In a hydrogen atom the first excited level lies above the ground level; the ground…
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Statistical foundations and the equilibrium ensembles · Statistical mechanics of ideal classical systems
Thermal Physics, Ch The Boltzmann factor, the canonical ensemble and the partition function
Problem
In a hydrogen atom the first excited level lies 10.2eV above the ground level; the ground level holds 2 states and the first excited level holds 8 states of equal energy. Take 1eV=1.602×10−19J. Treat the atoms as weakly coupled to a reservoir at temperature T and, because all higher levels and ionisation are far less populated still, ignore every level above the first excited one.
((a)) Estimate the fraction of the atoms in a room-temperature gas at 300K that are in the first excited level.
((b)) Estimate the same fraction in the atmosphere of a star at 6000K. Give each answer as a power of ten with one significant figure in the mantissa.