The absorption of light in the visible and U.V. region by a solution governed by a photophysical law known as the Beer-Lambert law.
When a beam of monochromatic radiation of a suitable frequency passes through the solution, it is absorbed by the solution; as a result, light emerging from the solution is reduced.
If I0 is the intensity of the incident beam and It is the intensity of the transmitted beam, so the intensity of the light absorbed Ia is,
The probability that the photons of a beam of intensity I will be absorbed by the sample is directly proportional to the concentration and thickness of the absorbing solution.
Mathematically expressed as,
Here, dI = change in intensity
dx= absorption of radiation thickness
c= concentration
α = proportionality constant
Minus sign is the reduction in intensity.
Now, integration equation (2) between the limits I =I0 at x=0 and I=I
Or
According to equation (4), a beam of monochromatic radiation intensity decreases exponentially with an increase in the thickness x and the concentration c of the absorbing medium. It is Beer-Lambert law.
α/2.303 =ε, and defining log (I0/I) is the absorbance A of the solution, and we get
ε = Absorption coefficient
The absorption coefficient is characteristic of the solute and depends upon the nature of the solvent, temperature and wavelength of the radiation.
What is the molar absorption coefficient?
If the concentration c is expressed in mol dm-3, pathlength b in cm the ε as dm3 mol-1 cm-1 is called the molar absorption coefficient.
The transmittance T, defined as,
Absorbance A and Transmittance T are related as,
Plot a graph A → C gives a straight line passing through the origin. And %T → C.
Beer’s law depends upon the solution concentration, and Lambert’s law depends on the path length.
Curve for Transmittance measurement.
Curve for an absorbance measurement.
Curve for Transmittance measurement.
Curve for an absorbance measurement.
Limitation of beer-lambert law
This law is not obeyed if monochromatic light is used. This law is applied only to dilute solutions. And this law is no longer for concentration solutions. At higher concentrations refractive index(n) of the solution also changes.
