real waves propagating through space, waves that carry energy distributed over continuous, non-localized spherical wave fronts. In the late 19th century, it seemed that Maxwell's theory could explain even the most complicated electromagnetic phenomena; so convincing were its successes that in 1886, the distinguished physicist Heinrich Hertz (l857-1894)-uncle of Gustav-wrote: "the wave theory of light is, from the point of view of human beings, a certainty." Hertz, as we shall see, was wrong.
the steps of Planck
It was Albert Einstein (1879-1955) who, in 1905, resurrected the notion that electromagnetic radiation is particle-like rather than wave-like in nature . But where did this idea originate? Einstein has written that the seeds of his 1905 theory were planted by research carried out at the turn of the century by the German physicist Max Planck (1858-1947). Although encouraged by his physics teacher to pursue a career as a musician, Planck persevered in physics. His teacher's advice was lousy; Planck's studies of radiation inside a heated cavity led, via a line of reasoning he himself described as an "act of desperation," to the concept of quantization of energy and thence to the birth of quantum physics.
Planck did not set out to revolutionize physics. Instead, following in the footsteps of his teacher G. R. Kirchhoff (1824-1887), he sought to understand why hot bodies glow. This phenomenon, which is called black-body radiation, may be familiar to you if you sculpt. Suppose you have crafted a clay pig. To harden the clay, you fire the pig-i.e., put it in a kiln (an oven) and heat to roughly 2000° F for about 10 to 12 hours. Suppose there is a tiny hole in the oven, too small to admit light but large enough to see through. At first, of course, you see darkness. But as the pig gets hotter and hotter, it begins to glow. As the temperature of the kiln further increases, this glow becomes orange, then yellow, then white, and fills the oven, obliterating all detail of the pig. Why?
Planck formulated this question in slightly more abstract terms, asking: what is the spectrum of electromagnetic radiation inside a heated cavity? More specifically: how does this spectrum depend on the temperature T of the cavity, on its shape, size, and chemical makeup, and on the frequency v of the electromagnetic radiation in it? By the time Planck got into the game, part of the answer was known. Kirchhoff and others had shown that once the radiation in the cavity attains equilibrium with the walls, the energy in the field depends on v and T but, surprisingly, is independent of physical
characteristics of the cavity such as its size, shape, or chemical composition.
The cavity, of course, encompasses a finite volume. Planck was interested in the radiative energy inside the cavity, not on effects that depend on its volume, so he worked in terms of an energy density. In particular, he sought an expression for the radiative energy density per unit volume p(v ,T ). If we multiply this quantity by an infinitesimal element of frequency, we obtain p(v, T )dv, the energy per unit volume in the radiation field with frequencies between v and v + dv at cavity temperature T.
Rather than confront the distracting complexities of a real heated cavity, Planck based his work on a model originally introduced by his mentor Kirchhoff. Kirchhoff called his model of a heated cavity in thermal equilibrium a "black-body radiator." A black body is simply anything that absorbs all radiation incident on it. Thus, a black body radiator neither reflects nor transmits; it just absorbs or emits.
From the work of W. Wien (1864-1928), Planck knew that the radiative energy density p(v, T) for a black body is proportional to v^3 and, from the work of J. Stefan (1835-1893), that the integrated energy density 
is proportional to T^4. But this information did not fully describe the dependence of p(v, T) on v and T; experimental evidence implied a further, unknown dependence on v/T.
is proportional to T^4. But this information did not fully describe the dependence of p(v, T) on v and T; experimental evidence implied a further, unknown dependence on v/T.
Wien had actually proposed an equation for the energy density of a black-body radiator, but the theoretical foundation of his theory was shaky. Moreover, his equation worked only in certain circumstances; it correctly explained the v and T dependence of p(v ,T) for low temperatures and high frequencies. But it predicted that heated black bodies should emit a blue glow at all temperatures-a prediction confounded by our pig. Planck knew of this defect in Wien's theory, for experiments published in 1901 by H. Rubens and F. Kurlbaum conclusively showed it to fail for high temperatures and low frequencies.
In his research, Planck focused on the exchange of energy between the radiation field and the walls. He developed a simple model of this process by imagining that the molecules of the cavity walls are "resonators"-electrical charges undergoing simple harmonic motion. As a consequence of their oscillations, these charges emit electromagnetic radiation at their oscillation frequency, which, at thermal equilibrium, equals the frequency v of the radiation field. According to classical electromagnetic theory, energy exchange between the resonators and the walls is a continuous process-i.e., the oscillators can exchange any amount of energy with the field, provided, of course, that energy is conserved in the process. By judiciously applying classical thermodynamics and a healthy dose of physical intuition to his model, Planck deduced an empirical formula for the radiative energy density:
In this equation, A and B are constants to be determined by fitting to experimental data; that's why it is called "empirical."
Equation (2.1) agreed beautifully with experimental data for a wide range of frequencies and temperatures. And, in the limit v approaches infinity and T approaches 0, it reduced properly to Wien's law. But Planck was concerned that he could not rigorously justify his formula. In a letter dated 1931, he wrote of his dissatisfaction: "a theoretical interpretation had to be supplied, at all costs, no matter how high . . . I was ready to sacrifice every one of my previous convictions about physical laws." Planck had to do just that.
The source:
Michael A. Morrison - Understanding Quantum Physics.
By. Fady Tarek
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