wave-Particle duality(part-3) photons
Complete planck's work
For his second assault on the energy density of a black body, Planck adopted a statistical method based on the concept of entropy as interpreted probabilistically by Ludvig Boltzmann (1844-1906). At one point in his derivation, Planck introduced a simplifying assumption (i .e., a trick to facilitate his mathematics). His ploy was conventional in mathematical analysis , and Planck expected to remove his assumption at the end. Planck was in for a rude shock.
assumption is both simple and radical. He knew that a classical black body could exchange any amount of energy with the walls of the cavity; nevertheless, for purposes of his derivation, Planck assumed that only discrete amounts of energy can be absorbed or emitted by the resonators that comprise the walls of the black body. He called these discrete amounts of energy "quanta." To each quantum Planck assigned an energy equal to an integral multiple of h*v, where h is the constant h =6.63 X 10^-34 J-sec. Having made this assumption, Planck easily derived the radiation law
where c = 3.0 X 10^8 m-sec is the speed of light and 
is Boltzmann's constant. Comparing this result with Eq. (2.1) in wave-Particle duality(part-2) planck's work, we see that in his new equation Planck derived expressions for the constants A and B that appeared in his empirical form.
is Boltzmann's constant. Comparing this result with Eq. (2.1) in wave-Particle duality(part-2) planck's work, we see that in his new equation Planck derived expressions for the constants A and B that appeared in his empirical form.
This derivation was the theoretical justification Planck sought for the distribution of radiation in a black body. But in laying the foundation for his theory, Planck paid an enormous price, for try as he might, he could not get rid of his artificial constant h. Setting h = 0 inevitably led to a result that disagreed with a huge body of experimental data. Yet, if h is non-zero, then Planck's theory is seriously at odds with physicists understanding of energy exchange as a continuous process. Planck's rash assumption heralded the strange new physics of the quantum, which dominated the physics community for the next three decades. But physicists, who were then and are today a rather conservative lot, did not take well to being told that their understanding of so basic a process as energy exchange was fundamentally incorrect. Attempts to derive Planck's result without making his drastic assumption failed, and for several years Planck's quanta languished in obscurity, largely ignored. Yet, Planck's assumption was nothing compared to the surprise Einstein had in store.
photons-Particles of Light
Einstein thought he saw an inconsistency in the way Planck used Maxwell's wave theory of electromagnetic radiation in his derivation. With characteristic intellectual courage, Einstein decided that this inconsistency implied a flaw not in Planck's theory but in Maxwell's. This radical contention shifted the emphasis in research on black bodies from the resonators that comprise the walls to the radiation field itself. Ultimately, it completely altered the way we think about light.
In 1905 Einstein proposed that the energy in an electromagnetic field is not spread out over a spherical wave front, as Maxwell would have it, but instead is localized in indivisible clumps-in quanta. Each quantum of frequency v, Einstein averred, travels through space at the speed of light, C = 3.0 X 10^8 m/sec, carrying a discrete amount of energy h*v and momentum h*v/c. Thus, in Einstein's model, light transports energy in the same way particles do. G. N. Lewis subsequently dubbed Einstein's quantum of radiation energy a photon, the name we use today. The photon model cast Planck's theory of black-body radiation in, so to speak, a new light. Planck thought that energy exchange between the resonators of the cavity and the field occurs in units of h*v because of some strange property of the resonators. To this Einstein said: No, the explanation is that the radiation field itself is quantized. Planck's result is consistent with this extraordinary notion; if the energy in the field is contained in photons-quanta of magnitude h*v-then of course only integral multiples of the photon energy can be exchanged with the walls.
The photon model explained more than just black-body radiation. One of Einstein's greatest achievements was using it to understand the photoelectric effect-the ejection of electrons from a metal, such as sodium, when light impinges on it. (You see the photoelectric effect in action every time an electric eye opens an elevator door for you or closes one on your foot.) Yet, the photon was too radical for physicists of the early 1900's, and Einstein's model of the electromagnetic field encountered strong opposition. Even as late as 1913-years after the publication of Einstein's work on the photoelectric effect-four distinguished German physicists (including Max Planck) wrote in a petition recommending Einstein's appointment to the Prussian Academy of Science:
... That he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta, cannot really be held too much against him, for it is not possible to introduce fundamentally new ideas, even in the most exact sciences, without occasionally taking a risk.
One year later the American experimentalist R. A. Millikan (1868-1953) reported a precise verification of Einstein's equation for the energy of a photon, E = h*v, and the first measurement of Planck's constant. Yet physicists still resisted abandoning their long-cherished idea that light was a wave. Then, in 1923, Arthur H. Compton (1892-1962) published the results of his x-ray scattering experiments, and drove the last nail into the coffin of the wave theory of light. Compton scattered x-rays-electromagnetic radiation with a wavelength around 10^-10 m and a frequency around 10^18 1/sec- from a thin layer of a light element such as carbon and measured the shift in the wavelength of the x-rays due to the scattering. His results were seriously at odds with the predictions of Maxwell's beleaguered theory. Compton's data clearly showed that the wavelength of the scattered radiation is larger than that of the incident radiation. After several foredoomed attempts to explain this result with classical theory, Compton tried the photon idea. If x-rays carry energy in localized clumps, he reasoned, then we can apply classical collision theory to their interaction with the electrons of the target. Compton used the classical laws of conservation of energy and linear momentum-as though he were analyzing a game of billiards-and was able to derive the correct expression for the wavelength shift. This analysis vindicated Einstein's idea. It was too much even for diehards: the photon was accepted.
The source:
Michael A. Morrison - Understanding Quantum Physics.
By. Fady Tarek
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