What is Spectroscopy?
• Spectroscopy: a general term for the science that deals
with the interactions of various types of radiation
(electromagnetic radiation and other forms of energy)
with matter
• Spectrometry and spectrometric methods:
-a large group of analytical methods that are based
on atomic and molecular spectroscopy
-the measurement of the intensity of radiation with a
photoelectric transducer or other type of electronic
device.
• Colorimetry: based on absorption of visible light.
Ch. 18 – Ch. 20
Spectrophotometry
Properties of Electromagnetic Radiation
Classical sinusoidal wave model
• Plane-polarized electromagnetic radiation of wavelength λ,
propagating along the x axis.
• The electric field of the plane-polarized light is confined to
a single plane.
• Ordinary, unpolarized light has electric field components in
all planes.
υ ×λ = c
c = 2.998 ×108 m/s
•υ: frequency (Hz)
•λ: wavelength
•c: the velocity of
radiation in vacuum
Properties of Electromagnetic Radiation
Particle model
• When EM radiation is emitted or absorbed, a
permanent transfer of energy from the emitting object
or to the absorbing medium occurs.
• It’s necessary to treat EM radiation not as a collection
of waves but rather as a stream of discrete particles
called photons or quanta.
• The discovery of the photoelectric effect in the late
nineteenth century.
E = hυ
E = hcυ~
h = 6.626 × 10 −34 J ⋅ s
υ~ = 1 / λ (wave number)
Electromagnetic Spectrum
Example: How much is the energy of CO2
increased per mole when it absorbs IR at 2300
cm-1?
ΔE = h υ = h
c
λ
= hcυ~
= (6.626 × 10 J ⋅ s)(2.998 × 10 m/s)(2300 cm )(100 cm/m)
= 4.6 × 10 J
-34
8
-1
- 20
( 4.6 × 10 J)(6.022 × 10 ) = 28 kJ/mol
- 20
23
E = hcυ~
υ~ = 1 / λ (wave number)
1
A Spectrum of White Light
Line Spectrum
A spectrum produced by a luminous gas or
vapor and appearing as distinct lines
characteristic of the various elements
constituting the gas.
Emission Spectrum
Hydrogen Line Emission Spectrum
The spectrum of bright lines, bands, or
continuous radiation characteristic of and
determined by a specific emitting substance
subjected to a specific kind of excitation.
Ground State
The state of least possible energy in a
physical system, as of elementary particles.
Also called ground level.
Excited State
Being at an energy level higher than the
ground state.
2
Methods of Interaction
Absorption Spectrum
• Light shinning on a sample causes electrons
to be excited from the ground state to an
excited state
• The wavelengths of that energy are
removed from transmitted spectra
M + hν → M *
M * → M + heat
(excited state)
(relaxation)
•Absorption of light increases the energy of a substance.
•Emission of light decreases its energy.
Types of Molecular Transitions
Interactions of Radiation and Matter
Electronic transition – electron between two orbitals
(UV-vis).
hν = Energy Difference of Orbitals
Vibrational transitions – vibrational states associated
with bonds holding molecule.
Rotational transitions – changes in rotational states,
about its center of gravity.
Overall change in Energy with an orbital of a molecule is:
E = Eelectronic + Evibrational + Erotational
Interactions of Radiation and Matter
Single-beam Absorbance Experiment
grating, prism or filter
Irradiance
out
Lamp or laser
Irradiance
in
Vibrational
energy
transferred
Pathlength
Irradiance (P): the energy per unit area in the light beam (W/m2).
Relaxation by
emitting heat
Transmittance (T): the fraction of original light not absorbed by the
sample. T = P/P0
Relaxation by emitting photons
Monochromatic light: consists of “one color” (one wavelength).
Chromophore: the part of a molecule responsible for light absorption
3
Derivation of Beer’s Law
Derivation of Beer’s Law
P
∫
P0
dP
= − ∫ βcdx
P
b
0
After integrate both sides:
dP = − β Pcdx
ln
dP: the change in irradiance
β: a constant of proportionality
c: concentration
dP
∫ = − ∫ βcdx
P
dP
= − βcdx
P
P
b
P0
0
P
P
= 2.303 × log = − βcb
P
P
0
log
Absorbance and Beer’s Law
β
P
=
cb = εcb
P 2.303
0
− log T = A = εcb
Relation between Transmittance and
Absorbance
• Absorbance (A): the amount light absorbed by the
sample is related to transmittance (T):
⎛P ⎞
A = log⎜ 0 ⎟ = − log T
⎝P⎠
• Beer’s law relates the absorbance of a chemical to its
concentration:
⎛P ⎞
A = log⎜ 0 ⎟ = − log T
⎝P⎠
P/Po
1
0.1
0.01
Aλ = ε λ bc
b : the pathlength, typically in cm, and c is the
concentration of the chemical species in M
ε : the molar absorptivity, the unit that tells how
much light is absorbed for a given wavelength. ε
has units of M-1 cm-1
Absorption Methods - Beer’s Law
A = abc = εbc
where a => absorptivity
b => path length
c => concentration
ε => molar absorptivity
0
%T
100
10
1
A
0
1
2
Absorption Methods - Beer’s Law
A = abc = εbc
A
c
• The light being shined on
the sample must be
monochromatic (one color
or wavelength)
• The analyte must not be
participate in a
concentration dependent
equilibrium
4
1.0
1 - 10 mg l
0.8
r = 0.8791
-1
• Real Limitations – high
concentrated solutions,
concentrated electrolyte
solutions (proximity
alters molecular
absorption).
NO 3 -N
0.6
0.4
Spectroscopic Procedure
• Have a spectrometer and cuvette(s)
– Single-beam instrument has one sample holder (swap blank
and sample)
– Double-beam instrument splits light output between two
holders (measure blank and sample)
– A baseline spectrum is a spectrum of a reference solution
(solvent or reagent blank)
0.2
0.0
0
2
4
6
[NO 3-N] (mg l
-1
8
10
)
HNO + H O ←⎯→ H O + NO −
2
2
3
2
• Chemical Limitations –
absorbing species
participate in association
or dissociation reactions,
e.g. weak acids in
concentrated solutions,
complexation.
Spectroscopic Procedure
• Keep the absorbance reading of the sample below 1.
Spectroscopic Procedure
• Try to do an analysis at the λmax
– Sensitivity is greatest at maximum absorbance
– Curve is relatively flat in case the monochromator drifts
and is off by a little in wavelength
– % transmittance is related logarithmically with concentration
(from 1-99% transmittance you can detect ~ 2 orders of
magnitude in analyte concentration)
– Any orders of magnitude greater than that will be detected in
the range of 0-1% T.
λmax.= 620 nm
0.5
550 nm
0.4
• Dilute the solution so that the transmittance reading is
not maxed out in that region (for accuracy)
0.3
510 nm
0.2
Absorbance
Abs
Limitations to Beer’s Law
0.1
0.0
-0.1
-0.2
350
400
450
500
550
600
650
700
Wavelength (nm)
Example: Find the absorbance and transmittance of a
0.0220 M solution with a molar absorptivity of 15.5
M-1 cm-1 in a 2.00 cm pathlength cell
Example: Consider a solution of benzene in hexane
(28.8 mg in 250 mL solution). If the absorbance of
your 1 cm cell is 0.266 at λ=200nm, what is the ε
value for benzene (FW: 78.11)?
Aλ = ε λ bc = (15.5 M -1cm -1 )(2.00 cm)(0.0220 M) = 0.68
log T = − A
T = 10 = 0.21
− 0.68
21% of the irradiated light emerges from the analyte
sample
c=
28.8mg C6H6
250 ml sol’n
1g
1000ml
1000mg 1L
c=[C6H6]=1.321x10-3M
1mol C6H6
78.11 g C6H6
ε=A /cb =A/c
ε=0.266/1.321x10-3
5
Example: A 22.5 mg sample of anthracene
(C14H10, MW=178.23) was dissolved in 100
mL ethanol and diluted by 50% four times.
The absorbance reading of a 1.0 cm cell of this
solution at 266 nm was still 0.93. What is ε?
[C14 H10 ] = (0.0225 g)/(178.22 g/mol) × ⎛⎜ 1 ⎞⎟
0.1 L
ε=
Wavelengths and Color
4
⎝2⎠
= 7.89 × 10 −5 M
A
0.93
=
= 1.2 × 10 4 M -1cm −1
bc (1.0)(7.89 × 10 −5 )
Analysis of Mixtures
MixtureAbs = ε xb[ x] + εY b[Y ] + ......
A1 = ε 1 (λ1 )c1b + ε 2 (λ1 )c 2 b
A2 = ε 1 (λ2 )c1b + ε 2 (λ2 )c 2 b
Isosbestic points
• Good evidence of presence of only 2 species
which interchange between themselves (e.g.
indicator dye with 2 states)
•What are the knowns and
unknowns in the above Eq.?
•Measure Abs at more
wavelengths than there are
components in the mixture.
•More wavelengths increase the
accuracy.
Emission Processes
Absorption vs. Emission Spectra
• Luminescence – emission of light from any
excited state of a molecule. more sensitive
than absorption measurements
– Fluorescence – emission of photon during
transition between states with same spin quantum
#’s (e.g. S1 →S0 )
– Phosphorescence - emission of photon during
transition between states with different spin
quantum #’s (e.g. T1 →S0 )
6
Emission Spectroscopy Experiment
Absorption vs. Emission Spectra
Emission Intensity at Low Concentration
⎛P ⎞
A = log⎜ ⎟ = ε bc
⎝P⎠
Irradiance striking central region : P = P 10 ε
Components of Optical Instruments
0
ex
−
'
0
Additional distance b : P = P 10 ε
'
−
'
2
Single Beam Instruments
ex b1 c
0
ex b 2 c
0
Emission intensity is proportional to the irradiance
absorbed in the central region of the cell : I = k ( P − P )
'
'
'
'
0
Double Beam Instruments
Emission intensity emerging from the cell :
I = I 10 ε
'
−
'
= k P 10
'
0
em b 3 c
−ε ex b1 c
= k ( P − P )10 ε
'
'
−
'
= k ( P 10 ε
(1 − 10
)10
−
'
em b 3 c
0
−ε ex b 2 c
0
ex b1 c
− P 10 ε 10 ε
−
−
ex b1 c
0
ex b 2 c
)10 ε
−
em b 3 c
−ε em b 3 c
(ε b c ln 10) (ε b c ln 10)
−
+ ...
2!
3!
I = kP0 c
∴ At low concentration : k P ε b c ln 10 ⇒
Q10
−ε ex b 2 c
2
= 1 − ε b c ln10 +
ex
2
ex
3
ex
2
2
'
0
ex
2
Instrumentation - Basic Components
Intensity of a Tungsten Filament and a
Deuterium Arc Lamp
(1) Light source
-Tungsten filament lamp (Visible: 320 - 2500 nm); Deuterium
arc lamp (UV: 200-400 nm); Nernst glower, globar (IR region).
7
Instrumentation - Basic Components
(1) Light source
-Tungsten filament lamp (Visible: 320 - 2500 nm); Deuterium
arc lamp (UV: 200-400 nm); Nernst glower, globar (IR region).
(2) Monochromators/Filters: select a narrow band of
wavelengths to pass on to the sample or detector.
-Gratings & Prisms: disperses light into its component
wavelengths
-Filters: filter (remove) wide bands of radiation from a signal;
Colored glass
Instrumentation - Basic Components
Grating vs. Prism
•Grating: a reflective or
transmissive optical
component with a series of
closely ruled lines; can
bend light (diffraction)
•Prism: can bend light
(refraction)
Cells for Spectrophotometry
(1) Light source
-Tungsten filament lamp (Visible: 320 - 2500 nm); Deuterium
arc lamp (UV: 200-400 nm); Nernst glower, globar (IR region).
(2) Monochromators/Filters: select a narrow band of
wavelengths to pass on to the sample or detector.
-Gratings & Prisms: disperses light into its component
wavelengths
-Filters: filter (remove) wide bands of radiation from a signal;
Colored glass
(3) Sample containers (cuvettes or cells)
-Glass, Plastic & Quartz (usually 1 cm); KBr/NaCl (IR)
Instrumentation - Basic Components
Detector Response
(1) Light source
-Tungsten filament lamp (Visible: 320 - 2500 nm); Deuterium arc
lamp (UV: 200-400 nm); Nernst glower, globar (IR region).
(2) Monochromators/Filters: select a narrow band of
wavelengths to pass on to the sample or detector.
-Gratings & Prisms: disperses light into its component wavelengths
-Filters: filter (remove) wide bands of radiation from a signal;
Colored glass
(3) Sample containers (cuvettes or cells)
-Glass, Plastic & Quartz (usually 1 cm); KBr/NaCl (IR)
(4) Detector: produces an electric signal when it is struck by
photons
-Phototubes, Photomultiplier tubes, & Photodiode array
•A function of wavelength of incident light
•The greater the sensitivity, the greater the current of voltage
produced by the detector for a given incident irradiance of
photons.
8