10. Experimental studies of a particular protein have determined the ratio of th
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Question
10. Experimental studies of a particular protein have determined the ratio of the unfolded (u) to the folded () state concentrations at equi- librium is K-[u/I] 0.4 at 20°C. As a first approximation, one may represent the pro- tein unfolding process as a simple statistical mechanical two-level system with energies, ef and eu, and degeneracies, gr and gu. (a) Write an expression for K in terms of the parameters, &r, Eu, gf, gu, and the temper- ature of the system, T. (b) If you assume that the folded and unfolded states have the same effective degeneracy,Explanation / Answer
A quantum mechanica treatment of the free carrier absorption by electrons in polar semiconductors has been constructed in terms of the Kane model. It takes into account overlap wavefunction factors, intermediate states in other bands, the finite optical phonon energy, and the effects of arbitrary spin orbit splitting on the electron energy and wavefunction. The scattering mechanisms considered include polar optical mode scattering, ionic scattering, piezoelectric and deformation coupled acoustic mode scattering, and electron-electron scattering.
The theory, in the appropriate limits, applies to a wide range of photon energies, electron concentrations, and lattice temperatures. It relates the dominant scattering mechanism involved in the various limits to the characteristic behavior of the absorption coefficient as a function of the photon energy. In particular, the dominant scattering mechanism for small carrier concentrations is found to be polar optical mode scattering, which exhibits a 3 dependence of the absorption coefficient times the index of refraction, (except at the lowest frequencies, where the expected 2 dependence is obtained).
Ionic, or impurity, scattering becomes important as the carrier concentration is increased, and the characteristic wavelength dependence of the electron cross section times the index of refraction varies from 4 to 3, and the absorption coefficient times the index of refraction from 4 to 2, depending on the ratio of the photon energy to the initial electron energies.
Comparisons are made with the available data over a wide range of photon energies, temperatures, and electron concentrations, for the III–V compounds InSb, InAs, InP, and GaAs.
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