Chapter1.pdf - Chapter 1 Dual Nature of Light and Matter...

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Chapter 1Dual Nature of Light andMatterThe phenomena that led to modern quantum theory are discussed in thischapter:some concerned the dual wave and particle nature exhibited byboth light and matter, while others involved the structure of the atom anda description of the spectral lines of Hydrogen.Yet others that implieda fundamental limit to the accuracy with which observables on an atomicscale can be measured. Modern quantum mechanics is a theory of matterand radiation, and describes these phenomena in a formalism that we willstudy in this book.It is important to gain a proper understanding of the historical develop-ments that led to the advent of quantum theory. The theory of light beganwith Sir Isaac Newton whose corpuscular theory in the 17thcentury couldexplain rectilinear propagation the phenomena of refraction and reflectionof. Several years later Huygens proposed a wave theory of light, but sinceNewton’s own attempts at a wave theory had failed and Newton enjoyedan unrivaled position of scientific authority, the Huygens’ wave theory wasthoroughly suppressed for many years, so much so that in the 18thcenturyonly two famous scientists, namely Euler and Benjamin Franklin, advocateda wave theory of light.In the late 18thand early 19thcentury experiments performed by Fresneland Young clearly demonstrated the phenomena of diffraction and interfer-ence. Fresnel demonstrated that Huygens’ wave theory accounted not onlyfor the rectilinear propagation of light, but that it could also account for thenewly discovered diffraction and interference properties of light.This ledto a temporary abandonment of the corpuscular theory of light in the 19thcentury, while the corpuscular theory of matter was gaining ground throughthe work of Maxwell, Boltzmann and Gibbs in statistical mechanics thatwas the foundation of kinetic theory of matter. The physics of 19thcenturycould thus be summarized as matter consisting of corpuscles and light con-1
2Chapter 1.Dual Nature of Light and Mattersisting of waves. This dualistic view of nature came to an impasse known asthe ultraviolet catastrophe at the end of 19thcentury when no wave theorycould explain observations of black-body radiation.1.1Black-body RadiationSuppose that a body is in a heat bath enclosure with temperatureT. Theamount of radiationdQλfalling on the body per unit area per unit timeand between wavelengthsλandλ+depends only onT.We definethe absorption coefficientaλso that the amount of radiation absorbed atwavelengthλby the body is given byaλdQλ. If the emitted energy per unitarea and unit time is defined byeλwe must havedQλ= (1-aλ)dQλ+eλfrom which we derive Kirchhoff’s law of cavity radiationeλ/aλ=dQλ/dλEλ(T),whereEλ(T) is the emissive power at the given wavelength and temperature:thus, all good emitters are also good absorbers.

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