BioPHYSICAL chemistry

differences are small and not resolved, result-
ing in a broad spectrum. Also, lines may be
broadened due to the uncertainty principle
but this is a significant contribution only for
molecules with extremely short-lived excited
states.
The technique of hole-burning spectroscopy
can be used to reveal how nuclear motion
affects absorbance spectroscopy (Figure 14.15).
These experiments are performed at tem-
peratures near 1 K, where almost all nuclear
motion stops. A very short laser pulse at a
well-defined wavelength strikes the sample,
causing all of the electrons associated with that
specific wavelength to saturate; that is, the number of electrons in the ground
and excited states match. The saturation results in loss of absorbance since
the amplitude is given by the population difference that is now zero. The
spectrum then has a “hole burned” at a specific part of the band. The hole
will have a width equivalent to what would be seen if there were no
significant heterogeneity in nuclear positions in the system. With time, the
electrons will decay back to their normal distribution and the absorption
recovers. By analyzing these types of spectra one can identify the vibrations
are associated with the absorbing cofactor.

The yield of fluorescence

The emission of a photon is not the only possible mechanism by which an
electron can undergo transition from an excited state to the ground state,
because other nonradiative pathways, which usually involve generating
heat instead of light, are also possible. The quantum yield of fluorescence
is a measure of the fraction of transitions that occur by fluorescence com-
pared to other pathways. The quantum yield is usually defined in terms
of rates. Excited electronic states typically decay with first-order kinetics.
The transition of the excited state to the ground state can be considered
as being a competition between two first-order processes: fluorescence
and nonradiative decay. If the fluorescence rate constant is kf, and the
nonradiative rate constants are each ki, then the yield of fluorescence is
just given by:

(14.27)

When other processes are present, the observed rate that the excited state
decays, kobs, will be faster than the rate that is due to fluorescence only.

φf f
fi
i

k

kk

=

+∑

CHAPTER 14 OPTICAL SPECTROSCOPY 305

Wavelength (nm)

Hole

burning

Absorbance (a.u.)

Figure 14.15

A hole-burning

experiment

triggered by a short

light pulse.