1. What is Spectroscopy?
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative energy as a function of its wavelength or frequency.
Spectrometry is the spectroscopic technique used to assess the concentration or amount of a given chemical (atomic, molecular, or ionic) species. In this case, the instrument that performs such measurements is a spectrometer, spectrophotometer, or spectrograph.
Spectroscopy/spectrometry is often used in physical and analytical chemistry for the identification of substances through the spectrum emitted from or absorbed by them.

2. What are electromagnetic waves?
Electricity can be static, like what holds a balloon to the wall or makes your hair stand on end.
Magnetism can also be static like a refrigerator magnet. But when they change or move together, they make waves - electromagnetic waves.
Electromagnetic waves are formed when an electric field (shown as blue arrows) couples with a magnetic field (shown as red arrows). The magnetic and electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave. James Clerk Maxwell and Heinrich Hertz are two scientists who studied how electromagnetic waves are formed and how fast they travel.
Electromagnetic waves are typically described by any of the following three physical properties: the frequency f, wavelength λ, or photon energy E.

3. Frequency
(a) and (b) represent two waves that are traveling at the same speed.
In (a) the wave has long wavelength and low frequency
In (b) the wave has shorter wavelength and higher frequency

4. Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object.
Electromagnetic radiation
Electromagnetic radiation (EM radiation or EMR) is a form of energy emitted and absorbed by charged particles, which exhibits wave-like behavior as it travels through space. EMR has both electric and magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy and wave propagation. In vacuum, electromagnetic radiation propagates at a characteristic speed, the speed of light.

10. What happens to absorbed radiation
It is possible for the packet of photonic energy to be absorbed, resulting in the promotion of one or more electrons to higher energy levels. That is, electromagnetic radiation is absorbed by the atom, which is converted from its ground to one of many possible excited states.
Since the energy of electrons in orbital is fixed, it should be clear that when an electron is promoted, a very specific amount of energy is required—corresponding to
the energy difference between the initial orbital and the final orbital.
Note that, if the photonic energy is very high, such as might be the case with x-rays, the electron may be totally removed from the atom, leaving an ion in its place.
Atoms generally do not stay in an excited state and they tend to relax to their ground states as quickly as possible. In doing so they must emit their excess energy as the electron falls to a lower orbital.
The end result is that the atoms emit their excess energy once again as light. And the light they radiate will correspond to a very specific set of photon energies.

11. Electrons in molecule
p, s, and n (non-bonding) electrons

12. Sigma and Pi orbitals

13. Electron transitions

14. Electron transitions
Antibonding molecular orbitals (MOs) are normally higher in energy than bonding MOs. Bonding and antibonding orbitals form when atoms combine into molecules as a result of the Pauli Exclusion Principle. Consider two hydrogen atoms that are initially far apart and are brought together. When they are far apart and isolated, the atoms have identical energy levels. However, as the spacing between the two atoms becomes smaller, the electron wave functions begin to overlap. The Pauli principle dictates that no two electrons in an interacting system may have the same quantum state. Therefore, each energy level of the isolated atoms splits into two molecular orbitals belonging to the pair, one lower in energy than the original atomic level and one higher. For example, the ground state energy level, 1s, splits into two molecular orbitals. Since the lower orbital is lower in energy than the original atomic orbitals of the separate atoms, it is more stable, and promotes the bonding of the two H atoms into H2. This is the bonding orbital. The higher orbital is higher in energy than the original atomic orbitals and is less stable, and therefore opposes the bonding. This is the antibonding orbital. In a molecule such as H2, the two electrons normally occupy the bonding orbital, since it is lower in energy, and therefore the molecule is more stable than the separate H atoms.
A molecular orbital becomes antibonding when there is less electron density between the two nuclei than there would be if there were no bonding interaction at all. When an MO changes sign (from positive to negative) at a nodal plane between two atoms, it is said to be antibonding with respect to those atoms. Antibonding orbitals are often labelled with an asterisk (*) on molecular orbital diagrams.

15. Roles of Chromophore and Auxochrome on absorption
A chromophore is the part of a molecule responsible for its color. The color arises when a molecule absorbs certain wavelengths of visible light and transmits or reflects others. Example- nitro, azo group etc.
A molecule containing a chromophore is called chomogen.
An auxochrome is a group of atoms attached to a chromophore which modifies the ability of that chromophore to absorb light or intensify the color.
There are mainly two types of auxochromes:
Acidic -COOH, -OH, -SO3H
Basic -NHR, -NR2, -NH2

16. Chromophoric Structure
Group Structure nm
Carbonyl > C = O 280
Azo -N = N
Nitro -N=O 270
Thioketone -C =S 330
Nitrite -NO
Conjugated Diene -C=C-C=C- 233
Conjugated Triene -C=C-C=C-C=C- 268
Conjugated Tetraene -C=C-C=C-C=C-C=C- 315
Benzene

17. Beer – Lambert Law
When c b

18. Exponential functions
Exponential functions look somewhat similar to functions you have seen before, in that they involve exponents, but there is a big difference, in that the variable is now the power, rather than the base. Previously, you have dealt with such functions as f(x) = x2, where the variable x was the base and the number 2 was the power.
In the case of exponentials, however, you will be dealing with functions such as g(x) = 2x, where the base is the fixed number, and the power is the variable.
Let's look more closely at the function g(x) = 2x. To evaluate this function, we operate as usual, picking values of x, plugging them in, and simplifying for the answers. But to evaluate 2x, we need to remember how exponents work. In particular, we need to remember that negative exponents mean "put the base on the other side of the fraction line".
So, while positive x-values give us values like these:

19. Beer – Lambert Law

20. Beer – Lambert Law ᵋ= molar absorptivity a=absorptivity, A= ᵋ b c
Transmittance, T = P / P0 % Transmittance, %T = 100 T

21. Relationship between absorbance and transmittance
The relationship between absorbance and transmittance is illustrated in the following diagram:
So, if all the light passes through a solution without any absorption, then absorbance is zero, and percent transmittance is 100%. If all the light is absorbed, then percent transmittance is zero, and absorption is infinite.

23. Why do we prefer to express the Beer-Lambert law using absorbance as a measure of the absorption rather than %T ?
Answer : To begin, let's think about the equations...
A=abc
%T = 100 P/P0 = e -abc
Now, suppose we have a solution of copper sulphate (which appears blue because it has an absorption maximum at 600 nm). We look at the way in which the intensity of the light (radiant power) changes as it passes through the solution in a 1 cm cuvette. We will look at the reduction every 0.2 cm as shown in the diagram below. The Law says that the fraction of the light absorbed by each layer of solution is the same. For our illustration, we will suppose that this fraction is 0.5 for each 0.2 cm "layer" and calculate the following data:
Path length / cm
0.2
0.4
0.6
0.8
1.0 %T
100 50 25
12.5
6.25
3.125
Absorbance
0.3
0.9
1.2
1.5

24. A = abc tells us that absorbance depends on the total quantity of the absorbing compound in the light path through the cuvette. If we plot absorbance against concentration, we get a straight line passing through the origin (0,0).
The linear relationship between concentration and absorbance is both simple and straightforward, which is why we prefer to express the Beer-Lambert law using absorbance as a measure of the absorption rather than %T.

25. Problems

26. Problems

27. Limitations of the Beer-Lambert law
The linearity of the Beer-Lambert law is limited by chemical and instrumental factors. Causes of nonlinearity include:
-deviations in absorptivity coefficients at high concentrations
(>0.01M) due to electrostatic interactions between molecules in close proximity
-scattering of light due to particulates in the sample
-fluoresecence or phosphorescence of the sample
-changes in refractive index at high analyte concentration
-shifts in chemical equilibria as a function of concentration
-non-monochromatic radiation, deviations can be minimized by using a relatively flat part of the absorption spectrum such as the maximum of an absorption band
-stray light

28. (1) Chemical effects - analyte associates, dissociates or reacts to give molecule with different ᵋ
(2) Physical effects - stray light, polychromatic radiation or noise
non-linear calibration curve