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Fractional excitation of a two-state ensemble

Temperature plays a role in determining the relevance of electronic, vibrational, and rotational spectral lines in room-temperature biomedical optics.

The ratio between any two states' populations is an exponential function of ∆E, the difference in their energies, and kT, the Boltzmann energy, ratio is exp (-∆E=kT). Taking Ng to be the number of molecules in the ground state (i.e., the electronic, vibrational, or rotational quantum number is at a minimum) at body temperature (37°C), and Ne to be the number in a particular excited state, calculate the fractional excitation Ne/(Ng + Ne)
of a two-state ensemble for the following cases:
(a) when the excited state corresponds to absorption of a 525 nm photon;
(b) when the excited state is a vibration with v (wavenumber)= 1030 cm-1
(c) when the excited state is a rotation with v (wavenumber)= 30 cm-1

Based upon these calculations, is it reasonable to assume that essentially any molecule a photon encounters in the body will be in its ground vibrational state? Its ground electronic state? Its ground rotational state?

Solution Summary

This solution provides step by step equations for calculating fractional excitation of a two-state ensemble.