Instrumental Analysis
Fundamentals of
Spectroscopy
1
(Absorption) Spectrophotometry
n General Stuff:
•Qualitative: Spectrum (a plot of A vs. l) is
characteristic of a specific species
•Quantitative: Absorbance at a particular l can be
related to the amount of absorbing species
Definitions and units
l .monochromatic wavelength (cm)
Po.incident radiant power (erg cm -2 s -1 )
P .transmitted radiant power (erg cm -2 s -1 )
b .absorption pathlength(cm)
2
Qualitative analysis: The spectrum
3
Molecular and Atomic Spectrometry
Spectrometry is the study of
electromagnetic radiation (EMR) and its
applications
To begin to understand the theory and
instrumental application of spectrometry
requires an understanding of the
interaction of EMR (i.e. light) with matter
4
Questions
What is nature of light?
Are their different types of light?
–How are they the same?
–How are they different?
How does light propagate?
5
What is Light?
Light is a form of energy
Light travels through space at extremely
high velocities
– The speed of light (c) ~ 3 x 1010 cm/sec or
186,000 miles per second
Light is classified as electromagnetic
radiation (EMR)
6
Characteristics of Light
Light behaves like a wave.
– That is, it can be modeled or characterized
with wave like properties.
Light also behaves like a particle.
– The photon and photoelectric effect.
Today, we envision light as a selfcontained packet of energy, a photon,
which has both wave and particle like
properties.
7
The Electromagnetic Spectrum
8
9
The Electromagnetic Spectrum
10
The EMR
Spectrum
Different portions of
the EMR spectrum
and different types of
spectroscopy involve
different parts
(quantum states) of
the atom
11
EMR Wave Characteristics
Wavelength (l) is the distance from one wave crest to
the next.
Amplitude is the vertical distance from the midline of a
wave to the peak or trough.
Frequency (v) is the number of waves that pass through
a particular point in 1 second (Hz = 1 cycle/s)
12
EMR Wave Characteristics
The frequency of a wave is dictated (or fixed) by
its source, it doesn’t change as the wave passes
through different mediums.
The speed of a wave (u), however, can change
as the medium through which it travels changes
umedium = lv = c/n
Where n = refractive index
nvacuum = 1
nair = 1.0003 (vair = 0.9997c)
nglass ~1.5 (vgas ~ 0.67c)
Since v is fixed, as l decreases, u must also
decrease
13
Wave Properties of
Electromagnetic Radiation
EMR has both electric (E) and magnetic
(H) components that propagate at right
angles to each other.
14
Particle Properties of EMR
The energy of a photon depends on its
frequency (v)
Ephoton = hv
h = Planck’s constant
h = 6.63 x 10-27 erg sec or 6.63 x 10-34 Js
15
Relationship between Wave and
Particle Properties of EMR
Ephoton = hv ; umedium = lv = c/n
With these two relationships, if you know one of
the following, you can calculate the other two
– Energy of photon
– Wavelength of light
– Frequency of light
Ephoton =
hc
ln
16
Relationship between Wave and
Particle Properties of EMR
Example: What is the energy of a 500 nm
photon?
 = c/l = (3 x 108 m s-1)/(5.0 x 10-7 m)
 = 6 x 1014 s-1
E = h =(6.626 x 10-34 J•s)(6 x 1014 s-1) = 4 x 10-19 J
17
How Light Interacts with Matter.
Atoms are the basic
blocks of matter.
They consist of heavy
particles (called protons
and neutrons) in the
nucleus, surrounded by
lighter particles called
electrons
18
How Light Interacts with Matter.
An electron will interact with a photon.
An electron that absorbs a photon will
gain energy.
An electron that loses energy must emit a
photon.
The total energy (electron plus photon)
remains constant during this process.
19
Characteristics of Absorption
Absorption is defined as the process by
which EMR is transferred, in the form of
energy, to the medium (s, l, or g) through
which it is traveling
Involves discrete energy transfers
Frequency and wavelength selective
– Ephoton = hv = c/l
20
Characteristics of Absorption
Involves transitions from ground state
energy levels to “excited” states
– The reverse process is called emission
For absorption to occur, the energy of the
photon must exactly match an energy level
in the atom (or molecule) it contacts
– Ephoton = Eelectronic transition
We distinguish two types of absorption
– Atomic
– Molecular
21
How Light Interacts with Matter.
Electrons bound to
atoms have discrete
energies (i.e. not all
energies are allowed).
Thus, only photons of
certain energy can
interact with the
electrons in a given
atom.
22
How Light Interacts with Matter.
Consider hydrogen, the
simplest atom.
Hydrogen has a specific
line spectrum.
Each atom has its own
specific line spectrum
(atomic fingerprint).
23
Energy Transitions and Photons
The energy of photon that can interact with a transition jump
depends on the energy difference between the electronic
levels.
24
Unique Atomic Signatures
Each atom has a specific set of energy levels, and thus a
unique set of photon wavelengths with which it can interact.
25
Energy Level Diagram
Absorption and emission
for the sodium atom in the
gas phase
Illustrates discrete energy
transfer
ΔEtransition = E1 - E0 = hv = hc/l
26
Molecular Absorption
More complex than atomic absorption
because many more potential transitions
exist
– Electronic energy levels
– Vibrational energy levels
– Rotational energy levels
Emolecule = Eelectronic + Evibrational + Erotational
– Eelectronic > Evibrational > Erotational
Result - complex spectra
27
Energy Level Diagram for
Molecular Absorption
28
Molecular Absorption Spectra of
Benzene in the Gas Phase
Electronic Transition
Vibrational Transition
Superimposed on the
Electronic Transition
Absorption Band –
A series of closely
shaped peaks
29
Molecular
Absorption
Spectra in the
Solution Phase
In solvents the
rotational and
vibrational transitions
are highly restricted
resulting in broad
band absorption
spectra
30
Beer’s Law
or the Beer-Lambert Law
Pierre Bouguer discovered that light transmission decreases
with the thickness of a transparent sample in 1729. This
law was later rediscovered by Lambert, a mathematician, and
then by Beer, who published in 1852 what is now known as
the Beer-Lambert-Bouguer law. Beer's 1852 paper is the one
that is often cited in older textbooks. Bouguer's contribution
is rarely mentioned and the law is known as either "Beer's law"
or "the Beer-Lambert law".
Consider a beam of light
with an (initial) radiant
intensity Po
The light passes through a
solution of concentration (c)
The thickness of the
solution is “b” cm.
The intensity of the light
after passage through the
solution (where absorption
occurs) is P
P0
hv
Concentration (c)
Spectroscopy Terms Describing
Absorption (Beer’s Law)
b
P
We Define
Transmittance (T) = P/P0 (units = %)
Absorbance (A) (units = none)
A = log (P0/P)
A = -log (T) = log (1/T)
A = abc (or εbc) <--- Beer’s Law
a = absorptivity (L/g cm)
b = path length (cm)
c = concentration (g/L)
ε = molar absorptivity (L/mol cm)
– Used when concentration is in molar units
Transmittance
T => transmittance
P
T = ----Po
b
Po
P
Example
P0 = 10,000
P = 5,000
-b-
P
5000
T 

 0.5
P0 10000
A = -log T = -log (0.5) = 0.3010
Beer’s Law
A = abc = ebc
A
c
Beer’s Law
A = ebc
Path Length Dependence, b
Readout
Absorbance
0.82
Source
Detector
Beer’s Law
A = ebc
Path Length Dependence, b
Readout
Absorbance
0.62
Source
b
Detector
Sample
Beer’s Law
A = ebc
Path Length Dependence, b
Readout
Absorbance
0.42
Source
Detector
Samples
Beer’s Law
A = ebc
Path Length Dependence, b
Readout
Absorbance
0.22
Source
Detector
Samples
Beer’s Law
A = ebc
Wavelength Dependence, a
Readout
Absorbance
0.80
Source
b
Detector
Beer’s Law
A = ebc
Wavelength Dependence, a
Readout
Absorbance
0.82
Source
Detector
Beer’s Law
A = ebc
Wavelength Dependence, a
Readout
Absorbance
0.30
Source
b
Detector
Beer’s Law
A = ebc
Wavelength Dependence, a
Readout
Absorbance
0.80
Source
b
Detector
Non-Absorption Losses
"Reflection and
scattering losses."
AKA
The Guinness Effect
Limitations to Beer’s Law
Real
– At high concentrations charge distribution effects
occur causing electrostatic interactions between
absorbing species
Chemical
– Analyte dissociates/associates or reacts with solvent
Instrumental
– ε = f(λ); most light sources are polychromatic not
monochromatic (small effect)
– Stray light – comes from reflected radiation in the
monochromator reaching the exit slit.
Chemical Limitations
A reaction is occurring as you record
Absorbance measurements
Cr2O72- + H2O
2H+ + CrO42CrO42Cr2O72A550
300
400
wavelength
500
A446
concentration
concentration
Instrumental Limitations - ε = f(λ)
How/Why does ε
vary with λ?
Consider a
wavelength scan for
a molecular
compound at two
different wavelength
bands
Larger the Bandwidth – larger deviation
In reality, a
monochromator can
not isolate a single
wavelength, but
rather a small
wavelength band
Instrumental Limitations – Stray Light
How does stray light effect Absorbance
and Beer’s Law?
A = -log P/Po = log Po/P
When stray light (Ps) is present, the
absorbance observed (Aapparent) is the sum
of the real (Areal) and stray absorbance
(Astray)
Instrumental Limitations – Stray Light
 Po  Ps 

Aapp = Areal + Astray = log 
 P  Ps 
As the analyte concentration increases
([analyte]↑), the intensity of light exiting the
absorbance cell decreases (P↓)
Eventually, P < Ps
Instrumental Limitations – Stray Light
Result – non-linear
absorption (Analyte
vs. Conc.) as a
function of analyte
concentration
– Similar to
polychromatic light
limitations
Emission of EMR
EMR is released when excited atoms or
molecules return to ground state
– Reverse of the absorption process
– We call this process “emission”
Initial excitation can occur through a
number of pathways
– Absorption of EMR
– Electrical discharge
– High temperatures (flame or arc)
– Electron bombardment
52
Emission of EMR
We distinguish several types of emission
1. Atomic
2. X-Ray
3. Fluorescence
Involves molecules
Resonance and non-resonance modes
4. Phosphorescence
Non-radiative relaxation
Similar to fluorescence only relaxation times are
slower than fluorescence
Involves metastable intermediates
53
Energy Level Diagrams and
Emission
54
Luminescence is the emission of light from any
substance and occurs from electronically excited
states.
It is formally divided into two categories:
Molecular fluorescence.
Molecular phosphorescence.
Its attractive feature is the inherent high sensitivity,
3 order of magnitude lower than absorption
measurements (ppb).
Fluorescence is emission of light from excited singlet states
(the electron in the excited state orbital is spin paired (has the
opposite spin) to the electron in the ground state orbital) –
therefore, return to the ground state is spin-allowed, and the
excited state lifetime is short (1 -10 ns).
Phosphorescence is emission of light from excited triplet
states (the electron in the excited orbital has the same spin
orientation as the ground state electron) –therefore, the
transition to the ground state is spin-forbidden, and the
excited state lifetime is long (ms to seconds or even minutes!)
Molecular chemiluminescence: emission from an excited
species that formed in the course of chemical reaction.
Jablonski Diagram
Deactivation Processes
Intersystem Crossing: transition with spin change (e.g. S to T).
As with internal conversion, the lowest singlet vibrational state overlaps one of upper
triplet vibrational levels and a change in spin state is thus more probable.
Intersystem crossing is most common in molecules that contain heavy atoms, such
as iodine or bromine (the heavy-atom effect).
Fluorescence: emission not involving spin change
(e.g. singlet→singlet),efficient, short-lived <10-5s.
Phosphorescence: emission involving spin change. Long-lived> 10-4s.
A triplet →singlet transition is much less probable than singlet →singlet
transition.
This transition may persist for some time after irradiation has been .
discontinued since the average lifetime of the excited triplet state with respect to
emission ranges from 10-4 to 10 s or more..
Dissociation: excitation to vibrational state with enough energy to break bond.
Predissociation: relaxation to state with enough energy to break bond
Fluorescence Quenching
Quenching is ANY process that decreases the amount of
fluorescence for a given number of input photons:
Collisional quenching –the excited state is de-activated via
diffusional contact with a quencher (dynamic quenching)
Fluorophores can form nonfluorescent complexes with
quenchers. This process is referred to as static quenching since it
occurs in the ground state and does not rely on diffusion or
molecular collisions.
attenuation of the emitted radiation by the fluorophore
Collisional Quenching
methyl viologen
How likely is fluorescence?
From the equation, it is clear that 0< φ< 1, and that
a high value for kr and a small value for knr lead to
the best quantum yield (i.e., fluorescence is faster
than all other competing processes).
It should be noted that a change in quantum yield
can occur owing to many factors (temperature, pH,
solvent, presence of quenchers, dimerization, etc)
and thus fluorescence intensity may not be directly
proportional to concentration.
Molecular Luminescence Spectroscopy
S0-common, diamagnetic (not affected by B fields).
D0-unpaired electron, many radicals, two equal energy states.
T1-rare, paramagnetic (affected by B fields).
Energy (S1) > Energy (T1) (difference is energy required to flip
electron spin).
Ground state Ground state Excited state
Singlet, So
Doublet, Do
Triplet, T1
emission
S1
Excited state
Singlet, S1
absorption
So
S1
So
What about Lifetimes?
Absorption
S1S0 very fast 10 -15 -10 -13 s
Relaxation
Resonant emission S1 S0 fast 10 -9 -10 -5 s (fluorescence)
common in atoms
strong absorber - shorter lifetime
Non-resonant emission S1S0 fast 10 -9 -10 -5 s (fluorescence)
common in molecules, have extremely fast vibrational relaxation
red shifted emission (Stokes shift)
Stokes Shifting- The energy of the emission is typically less than that of
absorption. Fluorescence typically occurs at lower energies or longer
wavelengths. this is called Stokes Shifting.
Non-resonant emission T1 S0 slow 10 -5 -10 s (phosphorescence)
Transitions between states of different multiplicities are improbable
(forbidden)
(e.g. T S or T S)
Fluorescence Quantum Yield - ratio of number of molecules fluorescing to number excited.
What Affects the fluorescence quantum yield?
(1) Excitation l
Short l's break bonds increase kpre-dis and kdis
rarely observed
 
  n
most common
  
emission is usually from lowest lying excited state
(2) Lifetime of state
Transition probability measured by e
Large e implies short lifetime
Largest fluorescence from short lifetime/high e state
   n (10 -9 -10 -7 s > 10 -7 -10 -5 s)
(3) Structure
Few conjugated aliphatics fluoresce
but
Many aromatics fluoresce
Desire short lifetime S1, no/slowly accessible T1
Fluorescence increased by # fused rings and substitution on/in ring
Emission Intensity –the factors that control
emission intensity include the presence of
heteroatoms, presence of aromatic rings,
overall structural rigidity, and resonance
stabilization.
Presence of heteroatoms: often this can
lead to unwanted π*→n transitions that are
likely to convert to the triplet state, and give
no fluorescence. All of the species shown
below are non-fluorescent
(4) Rigidity
Rigid structures fluoresce
Increase in fluorescence with chelation
Ethidium bromide