Spectrophotometry and colorimetry are concerned with measuring light absorption and transmission in solutions. Spectrophotometry covers the ultraviolet, visible, and infrared regions of the electromagnetic spectrum, while colorimetry focuses on the visible region. Beer's Law states that the absorbance of light is directly proportional to the concentration of an absorbing substance in solution. Absorbance follows the Beer-Lambert Law, which relates the intensity of transmitted light to properties of the absorbing medium. Atomic absorption spectrometry and atomic emission spectrometry are analytical techniques that use either absorption or emission spectroscopy to measure the concentration of elements in solutions.

2. Spectrophotometry property is mainly concerned with the
following regions of the spectrum:
ultraviolet, 185-400 nm;
visible 400-760 nm; and
infrared, 0.76- 15 µm.
Colorimetry is concerned with the visible region of the
spectrum.

3. Plane-polarized electromagnetic radiation showing the electric field, and
the direction of propagation.
Electric field component of planepolarized electromagnetic radiation.

4. Attenuation of a beam of radiation by Reflection and scattering losses with a
an absorbing solution.
soln contained in a typical glass cell.
When light impinges on a cuvette containing our molecule of interest (solute) in a
soln (solvent), other optical processes do or can occur:
• Transmission
• Reflection
• Refraction
• Scattering
• Luminescence
• Chiro-optical phenomena

5. THEORY OF SPECTROPHOTOMETRY AND
COLORIMETRY
When light (monochromatic or heterogeneous) falls upon a
homogeneous medium, a portion of the incident light is reflected, a
portion is absorbed within the medium, and the remainder is
transmitted. If the intensity of the incident light is expressed by Io,
that of the absorbed light by Ia, that of the transmitted light by It and
that of the reflected light by Ir , then:
For air-glass interfaces arising from the use of glass cells, it may be
stated that about 4 per cent of the incident light is reflected. Ir is
usually eliminated by the use of a control, such as a comparison cell,
hence:

6. Lambert's Law.
This law States that “when monochromatic light passes through
a transparent medium, the rate of decrease in intensity with the
thickness of the medium is proportional to the intensity of the light”.
(= the intensity of the emitted light decreases exponentially as the
thickness of the absorbing medium increases arithmetically ). We
may express the law by the differential eqn:
Eqn........ 1
it
l =l
dI
= − ∫ kl
∫
I
l =0
i0
It
ln = − kl
I
0
I is the intensity of the incident light of wavelength
λ, l (ell) is the thickness of the medium, and k is a
proportionality factor.
Integrating equation (1) and putting I = Io when l = 0,
we obtain:
or, stated in other terms,
Eqn..... 2

7. where Io is the intensity of the incident light falling upon an absorbing
medium of thickness(l ), It is the intensity of the transmitted light, and
k is a constant for the wavelength and the absorbing medium used.
By changing from natural to common logarithms we obtain:
Eqn....... 3
where K = k / 2.3026 and is usually termed the absorption coefficient. The
absorption coefficient is generally defined as the reciprocal of the
thickness (l cm) required to reduce the light to 1/10 of its intensity. This
follows from equation (3), since:
The ratio It/Io is the fraction of the incident light transmitted by a thickness (l)
of the medium and is termed the transmittance T.
Its reciprocal Io/It is the opacity, and the absorbance A of the medium (formerly
called the optical density ) is given by:*

8. Beer's Law.
The intensity of a beam of monochromatic light decreases
exponentially as the concn. of the absorbing substance increases
arithmetically.
This may be written in the form:
Eqn......4
where c is the concentration, and k/ and K/ are constants. Combining
equations (3) and (4), we have:
This is the fundamental equation of colorimetry and spectrophotometry, and is
often spoken of as the Beer-Lambert Law

9. The value of a will clearly depend upon the method of expression of the concn. If c
is expressed in mole L-1 and l in cm then a is given the symbol E and is called the
molar absorption coefficient or molar absorptivity (formerly the molar
extinction coefficient).
It will be apparent that there is a relationship between the absorbance A, the
transmittance T, and the molar absorption coefficient, since:

10. Real
Limitations
• Linearity is observed in the low concentration ranges(<0.01), but may
not be at higher concentrations.
• This deviation at higher concentrations is due to intermolecular
interactions.
• As the concentration increases, the strength of interaction increases and
causes deviations from linearity.
• The absorptivity not really constant and independent of concentration but e
is related to the refractive index (h ) of the solution :
• At low concentrations the refractive index is essentially constant-so e
constant and linearity is observed.

11. Absorption, emission, fluorescence
Schematic representation of absorption, emission, and fluorescence.

12. A blackbody emits a continuous spectrum
If you look directly at a blackbody, you will see this continuous spectrum
Clouds of gas absorb certain wavelengths (colors) of light
A continuous spectrum that hits a cloud of cool gas will be partially absorbed
The transmitted spectrum is called an absorption line spectrum (because certain
lines are absorbed), and is continuous except for the colors that were absorbed by the
gas.

13. •Anything that absorbs also emits.
•A cloud of cool gas that absorbs certain colors from a blackbody will emit
exactly those colors as the gas atoms de-excite
•If we look at the cloud without the blackbody in our line of sight, we will see an
emission line spectrum.
•The lines of emission have the same color as the absorption lines in the absorption line
spectrum
•If you added an emission line spectrum and an absorption line spectrum, you would get
a continuous spectrum.

15. Consider the simplified energy-level diagram shown in Fig. where
E0 represents the ground state in which the electrons of a given
atom are at their lowest energy level and E1, E2, E3, etc., represent
higher or excited energy levels.
Transitions between two quantised energy
levels, Say from E0 to Et, correspond to the
absorption of radiant energy, and the
amount of energy absorbed (ΔE)
is determined by Bohr's equation
The relationship between the ground-state and excited-state
populations is given by the Boltzmann equation
Nt = no. of atoms in the excited state,
No = number of ground state atoms,
g /go = ratio of statistical weights for
ground and excited states,

16. Atomic Absorption Spectrometry (AAS)
In this method, the atomic vapours
containing free atoms of an element in the
ground state are subjected to a UV-VIS
radiation source emitting a characteristic
frequency of the element present in atomic
vapours.
The radiation is absorbed and the intensity
of the radiation is attenuated. The absorbed
radiation causes excitation of electrons from
the ground state to an excited level.
The extent of absorption is a quantitative
measure of the concn. of the atomic vapours
of the element in the ground state. It is an
electronic excitation and the energy of
transitions lies in the to UV-VIS region of
the electromagnetic spectrum.

17. Atomic Emission Spectrometry (AES)
In this method, a sample is normally excited
by the thermal energy of a flame, argon plasma
or an electrical discharge. The atoms in the
sample absorb thermal energy, causing the
excitation of the outer orbital electrons.
As the excited state is short lived, the excited
atoms return back to the ground state after a
very short lifetime (typically10-6 to 10-9 s).
This is accompanied by the emission of EMR,
normally in the form of light in the UV-VIS
region.
The wavelength of the emitted radiation and
its intensity provide the qualitative and
quantitative information about the analyte.
The atomic emission spectroscopy employing
flame as a means of excitation is called flame
photometry or flame emission spectroscopy
(FES).

18. Electrons in a molecule can be classified in 3 different types.
1. Electrons in a single covalent bond (σ-bond): these are
tightly bound and radiation of high energy (short
wavelength) is required to excite them.
2. Electrons attached to atoms such as chlorine, oxygen or
nitrogen as 'lonepairs': these non-bonding electrons
can be excited at a lower energy (longer wavelength)
than tightly bound bonding electrons.
3. Electrons in double or triple bonds (π-orbitals) which can
be excited relatively easily. In molecules containing a
series of alternating double bonds (conjugated
systems), the π-electrons are delocalised and require
less energy for excitation so that the absorption rises
to higher wavelengths.

19. A diagram showing the various kinds of electronic excitation that may occur in
organic molecules is shown above. Of the six transitions outlined, only the two
lowest energy ones (left-most, colored blue) are achieved by the energies
available in the 200 to 800 nm spectrum. As a rule, energetically favored
electron promotion will be from the highest occupied molecular orbital
(HOMO) to the lowest unoccupied molecular orbital (LUMO), and the resulting
species is called an excited state

20. Basic components of an atomic spectrophotometer

22. Operation principle of AAS
Light source – hollow cathode lamp. Each element has its own unique lamp.
Atomic cell – flame (gas mixture) or graphite furnance (accepts solutions,
slurries, or even solids).
Detector – photomultiplier.
After G.Ma and G.W. Gonzales, http://www.cee.vt.edu

23. PRINCIPLE OF AAS
At the temperature of an air/acetylene flame (~2300oC) atoms of many
elements exist largely in the ground state. When a beam of
radiant energy that consists of the emission spectrum for the element
that is to be determined is passed through the flame, some of the
ground state atoms absorb energy of characteristic wavelengths
(resonance lines) and are raised to a higher energy state. The
radiation not removed by absorption is isolated by a monochrometer
and detected by a photomultiplier. For example, at 283.3 nm,
Pb ---> Pb* by absorption of a photon
The amount of radiant energy absorbed as a function of concentration of
an element in the flame is the basis of atomic absorption spectroscopy.
The amount of light absorbed is proportional to the elemental
concentration, assuming Beer‘s Law holds.

24. The exact mechanism of the excitation process in the hollow cathode lamp (hcl) is
of interest.
Figure 1. is a close-up view of a typical lamp and of the mechanism. The lamp itself is
a sealed glass envelope filled with argon or neon gas. When the lamp is on, neon
atoms are ionized, as shown, with the electrons drawn to the anode (+ charged
electrode), while the neon ions, Ne+, "bombard" the surface of the cathode (charged electrode). The metal atoms, M, in the cathode are elevated to the excited
state and are ejected from the surface as a result of this bombardment. When the
atoms return to the ground state, the characteristic line spectrum of that atom is
emitted. It is this light, which is directed at the flame, where unexcited atoms of the
same element absorb the radiation and are themselves raised to the excited state. As
indicated previously, the absorbance is measured and related to concn.
Fig1. The hcl and the process of metal atom excitation and light emission

25. Hollow Cathode Lamp:
the light from this lamp is exactly the light required for the analysis, even
though no monochromator is used. The reason for this is that atoms of the
metal to be tested are present within the lamp, and when the lamp is on, these
atoms are supplied with energy, which causes them to elevate to the excited
states. Upon returning to the ground state, exactly the same wavelengths that
are useful in the analysis are emitted, since it is the analyzed metal with
exactly the same energy levels that undergoes excitation.
Illustration of how the light emitted by the hollow cathode
lamp is the exact wavelength needed to excite the atoms in the flame .

26. To a first approximation, absorption by free atoms is similar to absorption
by molecules and there is a linear relationship between absorbance and the
“concn” of the sample. This relationship is given by the Beer-Lambert Law
it is found that B-L relationship cannot
be sustained because flame atomizers
are generally used as the “sample cell”
and the population of free atoms in a
flame is far from homogeneous.
Homogeneity of the sample is a basic
Kν =absorption coefficient at the
requirement for the application of
frequency ν
Beer’s Law.
e = charge of the electron,
m = mass of the electron, c = the speed of light,
N = the no. of free absorbing atoms in the light path
f = is the oscillator strength of the absorption line.
It can be seen that there are a number of constants in this equation.
The only variables are N, the total number of atoms in light path, and f the
oscillator strength. The relationship between them and the total amount of light
absorbed is a basis for quantitative analysis.

29. PRINCIPLE OF FLAME PHOTOMETRY
For a few elements, such as the alkali metals Na and K, an air/
acetylene flame is hot enough not only to produce ground state atoms,
but to raise some of the atoms to an excited electronic state. The
radiant energy emitted when the atoms return to the ground state is
proportional to the concentration and is the basis of flame emission
spectroscopy. i.e., at 589 nm,
Na -------> Na* (energy from flame)
Na* -------> Na + hn (at 589 nm)

30. PRINCIPLE OF FLAME PHOTOMETRY
This method is based upon the measurement of intensity of radiation emitted, in
the visible region, when a metal atom is introduced into a flame. The wavelength
of the radiation (or the colour), emitted tells us what the element is, and the
intensity of the radiation tells us how much of the element is present.
In a typical flame photometric experiment, a solution containing the relevant
substance to be analysed is aspirated into the burner and dispersed into the
flame as a fine spray. This process is called nebulisation.
The five processes occurring in the flame can be summarised as follows.
i) Desolvation ii) Vapourisation
iii) Atomisation iv) Excitation
v) Emission of radiation:
Electrons in the excited state are very
unstable and move back down to the
ground state or a lower energy state quite
quickly. As they do so, they emit the energy
in the form of radiation of characteristic
wavelength, which is measured by a
detector.

31. Within the flame, there are many more atoms in the ground state than
in the excited state. For Zn, for instance, in a 2000K flame, there are
7.3 X 1015 atoms in the ground state for every excited atom.
The alkali metals are elements with unocuppied atomic orbitals of
low enough energy to be sufficiently populated by a flame.
The intensity of the light emitted could be described by the
Scheibe-Lomakin Equation: I = k × c n

32. •
•
•
•
•
•
•
Widths of atomic lines are quite
important in atomic spectroscopy.
Narrow lines in atomic and emission
spectra reduce the possibility of
interference due to overlapping lines.
Atomic absorption and emission lines
consists of a symmetric distribution of
wavelengths that centers on a mean
wavelength (λ 0) which is the wavelength
of maximum absorption or maximum
intensity for emitted radiation.
The energy associated with λ 0 is equal to
the exact energy difference between two
quantum
states
responsible
for
absorption or emission.
A transition between two discrete, singlevalued energy states should be a line with
line-width equal to zero.
However, several phenomena cause line
broadening in such a way that all atomic
lines have finite widths.
Line width or effective line width (∆λ 1/2) of
an atomic absorption or emission line is
defined as its width in wavelength units
when measured at one half the maximum
Atomic Line Widths
Sources of broadening:
(1) Uncertainty effect
(2) Doppler effect
(3) Pressure effects due to collisions
(4) Electric and magnetic field effects
32

33. •
•
•
•
•
Uncertainty Effect
It results from the uncertainty principle postulated in 1927
by Werner Heisenberg.
One of several ways of formulating the Heisenberg
uncertainty principle is shown in the following equation:
Δt x ΔE = h/2π
The meaning in words of this equation is as follows: if the
energy E of a particle or system of particles – photons,
electrons, neutrons or protons – is measured for an exactly
known period of time Δt, then this energy is uncertain by at
least h/ 2πΔt.
Therefore, the energy of a particle can be known with zero
uncertainty only if it is observed for an infinite period of
time.
For finite periods, the energy measurement can never be
more precise then h/ 2πΔt.
• The lifetime of a ground state is typically long, but the lifetimes of
excited states are generally short, typically 10-7 to 10-8 seconds.
• Line widths due to uncertainty broadening are called natural
line widths and are generally 10-5nm or 10-4Å.
33

34. The "natural line width" indicates the lower limit of the absorption lines width.
It can be calculated from the uncertainty principle which states that
where Δτ is the lifetime of the excited state and ΔE the range of
energy over which the line emits, i.e. the line width in terms of
energy.
Note: ∆λ = ∆λ1/2

35. •
•
•
Doppler Effect
In a collection of atoms in a hot
environment, such as an atomizer,
atomic motions occur in every
direction.
The magnitude of the Doppler shift
increases with the velocity at which the
emitting
or
absorbing
species
approaches or recedes the detector.
For relatively low velocities, the
relationship between the Doppler shift
(Δλ) and the velocity (v) of an
approaching or receding atom is given
by:
Δ λ / λ 0= v / c
Where λ 0 is the wavelength of an un-shifted line
of a sample of an element at rest relative to the
transducer, and c is the speed of light.
•
∆λ
•
Emitting atom moving: (a) towards a
photon detector, the detector sees wave
crests more often and detect radiation of
higher frequency; (b) away from the
detector, the detector sees wave crests
less frequently and detects radiation at
lower frequency.
The result is an statistical distribution of
frequencies and thus a broadening of
35
spectral lines.

36. Pressure Effects Due to
Collisions
E2
Energy (eV)
• Pressure or collisional broadening is
caused by collisions of the emitting
or absorbing species with other
atoms or ions in the heated medium.
• These collisions produce small
changes in energy levels and hence a
range of absorbed or emitted
wavelengths.
• These collisions produce broadening
that is two to three orders of
magnitude grater than the natural line
widths.
• Eg. :Hollow-cathode lamps (HCL):
• Pressure in these lamps is kept really
low
to
minimize
collisional
broadening.
• Glass tube is filled with neon or
argon at a pressure of 1 to 5 torr.
λΑ
E2
λΕ
λΑ ’
E1
λΕ’
E1
Atom 1
Atom 2
36

39. Intensity of the Signal
The intensity of a signal depends on the population of the energy
level from which the transition is originating and the probability of
such a transition.
According to the Boltzmann statistical distribution, the population
of the ground state i.e., the number of species in the ground state is
highest and it keeps on decreasing as we go to higher energy levels.
In case of the atoms the population of any excited state relative to
that of the ground state is given by the following formula.

40. N* and N0 = Number of atoms in excited state
and ground state, respectively,
E = Energy difference between ground and
excited state (in J),
g* and g0 = Statistical factors that depend on
the degeneracies of the levels involved,
k = Boltzmann constant (= 1.28 × 10-23 J k-1),
T = Absolute temperature.
According to Eq. after the ground state, the lowest energy excited state will be
most populated and the population of the higher excited states would decrease
progressively. Eq. can be used to determine the population of an excited state
with respect to the ground state.

41. Intensity Concentration Relationship
The intensity of the emitted radiation (P) is proportional to the no. of excited
atoms N*.
we see that the number of atoms in the excited state, N*, at a given temperature
are proportional to N0 . Therefore, we can write the following.
P = K. C
(as, N0 is directly proportional to metal concn)
Thus, the intensity of the emitted light will be directly proportional
to the concentration of the element introduced into the flame.

42. Quantum or Wave Mechanics
L. de Broglie
(1892-1987)
• Light has both wave & particle
properties
• de Broglie (1924) proposed that
all moving objects have wave
properties.
• For light: E = hν = hc / λ
• For particles: E = mc2 (Einstein)
Therefore, mc = h / λ
and for particles
(mass)x(velocity) = h / λ
λ for particles is called the de Broglie wavelength

43. Origins of Atomic Spectroscopy
Spectroscopy of atoms or ions do not involve vibrations or rotation transitions.
Transition involves promoting an electron from a ground state to a higher empty atomic
state orbital, this state is referred to as the excited state.
Shown to the right is the three sodium absorption and emission process and the
emission lines. Atomic p-orbitals are in fact split into two energy levels for the multiple
spins of the electron. The energy level is so small however that a single line observed. A
high resolution would show the line as a doublet.

44. For the element sodium, two inner shells are completely filled and
there is one electron in the outer third shell.
This electron is said to be in an s orbital. However, the remaining
orbitals of the third shell and all the orbitals of the fourth, fifth and sixth
shells, etc., are empty. When the outer electron of sodium is in the s
orbital the atom is said to be in the “ground state” or the “unexcited
state”. If the atom absorbs radiation the electron undergoes a transition
to one of the empty orbitals at the higher energy levels.
From Grotrian diagram it can be seen that the s electron can undergo
transition to various p orbitals. These in turn exhibit fine structure as
a result of the electron in a p orbital spinning in either of
two possible directions within the orbital. There is a slight difference
in the energy of such an electron depending on its direction of spin,
i.e. the spin quantum number.

45. Optical Atomic Spectra
•
•
•
•
•
•
Figure 8-1a shows the energy level diagram for sodium.
A value of zero electron volts (eV) is arbitrarily assigned to
orbital 3s.
The scale extends up to 5.14eV, the energy required to
remove the single 3s electron to produce a sodium ion.
5.14eV is the ionization energy.
A horizontal line represents the energy of and atomic orbital.
“p” orbitals are split into two levels which differ slightly in
energy:
3s → 3p: l = 5896Å or 5890Å
3s → 4p: l = 3303Å or 3302Å
3s → 5p: l = 2853.0Å or 2852.8Å
There are similar differences in the d and f orbitals, but their
magnitudes are usually so small that are undetectable, thus
only a single level is shown for orbitals d.
Spin-orbit coupling

46. C. Hollow cathodes
An illustration of the hollow cathode is given in Figure 2. In this system the
metal of interest is used as the material from which the cathode is made.
The light source is filled with an inert gas, such as neon, which is
ionized by the anode. The positively charged neon ions are then attracted by
the negative charged cathode and accelerated towards it.
On arrival at the cathode the neon strikes the surface of the cathode. If it has
sufficient energy it causes atoms of the cathode to be ejected. This process is
called “sputtering”.
The sputtered atoms are invariably excited
and emit radiation characteristic
of the cathode metal(s). The emitted lines
are generally very narrow in band width .
The sample atoms absorb only at their own
characteristic wavelengths.
It is therefore essential that the light source
emit at Exactly the same wavelength.
This can be accomplished by using a
hollow cathode made of the same element as the element being determined.