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For a diatomic molecule at sufficiently high temperatures, the equipartition of energy theorem distributes an equal portion of the energy, equal to ... , among each quadratic term in the Hamiltonian. Here ... is the Boltzmann constant and ... is the absolute temperature. Three of the degrees of freedom are translations, two are rotations, and one is vibration. The vibrational degree of freedom contributes an energy ... since the associated kinetic energy and potential energy are both quadratic forms. The temperature should not be too high (say, ... K), otherwise electronic degrees of freedom might be excited.
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