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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.

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