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Introduction to
Analytical Chemistry
CHAPTER 14
SPECTROSCOPIC
METHODS OF ANALYSIS
AND INSTRUMENTS FOR
MEASURING ABSORPTION
Figure 14-1
Figure 14-1 Wave nature of a beam of single-frequency electromagnetic radiation. In (a), a
plane-polarized wave is shown propagating along the x-axis. The electric field oscillates in a
plane perpendicular to the magnetic field. If the radiation were unpolarized, a component
of the electric field would be seen in all planes. In (b), only the electric field oscillations are
shown. The amplitude of the wave is the length of the electric field vector at the wave
maximum, whereas the wavelength is the distance between successive maxima.
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14A-1 Wave Properties
 Radiant Power and Intensity
 The radiant power P in watts (W) is the energy of a beam
that reaches a given area per unit time. The intensity is the
radiant power-per-unit solid angle.
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14A-2 The Particle Nature of Light:
Photons
(14-3)
 where h is Planck’s constant (6.63×10¯³⁴ J s).
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Figure 14-3
Figure 14-3 The regions of the electromagnetic spectrum. Interaction of an analyte with
electromagnetic radiation can result in the types of changes shown. Note that changes in electron
distributions occur in the UV/visible region. The wavenumber, wavelength, frequency, and energy are
characteristics that describe electromagnetic radiation. [From C. N. Banwell, Fundamentals of
Molecular Spectroscopy, 3rd ed. (New York; McGraw-Hill, 1983), p. 7.]
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14B-2 What Do Spectroscopists
Measure?
 Spectroscopists use the interactions of radiation with
matter to obtain information about a sample.
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Figure 14-4
Figure 14-4 Emission or chemiluminescence processes. In (a), the sample is excited by the application of thermal,
electrical, or chemical energy. These processes do not involve radiant energy and are therefore called nonradiative
processes. In the energy-level diagram (b), the dashed lines with upward-pointing arrows symbolize these
nonradiative excitation processes, whereas the solid lines with downward-pointing arrows indicate that the analyte
loses its energy by emission of a photon. In (c), the resulting spectrum is shown as a measurement of the radiant
power emitted PE as a function of wavelength, λ.
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Figure 14-5
Figure 14-5 Absorption methods. Radiation of incident radiant power P0 can be absorbed by the
analyte, resulting in a transmitted beam of lower radiant power P. For absorption to occur, the
energy of the incident beam must correspond to one of the energy differences shown in (b). The
resulting absorption spectrum is shown in (c).
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Figure 14-6
Figure 14-6 Photoluminescence methods (fluorescence and phosphorescence). Fluorescence and phosphoresecence result from
absorption of electromagnetic radiation and then dissipation of the energy by emission of radiation (a). In (b), the absorption can
cause excitation of the analyte to state 1 or state 2. Once excited, the excess energy can be lost by emission of a photon
(luminescence shown as solid line) or by nonradiative processes (dashed lines). The emission occurs over all angles, and the
wavelengths emitted (c) correspond to energy differences between levels. The major distinction between fluorescence and
phosphorescence is the time scale of emission, with fluorescence being prompt emission and phosphorescence being delayed
emission.
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14C-1 The Absorption Law:
Describing the Absorption Process
 The absorption law, also known as the Beer–Lambert
law or just Beer’s law, tells us quantitatively how the
amount of attenuation depends on the concentration
of the absorbing molecules and the pathlength over
which absorption occurs.
 The transmittance T
(14-4)
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Figure 14-7
Figure 14-7 Attenuation of a beam of radiation by an absorbing solution. The larger arrow on the
incident beam signifies a higher radiant power than is transmitted by the solution. The pathlength of
the absorbing solution is b, and the concentration is c.
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14C-1 The Absorption Law:
Describing the Absorption Process
 The absorbance A
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14C-1 The Absorption Law:
Describing the Absorption Process
 Measuring Transmittance and Absorbances
 The power of the beam transmitted through a cell
containing the analyte solution is compared with one that
traverses an identical cell containing only the solvent or a
reagent blank.
(14-5)
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14C-1 The Absorption Law:
Describing the Absorption Process
 Beer’s Law³
(14-7)



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a is a proportionality constant called the absorptivity.
c has the units of grams per liter (g L-¹)
b has the units of centimeters (cm)
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14C-1 The Absorption Law:
Describing the Absorption Process
 Beer’s Law³
 When we express the concentration in Equation 14-7 in
moles per liter and b in centimeters, proportionality
constant,called the molar absorptivity.
(14-8)
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14C-1 The Absorption Law:
Describing the Absorption Process
 Using Beer’s Law
 Beer’s law also applies to solutions containing more
than one kind of absorbing substance.
(14-9)
 where the subscripts refer to absorbing components 1,
2, . . . , n.
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Example 14-1
 A 7.50×10¯⁵ M solution of potassium permanganate
has a transmittance of 36.4% when measured in a 1.05cm cell at a wavelength of 525 nm. Calculate (a) the
absorbance of this solution and (b) the molar
absorptivity of KMnO₄.
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Example 14-1
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14C-2 Limits to Beer’s Law
 Real Limitations to Beer’s Law
 Beer’s law describes the absorption behavior of dilute
solutions.
 At concentrations exceeding about 0.01 M, the average
distances between ions or molecules of the absorbing
species are diminished to the point where each particle
affects the charge distribution, and thus the extent of
absorption.
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14C-2 Limits to Beer’s Law
 When ions are in close proximity, the molar
absorptivity of the analyte can be altered because of
electrostatic interactions.
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14C-2 Limits to Beer’s Law
 Chemical Deviations
 As shown in Example 14-3, deviations from Beer’s law
appear when the absorbing species undergoes
association, dissociation, or reaction with the solvent to
give products that absorb differently from the analyte.
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Example 14-3
 Consider a solution of an indicator with an acid
dissociation constant of 1.42×10¯⁵ and a molar
analytical concentration ctotal . Mass balance requires
that
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Example 14-3
 For all practical purposes the indicator is entirely in the
acid form in 0.1 M HCl; that is, ctotal = [HIn]. Likewise, in
0.1 M NaOH, the indicator is completely in its conjugate
base form, and ctotal = [In¯]. The molar absorptivities
of the indicator species at 430 nm and 570 nm are
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Example 14-3
 Although both species individually obey Beer’s law,
plots of absorbance versus concentration of unbuffered
solutions of the indicator are nonlinear, as shown in
Figure 14-10, because the indicator equilibrium shifts
as its concentration changes. However, if we know the
equilibrium concentrations of HIn and In, we may
calculate the observed absorbances. Thus, for a
solution with ctotal = 2.00 10¯⁵ M and using 1.00 cmcells,
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Example 14-3
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Example 14-3
 Finally, if 1.00-cm cells are used,
 CHALLENGE: Perform calculations to confirm that A430 =
0.596 and A570 = 0.401 for a solution in which the
analytical concentration of HIn is 8.00 × 10¯⁵ M.
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Figure 14-10
Figure 14-10 Chemical deviations from Beer’s
law for unbuffered solutions of the indicator
HIn. The absorbance values were calculated
at various indicator concentrations as shown
in Example 14-3. Note that there are positive
deviations at 430 nm and negative deviations
at 570 nm. At 430 nm, the absorbance is
primarily due to the ionized In form of the
indicator and is in fact proportional to the
fraction ionized. The fraction ionized varies
nonlinearly with total concentration. At lower
total concentrations ([HIn] [In]), the fraction
ionized is larger than at high total
concentrations. Hence, a positive error
occurs. At 570 nm, the absorbance is due
principally to the undissociated acid HIn. The
fraction in this form begins as a low amount
and increases nonlinearly, with the total
concentration giving rise to the negative
deviation shown.
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14C-2 Limits to Beer’s Law
 Instrumental Deviations
 Beer’s law strictly applies only when measurements are
made with monochromatic source radiation. In practice,
polychromatic sources are used in conjunction with a grating
or a filter to isolate a nearly symmetric band of wavelengths
around the wavelength to be employed.
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Figure 14-11
Figure 14-11 The effect of
polychromatic radiation on Beer’s law.
In the absorption spectrum at the top,
the absorptivity of the analyte is seen
to be nearly constant over band A from
the source. Note in the Beer’s law plot
at the bottom that employing band A
gives a linear relationship. In the
spectrum, band B coincides with a
region of the spectrum over which the
absorptivity of the analyte changes.
Note the marked Beer’s law deviation
that results in the lower plot.
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14C-2 Limits to Beer’s Law
 Instrumental Deviations
 Stray radiation, commonly called stray light, is defined
as radiation from the instrument that is outside the
nominal wavelength band chosen.
 When measurements are made in the presence of stray
light, the observed absorbance is given by
 Ps is the radiant power of the stray light.
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Figure 14-12
Figure 14-12 Deviation from Beer’s
law caused by various levels of
stray light. Note that absorbance
begins to level off with
concentration at high stray light
levels. Stray light always limits the
maximum absorbance that can be
obtained because when the
absorbance is high, the radiant
power transmitted through the
sample can become comparable to
or lower than the stray light level.
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14C-4 Molecular Absorption
Transitions
 Three types of energy changes occur when molecules
are excited by ultraviolet,visible, and infrared radiation.
electronic transition
 vibrational transitions
 rotational transitions

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Figure 14-14
Figure 14-14 Types of molecular
vibrations. The plus sign indicates
motion from the page toward the
reader; the minus sign indicates
motion in the opposite direction.
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Figure 14-15
Figure 14-15 Energy-level diagram
showing some of the energy changes
that occur during absorption of
infrared (IR), visible (VIS), and
ultraviolet (UV) radiation. Note that
with some molecules a transition
from E0 to E1 may require UV
radiation instead of visible radiation
shown. With other molecules, the
transition from E0 to E2 may occur
with visible radiation instead of UV
radiation.
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14C-4 Molecular Absorption
Transitions
 Infrared Absorption.
 Infrared radiation is generally not of sufficient energy to
cause electronic transitions but can induce transitions in the
vibrational and rotational states associated with the ground
electronic state of the molecule.
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14C-4 Molecular Absorption
Transitions
 Ultraviolet and Visible Absorption.
 The center arrows in Figure 14-15 suggest that the
molecules under consideration absorb visible radiation of
five wavelengths (λ'1 to λ‘5), thereby promoting electrons to
the five vibrational levels of the excited electronic level E1 .
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Figure 14-16
Figure 14-16 Typical ultraviolet
absorption spectra. The compound is
1,2,4,5-tetrazine. In (a), the spectrum is
shown in the gas phase where many
lines due to electronic, vibrational, and
rotational transitions are seen. In a
nonpolar solvent (b), the electronic
transitions can be observed, but the
vibrational and rotational structure
have been lost. In a polar solvent (c),
the strong intermolecular forces have
caused the electronic peaks to blend
together to give only a single, smooth
absorption peak. (From S. F. Mason, J.
Chem. Soc., 1959, 1265. With
permission.)
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14D Instrument Components
 The first two instrumental configurations, for
absorption and fluorescence,require an external source
of radiation.
 In emission spectroscopy (Figure 14-17c), the sample
itself is the emitter and no external radiation source is
needed.
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Figure 14-17
Figure 14-17 Components of various types of
instruments for optical spectroscopy. In (a), the
arrangement for absorption measurements is shown.
Note that source radiation of the selected wavelength
is sent through the sample and that the transmitted
radiation is measured by the detector/signal
processing/readout unit. With some instruments, the
position of the sample and wavelength selector is
reversed. In (b), the configuration for fluorescence
measurements is shown. Here, two wavelength
selectors are needed to select the excitation and the
emission wavelengths. The selected source radiation
is incident on the sample and the radiation emitted is
measured, usually at right angles to avoid scattering.
In (c), the configuration for emission spectroscopy is
shown. Here, a source of thermal energy, such as a
flame, produces an analyte vapor that emits radiation
that is isolated by the wavelength selector and
converted to an electrical signal by the detector.
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14D-1 Selecting Optical Materials
 Figure 14-18 shows the usable wavelength range for
several optical materials that find use in the UV, visible,
and IR regions of the spectrum.
 In the UV region, at wavelengths shorter than about
380 nm, glass begins to absorb and fused silica or
quartz must be substituted. Also, glass, quartz, and
fused silica all absorb in the IR region at wavelengths
longer than about 2.5 m. Hence, optical elements for IR
spectrometry are typically made from halide salts.
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Figure 14-18
Figure 14-18 Transmittance ranges for various optical materials. Simple glasses are fine in the visible
region, whereas fused silica or quartz is necessary in the UV region (380 nm). Halide salts (KBr, NaCl,
AgCl) are often used in the IR, but they have the disadvantages of being expensive and being
somewhat water soluble.
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14D-2 The Source of It All
 Spectroscopic sources are of two types: continuum
sources, and line sources.
 Sources can also be classified as continuous sources,
which emit radiation continuously with time, or pulsed
sources, which emit radiation in bursts.
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Table 14-2
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14D-2 The Source of It All
 Other UV/Visible Sources
 line sources are also important for use in the UV/visible
region.
 Low-pressure mercury arc lamps
 Hollow cathode lamps
 Lasers
 Tunable dye lasers can be scanned over wavelength ranges
of several hundred nanometers when more than one dye is
used.
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14D-2 The Source of It All
 Continuum Sources in the IR Region
 Globar source
 A Nernst glower
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14D-3 Selecting the Desired
Wavelength
 Many instruments employ a monochromator or filter to
isolate the desired wavelength band
 Monochromators generally employ a diffraction grating
to disperse the radiation into its component
wavelengths as shown in Figure 14-22a.
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14D-3 Selecting the Desired
Wavelength
 By rotating the grating, different wavelengths can be
made to pass through an exit slit.
 The wavelength range passed by a
monochromator,called the spectral bandpass or
effective bandwidth.
 Polychromator contains multiple exit slits and multiple
detectors that allow many discrete wavelengths to be
measured simultaneously.
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14D-3 Selecting the Desired
Wavelength
 Filters used for absorption measurements are typically
interference filters. These filters transmit radiation over
a bandwidth of 5 to 20 nm. Radiation outside the
transmitted bandpass is removed by destructive
interference.
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Figure 14-22
Figure 14-22 Types of
monochromators: (a) grating
monochromator and (b) prism
monochromator. The
monochromator design in (a) is a
Czerny–Turner design, whereas the
prism monochromator in (b) is a
Bunsen design. In both cases, λ1> λ2 .
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14D-4 Detecting and Measuring
Radiant Energy
 The term transducer is used to indicate the type of
detector that converts quantities.
 into such electrical signals that can be subsequently
amplified, manipulated, and finally converted into
numbers proportional to the magnitude of the original
quantity.
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14D-4 Detecting and Measuring
Radiant Energy
 Types of Transducers
 All photon detectors are based on the interaction of
radiation with a reactive surface to produce electrons (
photoemission) or to promote electrons to energy states in
which they can conduct electricity (photoconduction).
 Only UV, visible, and near-IR radiation possess enough
energy to cause photoemission to occur.
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14D-4 Detecting and Measuring
Radiant Energy
 Types of Transducers
 Photoconductors can be used in the near-, mid-, and far-IR
regions of the spectrum.
 we detect IR radiation by measuring the temperature rise of
a blackened material located in the path of the beam or by
measuring the increase in electrical conductivity of a
photoconducting material when it absorbs IR radiation.
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Table 14-3
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Figure 14-23
 Figure 14-23 A phototube and accompanying circuit. The photocurrent
induced by the radiation causes a voltage across the measuring resistor; this
voltage is then amplified and measured.
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Figure 14-24
Figure 14-24 Diagram of a photomultiplier tube:
(a) pictorial view, (b) cross-sectional view, (c)
electrical diagram illustrating dynode polarization
and photocurrent measurement. Radiation
striking the photosensitive cathode (b) gives rise
to photoelectrons by the photoelectric effect.
Dynode D1 is held at a positive voltage with
respect to the photocathode.
Electrons emitted by the cathode are attracted to
the first dynode and accelerated in the field.
Each electron striking dynode D1 thus gives rise
to 2 to 4 secondary electrons. These secondary
electrons are attracted to dynode D2, which is
again positive with respect to dynode D1. The
resulting amplification at the anode can be 106
or greater. The exact amplification
factor depends on the number of dynodes and
the voltage difference between each dynode.
This automatic internal amplification is one of the
major advantages of photomultiplier tubes. With
modern instrumentation, the arrival of individual
photocurrent pulses can be detected and
counted instead of being measured as an
average current. This technique, called photon
counting, is advantageous at very low light levels.
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14D-4 Detecting and Measuring
Radiant Energy
 Photoconductive Cells.
 Photoconductive cells are transducers that consist of a
thin film of a semiconductor material
 Deposited often on a nonconducting glass surface and
sealed in an evacuated envelope. Absorption of
radiation by these materials promotes nonconducting
valence electrons to a higher energy state, which
decreases the electrical resistance of the
semiconductor
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14D-4 Detecting and Measuring
Radiant Energy
 Silicon Photodiodes and Photodiode Arrays
 Photodiodes are semiconductor pn junction devices
that respond to incident light by forming electron–hole
pairs
 Silicon photodiode detectors respond extremely
rapidly, usually in nanoseconds. They are more
sensitive than vacuum phototubes, but considerably
less sensitive than photomultiplier tubes.
 Silicon photodiodes can also be fabricated in arrays of
1000 or more detectors
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14D-4 Detecting and Measuring
Radiant Energy
 Charge-Transfer Devices
 Charge-coupled devices (CCDs) and charge-injection
devices (CIDs) are appearing in ever-increasing numbers
in modern spectroscopic instruments.
 They are the solid state equivalent of the photographic
plate.In both the CCD and the CID, photogenerated
charges are collected and then measured.
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14E Uv/Visible Photometers and
Spectrophotometers
 A spectrometer is a spectroscopic instrument that
employs a monochromator or polychromator in
conjunction with a transducer to convert the radiant
intensities into electrical signals. Spectrophotometers
are spectrometers that allow measurement of the ratio
of the radiant powers of two beams, a requirement to
measure absorbance (recall from Equation14-6 that
A = log P0/P ≈ log Psoivent/Psolution)
 Photometers employ a filter for wavelength selection in
conjunction with a suitable radiation transducer.
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Figure 14-26
Figure 14-26 The Spectronic 20
spectrophotometer. A photograph of
the instrument is shown in (a), and the
optical diagram is seen in (b). (Courtesy
of Spectronic Instruments, Inc., 820
Linden Avenue, Rochester, NY 14625).
Radiation from the tungsten filament
source passes through an entrance slit
into the monochromator. A reflection
grating diffracts the radiation, and the
selected wavelength band passes
through the exit slit into the sample
chamber. A phototube converts the
light intensity into a related electrical
signal that is amplified and displayed on
an analog meter.
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Figure 14-27
Figure 14-27 Instrumental designs for
UV/visible photometers or
spectrophotometers. In (a), a single-beam
instrument is shown. Radiation from the filter
or monochromator passes through either the
reference cell or the sample cell before striking
the photodetector. In (b), a double-beam-inspace instrument is shown. Here, radiation
from the filter or monochromator is split into
two beams that simultaneously pass through
the reference and sample cells before striking
two matched photodetectors. In the doublebeam-in-time instrument (c), the beam is
alternately sent through reference and sample
cells before striking a single photodetector.
Only a matter of milliseconds separate the
beams as they pass through the two cells.
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14E-3 Multichannel Instruments
 With multichannel systems, the dispersive system is a
grating spectrograph placed after the sample or
reference cell. The photodiode array is placed in the
focal plane of the spectrograph.
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Figure 14-28
Figure 14-28 Diagram of a
multichannel spectrometer
based on a grating spectrograph
with a photodiode array
detector.
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14F-1 Dispersive Infrared
Instruments
 Older IR instruments were invariably dispersive double-
beam designs.
 Infrared radiation, in contrast, is not sufficiently
energetic to bring about photodecomposition.
 Therefore, the cell compartment is usually located
between the source and the monochromator in an IR
instrument.
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14F-2 Fourier Transform
Instruments
 Fourier transform IR instruments contain no dispersing
element, and all wavelengths are detected and
measured simultaneously.
 An interferometer is used to produce interference
patterns that contain the infrared spectral information.
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14F-2 Fourier Transform
Instruments
 The major advantages of FTIR instruments over
dispersive spectrometers include better speed and
sensitivity, better light-gathering power, more accurate
wavelength calibration, simpler mechanical design, and
the virtual elimination of the contribution from stray
light and IR emission.
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THE END
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