1. Thermal equilibration: radiative and nonradiative contributions. A collection oftwo-level atoms in a crystal is coupled both to the electromagnetic surroundingswith radiative decay rate Yrad and to the crystal-lattice surroundings with decayrate Ynr. Suppose the electromagnetic surroundings are somehow held at a fixedtemperature Trad which is different from the fixed temperature Tür of the crystallattice. Derive a formula for the steady-state equilibrium value of the Boltzmanntemperature Ta for the level populations of the two-level atoms in this case, asa function of the two surrounding temperatures Trad and Thr, the normalizedenergy gap ħw/k, and the ratio Yrad/Ynr.

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