Page 326 - Instant notes

Physical Chemistry 312

i.e. the Beer-Lambert law for the intensity, I, of transmitted radiation is:
I=I 0exp(−σ[X]l)

The constant σ is called the absorption coefficient or extinction coefficient.
The Beer-Lambert law is often written in terms of logarithms to the base 10, in which
case, by writing σ=ε ln10:

The constant ε is another form of the absorption (extinction) coefficient. The constants σ
and ε are related directly to the transition probability f or the spectral transition. The
−1
dimensions of σ and ε are (concentration×length) but the exact units depend on the units
used for the species concentration (e.g. molar or molecular units) and path length. Care
must be taken to determine whether values of absorption coefficient are referenced to
logarithms of absorption intensity ratios to base e or to base 10. The convention is as
written here. In either form, it can be seen that transmitted intensity decreases
exponentially with the length of sample through which the radiation passes.
The ratio of the transmitted intensity to the incident intensity, I/I 0, is called the
transmittance, T, so log
log T=−ε[X]l

The absorbance (or optical density) of the species,

−A
is related to transmittance through, T=10 .

Linewidths
Spectral lines are not infinitely narrow since that would violate a variant of the
Heisenberg uncertainty principle (Topic G4) which states that the energy of a state
existing for a time, τ, is subject to an uncertainty, δE, of magnitude:

Since no excited state has an infinite lifetime, the spectral transition corresponding to the
energy separation between two states is spread over a finite width of energy. The energy
uncertainty inherent to states that have finite lifetimes is called lifetime broadening.
Two processes contribute to the finite lifetime of excited states:
(i) The rate of spontaneous emission of radiation as an excited state collapses to a lower
state (a fundamental property of the molecule) establishes an intrinsic minimum
natural linewidth to the transition, δE nat≈ћ/τ nat where τ nat is the natural lifetime to
spontaneous decay.