Question

# rapidly from nearly unit to nearly zero over function spread an energy range of a few times kT. As the temperature increases further the effect becomes more pronounced until at

very high temperature the distribution becomes very disffuse and spread out. As this occurs the fermi energy moves downward very slowly at first then more rapidly when E=Ef f(E) has the more downward very slowly 1/2 which allows its position to be clearly observed in figure. Q.NO.17 Find range of energy over which the probability of occupation of a quantum state of a system obey fermi-Dirac statics drops from 0.9 to 0.1 . What does this answer became if the occupation limits are 0.99 to 0.01? The fermi distribution proper as given by f(\varepsilon)=\frac{1}{\left.1+e^{c \varepsilon-\varepsilon_{f}}\right) \mid k r} At temperature T=0 this function is seem to become a step function of the form f(E)=0.9 E=0.9 Ef=0.1 (E>Ef)=0 As the temperature increases the edges of step function become slightly rounded and function spreads out varying.

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