The electron can be either bound or unbound to the impurity atom, but the electron can...

The electron can be either bound or unbound to the impurity atom, but the electron can also have one of 2 spins when bound. Since electrons move back and forth between the impurity atom and lattice, they are in diffusive equilibrium, and there is a chemical potential μ which is the same for all states.

(a) Calculate the grand partition function for this system, and the probability that the electron is bound and unbound. Express your answers in terms of I, μ, and T (the temperature of the electrons). First list all the possible states.

(b) We can model the “sea” of electrons in the lattice as an ideal gas with temperature T = 300 K. There are about 1023 impurity atoms per cubic meter, each of which contributes about one electron to the “sea”. What is the chemical potential of this electron gas? Express your answer in electron volts.

(c) Let’s assume the ionization energy is I = 0.044 eV (a typical value). Calculate the numerical probability that an electron is unbound.

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genius_generous answered 2 years ago

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