Question

what is the probability of sodium crystal in three dimensional at a given energy level when the temperature is 300K

Answer 1

The distribution function at non-zero temperature is given by the Fermi distribution function. The Fermi distribution function determines the probability that an orbital of energy E is occupied at thermal equilibrium

$$f(E)=\frac{1}{e^{\frac{E-\mu}{kT}}+1}$$