An atom has three non-degenerate states of energies
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Statistical foundations and the equilibrium ensembles · Statistical foundations and the equilibrium ensembles
Thermal Physics, Ch The Boltzmann factor, the canonical ensemble and the partition function
Problem
An atom has three non-degenerate states of energies 0, ε and 2ε. It is weakly coupled to a reservoir at a temperature T such that kBT=2ε. Give numerical answers to three significant figures; energies as multiples of ε.
((a)) Evaluate the partition function Z of one atom.
((b)) Find the probability of each of the three states.
((c)) Find the mean energy U of one atom as a multiple of ε.
((d)) Three such atoms sit at three distinct fixed sites and do not interact. Evaluate the partition function of the set of three, and their total mean energy as a multiple of ε.