* -20.66 eV Red Green E3 E2 18.70 eV Ground state E1 Figure TP41.1 Think-Pair-Share Problem 1 and Problem 35. ENERGY
The number N of atoms in a particular state is called the population of that state. This number depends on the energy of that state and the temperature. In thermal equilibrium,the population of atoms in a state of energy En is given by a Boltzmann distribution expression
N = Nge-(En-Eg)/kBT
where Ng is the population of the ground state of energy Eg , kB is Boltzmann’s constant, and T is the absolute temperature. For simplicity, assume each energy level has only one quantum state associated with it. (a) Before the power is switched on, the neon atoms in a laser are in thermal equilibrium at 27.0°C. Find the equilibrium ratio of the populations
of the states E4* and E3 shown for the red transition in the figure. Lasers operate by a clever artificial production of a “population inversion” between the upper and lower atomic energy states involved in the lasing transition. This term means that more atoms are in the upper excited
state than in the lower one. Consider the E4*- E3 transition as shown. Assume 2% more atoms occur in the upper state than in the lower. (b) To demonstrate how unnatural such a situation is, find the temperature for which the Boltzmann distribution describes a 2.00% population inversion.
(c) Why does such a situation not occur naturally?
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