The Beer-Lambert law describes the relationship between the concentration of a substance in solution and the amount of light it absorbs. It states that absorbance is directly proportional to concentration and path length. Mathematically, it can be expressed as: A = ε * c * l, where A is absorbance, ε is the molar absorptivity, c is concentration, and l is path length. The Beer-Lambert law is important in quantitative analysis using UV-visible spectroscopy. It is only applicable to monochromatic light and at low concentrations where molecule interactions can be ignored.

1. BEER-LAMBERT'S
LAW

2. The Beer –Lambert Law
When a monochromatic light of initial intensity Io passes through a
solution in a transparent vessel, some of the light is absorbed so that the
intensity of the transmitted light I is less than Io .
There is some loss of light intensity from scattering by particles in the
solution and reflection at the interfaces, but mainly from absorption by
the solution.
The relationship between I and Io depends on the path length of the
absorbing medium, l, and the concentration of the absorbing solution,c.
These factors are related in the laws of Lambert and Beer

3. Lambert’s law
When a ray of monochromatic light passes through an
absorbing medium its intensity decreases exponentially as
the length of the absorbing medium increases

4. Beer’s law :
When a monochromatic light passes through an absorbing
medium its intensity decreases exponentially as the concentration
of the absorbing medium increases.

5. The Beer-Lambert Law, also known simply as Beer's Law, is
a fundamental principle in analytical chemistry and
spectroscopy that describes the relationship between the
concentration of a substance in a solution and the amount
of light it absorbs. This law is particularly important in the
field of UV-visible spectroscopy, where it is used to
quantitatively analyze the concentration of a solute in a
solution based on its absorbance of light.

6. Mathematically, the Beer-Lambert Law is expressed as:
A = ε * c * l
Where:
● A is the absorbance of the solution, a dimensionless quantity that
indicates how much light is absorbed by the solution.
● ε (epsilon) is the molar absorptivity (also called molar extinction
coefficient), which is a constant specific to the substance being
analyzed. It represents how strongly the substance absorbs light at
a particular wavelength.
● c is the concentration of the substance in the solution, typically
measured in molarity (moles per liter).
● l is the path length that the light travels through the solution, usually

8. ABSORBANCE VS
CONCENTRATION

9. LIMITATIONS
The limitations of Beer-lambert law are given as:
1. Beer-Lambert law is only valid on monochromatic light
2. This law is applicable under a low concentration range
where interactions between molecules are not considered.
3. This law is also invalid when radiations of very high
intensities are used.

10. DEVIATION OF BEER-LAMBERT’S LAW
When a plot of absorbance as a function of concentration at a
particular path and wavelength of monochromatic is drawn, a straight
line passing through the origin is obtained. But when concentration is
very high, a plot of absorbance and concentration deviates from
linear behavior.

11. The main causes of such deviation from Beer Lambert’s law are
given as:
1. The deviation may occur when the light of a single wavelength is
not used
2. Polymerization of solutes during the measurements
3. Association, dissociation, or ionization of solutes causes
deviation
4. Presence of some other substance that absorbs at the same
wavelength as the solute may cause deviation.
5. The presence of some impurities in the colored compounds may
cause deviation

12. FRANCK-
CONDON
PRINCIPLE

13. The Franck-Condon principle is a fundamental concept in
molecular spectroscopy that describes the transitions of
a molecule between its different electronic energy
levels during a spectroscopic process, such as
absorption or emission of light. This principle is named after
the scientists James Franck and Edward Condon,
who developed it in the early 20th century.

14. In 1925, before the development of the Schrödinger
equation, Franck put forward qualitative arguments to
explain the various types of intensity distributions found in
vibronic transitions.
His conclusions were based on the fact that an electronic
transition in a molecule takes place much more
rapidly than a vibrational motion of the nuclei that the
instantaneous internuclear distance and the velocity of
the nuclei can be considered remain unchanged
during the electronic transition (later used as Born-
Oppenheimer Approximation).

15. This means in the diagrams
showing the potential energy
curve of the two electronic
states of the molecule, the
transition must be
represented by the vertical
lines, i,e. the most probable or
most intense transition will be
those represented by the
vertical lines.

16. Figure demonstrating the Franck principle: for re’ > re’’ (left) and re’ =
re’’ (right). The vibronic transition A → B is the most probable in both
cases.

17. When a molecule absorbs or emits light, it undergoes a change in its
electronic energy levels.
The electrons in the molecule move from one energy level to another.
Since the mass of the atomic nuclei is much larger than that of the
electrons, the nuclei do not move appreciably during these rapid
electronic transitions.
This is because the timescale for nuclear motion is typically much
slower compared to the timescale of electronic transitions.
IN SIMPLE TERMS

18. The Franck-Condon principle tells us that the probability of
observing a particular vibrational transition depends on the overlap
between the vibrational wavefunctions of the initial and final
electronic states. In other words, the more similar the vibrational
states are in the initial and final electronic energy levels, the more
likely the transition is to occur.
Overall, the Franck-Condon principle provides a useful
framework for understanding and predicting the outcomes of
electronic and vibrational transitions in molecules during
spectroscopic processes. It's an important concept in fields
such as spectroscopy, photochemistry, and molecular physics.

19. THANK YOU!