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4. Show that the chemical potential u (T) of a free electron gas in two dimensions is given by u(T) = k₂T ln exp дnh² mk T H-] where n is the density of electrons per unit area. In the limit that T = 0, show that u (0) gives the correct EF calculated in question 1(c).

4. Show that the chemical potential u (T) of a free electron gas in two dimensions is given by u(T) = k₂T ln exp дnh² mk T H-] where n is the density of electrons per unit area. In the limit that T = 0, show that u (0) gives the correct EF calculated in question 1(c).

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4. Show that the chemical potential μ (T) of a free electron gas in two dimensions is given by μ(T) = k₂T ln exp anħ² mk T -1 where n is the density of electrons per unit area. In the limit that T = 0, show that μ (0) gives the correct E- calculated in question 1(c).
Transcribed Image Text:4. Show that the chemical potential μ (T) of a free electron gas in two dimensions is given by μ(T) = k₂T ln exp anħ² mk T -1 where n is the density of electrons per unit area. In the limit that T = 0, show that μ (0) gives the correct E- calculated in question 1(c).
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