Consider a collection of 10,000 atoms of rubidium-87, confined inside a box of volume (10−5 m)3.
(a) Calculate ϵ0, the energy of the ground state. (Express your answer in both joules and electron-volts.)
(b) Calculate the condensation temperature, and compare kTc to ϵ0.
(c) Suppose that T=0.9Tc. How many atoms are in the ground state? How close is the chemical potential to the ground-state energy? How many atoms are in each of the (threefold-degenerate) first excited states?
(d) Repeat parts (b) and (c) for the case of 106 atoms, confined to the same volume. Discuss the conditions under which the number of atoms in the ground state will be much greater than the number in the first excited state.