BioPHYSICAL chemistry

may be possible to identify the relative amount of each

state if they have different spectra. If the spectrum of

each pure component is known then it is possible to

determine the amount of each component by measur-

ing the absorption at multiple wavelengths.

Assume that there are two components, A and B, wih

concentrations [A] and [B], respectively (Figure 14.6). The

total absorption at a given wavelength is given by:

A=AA+AB=(εA[A] +εB[B])l (14.12)

If the spectrum is measured at two different wave-

lengths, λ 1 and λ 2 , then the absorption at each wave-

length is given by:

A(λ) 1 =(εA(λ) 1 [A] +εB(λ) 1 [B])l

A(λ) 2 =(εA(λ) 2 [A] +εB(λ) 2 [B])l

(14.13)

Since there are two unknowns, [A] and [B], and two

equations, it is possible to solve these equations for the

unknowns. Some algebra yields:

(14.14)

There may be a point in the spectrum at which the spectrum does not

change as the relative concentrations of A and B change because the extinc-

tion coefficients are equal at this point; this is known as an isosbestic point.

Having an isosbestic point demonstrates that the sample consists of two

components in equilibrium with no intermediates and provides a useful

reference point for spectral measurements.

Transitions

What determines the wavelength at which a molecule absorbs light?

The absorption of light is associated with a transition of an electron from

one state to another. Because the energies of the electronic states are

quantized, the energy of the photon that can be absorbed is also quantized

(Figure 14.7). Based upon the conservation of energy, the frequency of

the light emitted when an electron makes a transition from state 1 to

state 2 is:

[]

() () () ()

() ()

B

AAAA

AB

=

ελ λ−ελ λ

ελελ

12 21

12 −ελελAB() () 21

[]

() () () ()

() ()

A

BBAA

AB

=

ελ λ−ελ λ

ελελ

21 12

12 −ελελAB() () 21

296 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY

Wavelength λ

Spectrum of

species A

Spectrum of

species B

Spectrum of

solution with

both A and B

A(λ 1 )

A(λ 2 )

Absorbance A

Figure 14.6The contributions of
different components (A and B) in an
optical spectrum can be separated with
measurements at different wavelengths.
At an isosbestic point the absorption
does not change as the relative
concentrations of the components
change.