Many diatomic molecules can be well approximated by ideal springs. The only difference imposed by quantum physics is that as a result of quantum rules, they are not allowed to have any amplitude, but only those that correspond to certain allowed energies. This is true for most potentials, but in the oscillator the allowed energies are equally spaced.
The true potential energy and the allowed energies for a diatomic molecule are shown in part A of the figure at the right. In part B are shown an approximate harmonic oscillator model (ideal spring) for that system with its allowed energies. You can see that the first four levels (E_{0},…E_{3}) are well described by the oscillator model.


Suppose the energy spacing between the levels in the oscillator model is 0.15 eV. If the diatomic molecule is in air at 300K, what is the probability of finding the molecule in the state E_{1} instead of in the ground state, E_{0}? In the state E_{2}? Be sure to explain (briefly) your reasoning.
(You may find some of the following numbers useful: at T = 300K, k_{B}T = 0.025 eV/molecule; RT = 2.4 kJ/mole.)
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