Instrumental Methods are more sensitive and selective but
less precise (on the order of 1 to 5% or so)
They are also more expensive
Amount of analyte
Degree of Precision and accuracy
Sensitivity, selectivity and cost
4Dr. Sajjad Ullah, ICS-UoP
SpectroscopyisthestudyofinteractionofEMR withmatter.
Spectroscopicmethodsofanalysisuse measurementsoftheamountof
EMR thatisabsorbed, emittedorscatteredbya sampletoperforman
assay.
EMR isa formofenergy
EMR possessthepropertiesofbothdiscreteparticles(photons) and
wave(Dual nature, E = hn)
5Dr. Sajjad Ullah, ICS-UoP
C= Light travelling speed:
in a vacuum: c=2.998 x 10
8
m s
-1
(n=1 exactly, in air n=1.0002926)
in other media: c/n(n= refractive index, generally >1)
Therefore:
Energy is inversely proportionalto wavelength
but proportionalto frequency or wavenumber
The relationship between energy (E) and frequency (n) :
E= hn= hc/l= hc/nl
h = Planck’s constant (6.626 x 10
-34
J s)
n= frequency(most common units = cm
-1
), n = 1/T
n= refractive index = c/V
Light is energy in the form of electromagnetic field
Properties of light/EMR (photon)
Wavelength(l): Crest-to-crest distance between waves
Frequency (n): Number of complete oscillations that the wave makes each second
units: number of oscillations/sec or s
-1
or Hertz |(Hz)
6
V= ln = c/n
Where V= velocity
Dr. Sajjad Ullah, ICS-UoP
70.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
1.62
1.63
l m)
n
(
SiO
2
)
CauchyEquation
SiO
2
Dispersion= slope=
Refractive index is different for diffrent Wavelengths
Dr. Sajjad Ullah, ICS-UoP
8
http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html#c2
SpectralRegions
Dr. Sajjad Ullah, ICS-UoP
R.M. Christie, ColourChemistry, Royal SocietyofChemistry, 2001, page. 14
Dr. Sajjad Ullah, ICS-UoP 14
Green
Red
Blue
Colourand Electronic Spectra
Dr. Sajjad Ullah, ICS-UoP 15
E
1: Energy ofthefundamental electronicstate
E
2: Energy oftheexcitedelectronicstate
Refrence: C. N. Banwell, thefundamental ofmolecular spectrocopy, p-13
If the same
molecule both
Emits and absorbs,
how We get signal
of absorption
Only?
Dr. Sajjad Ullah, ICS-UoP 16
17
Pavia, Lampman, Criz, Vyvyan, Introduction to Spectroscopy. p383
Dr. Sajjad Ullah, ICS-UoP
18https://www.youtube.com/watch?v=wxrAELeXlek
Dr. SajjadUllah, ICS-UoP
19
Quantitaiveanalysisbyabsorptionspectroscopy
(L.mol
-1
.cm
-1
)
Straight Line Equation: Y = mX+ C
or X= Y-C/m
X= Concentration
Y= Absorbance
m= Slope
C= intercept
Dr. SajjadUllah, ICS-UoP
20
Electronsinvolvedin electronicTransitions
4-Π-bondingē
s:
ē
sinvolvedin Π-bonding, presentin unsaturatedHCs.
Absorbin nearUV orVisibleregion
1-ClosedShell elctron:
Theseare innershellē
s, notinolvedin bonding.
RequirehigherenergyX-raysfor theirexcitation
2-Single bonded(σ-electons):
single-bondedē
spresente in satutratedHCs.
Absorbin FarUV region(10-200 nm)
3-non-bondingē
s:
Lonepairofē
snotinolvedbonding, usuallypresent
onheteroatoms(Ö, S
:
, N
:
and X
:
).
They absorb in near UV-region, andvisbleregion(if
the heteroatom is presente in unsaturated HCs.
Unfortunatelywaterandmostsolventsabsorbin thisregion
CH
4
NH
3
Dr. Sajjad Ullah, ICS-UoP
21Dr. Sajjad Ullah, ICS-UoP
22
Pavia, Lampman, Criz, Vyvyan, Introduction to Spectroscopy. p393
ketone
Methylamine
Dr. SajjadUllah, ICS-UoP
23
n →σ* (l= 150 -250 nm)
Saturated compounds containing Heteroatos(O, S, N, X),
Examples: CH
3OH (183 nm), CH
3I (258 nm), CH
3NH
2(213 nm)
σ→σ* (lbelow 150 nm)
Saturated HCs, High energy required, trasitionsoccur vacuum UV range
Examples: CH
4: l= 125 nm, C
2H
6= 135 nm
N
2absorbs below 160 nm
O
2 absorbs below 200 nm
→* (near UV; visible, Generally 160-190 nm)
Unsaturated compounds, double and triple bonds and benzene rings, large
Ɛ values (1000 -15000 L.mol
-1
cm
-1
), their l
maxdepends on substitutents
Examples: Ethylene 171 nm, butadiene (conjugated system) 217 nm
R-Cl (169 nm) <R-Br< R-I (258 nm)
n →* (near UV and Vis region), ocuurat lower E than →*
Unsaturated compounds with Heteroatoms, aldehydes, ketones, -C≡N, NO
2
Ɛ =10 -100 L.mol
-1
cm
-1
Examples: acetone 277 nm, nitrobutene665 nm
Dr. SajjadUllah, ICS-UoP
24
n →σ* at 150 nm has
not been shown
Ɛ =15
L.mol/cm
Ɛ =900 L/mol.cm
Dr. SajjadUllah, ICS-UoP
25
UV spectrum of acetone showing the π → π∗and n → π∗transitions
n →σ* at 150 nm has
not been shown
Ɛ =15 L.mol/cm
Ɛ =900 L/mol.cm
Dr. Sajjad Ullah, ICS-UoP
26
Pavia, Lampman, Criz, Vyvyan, Introduction to Spectroscopy. p393
Dr. Sajjad Ullah, ICS-UoP
27
Pavia, Lampman, Criz, Vyvyan, Introduction to Spectroscopy. p393
Dr. Sajjad Ullah, ICS-UoP
28Dr. Sajjad Ullah, ICS-UoP
29
Selection Rules for Electronic Trnsitions
For any electronic transition to occur, △E= difference b/w HOMO and LUMO
However, even under such conditions, absorption of energy may not be observed
or observed with low intensity. Why?
Becausetherearecertainrequirementssummarizedin
quantum-mechanicalselectionrulesthatmustbe
satisfiedifatransitionistooccurwithhigher
probability
AllowedTranstionsaretheoneswhichhavehigh
probabilitytotakeplace
ForbiddenTranstionsaretransitionsoflowprobability
Theoreticallyalltransitionsare
possiblebutpracticallyonly
certaintransitionsareofhigh
intensity
Dr. Sajjad Ullah, ICS-UoP
30
Selection Rules for Electronic Trnsitions
1-Spin Multiplicity Rule: △S= 0
2-LaporteRule: △l= ±1, △m= 0,±1
3-Simultaneous excitation of more than one e is forbidden
Such transition that obey these rules occur with high probability
and are called allowed transition
Dr. Sajjad Ullah, ICS-UoP
31
1-Spin Multiplicity Rule: △S= 0
“ the promoted electron be promoted without a change in its spin orientation”.
Ground state
(singlet)
(triplet)(singlet)
Two possible excited states
2S+1= 1 (singlet)
2S + 1= 3 (triplet)
(allowed) (forbidden)
Singlet-to-singlet transition are allowed
Singlet-to-triplet transitonsare forbidden
Dr. Sajjad Ullah, ICS-UoP
32
Thustransitions are forbidden forΔl=0
(i.e, between like atomic orbitals such as s-s, p-p, d-d, f-f)
2-LaporteRule: △l= ±1, △m= 0,±1
“transitions from symmetrical to symmetrical are forbiddenwhile
transitions from symmetrical to asymmetrical are allowed”.
Thisruleisbasedonsymmetryoftheinitialandfinalstates.whenEMRis
absorbed,electricalinworkdoneanddipolemomentchanges.Ifthedistribution
ofe
-
beforeandafterabsorptionisthesame,thetransitionisforbidden.Onthe
otherhand,ifthealteredelectronicdistributionisasymmetricaltotheoriginal
electrondistributions,achangeindipolemomentisobservedandtheTransitions
areallowed.
l = orbital quantum number
m = magnetic quantum number
Dr. Sajjad Ullah, ICS-UoP
33
https://www.youtube.com/watch?v=hWo2b -i6UiE
Dr. SajjadUllah, ICS-UoP
34
Simultaneous excitation rule
“Simultaneous excitation of more than one e is forbidden”.
Ground state
(singlet)
(allowed)(forbidden)
Two possible excited states
Only one e
-
can be excited at a time!
Dr. Sajjad Ullah, ICS-UoP
35
Allowed and Forbidden Trasitions
Transition type
Approximate ɛ
Spin forbidden, Laporteforbidden 0.1
Spin allowed, Laporteforbidden 10
Spin allowed, Laporteallowed (charge transfer) 10,000
Thus the intensity of absorption can be expresses in terms of molar absorptivity.
A transition of unit probability will give ɛ= 10
5
(high intensity allowed transition, e.g.; π-π*).
Transitions with ɛ <10
3
are forbidden (e.g., n-π* have ɛ~100)
Spin forbidden, Laporteallowed 10
-
5 to 1
Dr. Sajjad Ullah, ICS-UoP
Instrumentation of UV-Visible
Spectroscopy
CourseInstructor: Dr. Sajjad Ullah
Part-II
Instrumentation of Spectroscopy
Mostofthespectroscopicinstrumentsinthe
UV/visibleandIRregionsaremadeupoffive
components,
1.a stable sourceof radiant energy;
2.a wavelength selector that isolates a limited
region of the spectrum for measurement;
3.one or more sample containers/cells;
4.a radiation detector, which converts radiant
energy to a measurable electrical signal;
5.a signal processing and readout unit.
38
Diagaram of Istrument used for absorption measurements
Recommended: https://www.youtube.com/watch?v=pxC6F7bK8CU
Source: R. D. Braun, Introduction to instrumental analysis, 1987, p 141
Aspectrophotometerisan
instrumentthatresolves
polychromaticradiationinto
differentλsandmeasure
absorbanceataspecificλ
absorption measurements
fluorescence measurements
emission spectroscopy
excitationλ
emissionλ
Douglas A. Skoog, F. James Holler, Stanley R. Crouch Principles of Instrumental Analysis sixth
edition 2006, p-165
The source of EMR is chosen according to the spectral range to be studied
Douglas A. Skoog, F. James Holler, Stanley R. Crouch Principles of Instrumental Analysis , sixth
edition 2006, p-167
The source of EMR is chosen according to the spectral range to be studied
Continuum Sources in the UV/Visible Region
Tungstenfilamentlamp:
Incandescent;
λrange:320to2500nm.
Temperatureofoperation=2900K(usefulrangeofλ350to2200nm.
Theλofmaximumemissionistemperature(orfilamentvoltage)dependent:higher
Tleadstoashifttoshorterλregion(butalsoshorterlife-timeduetosublimation
ofWfromfilament).
Tungsten/halogenlamps(quartz/halogenlamps)
containasmallamountofiodineorbrominewithinthequartzenvelopethat
housesthefilament.Quartzallowsthefilamenttobeoperatedatatemperature
(3500K),sohigherintensitiesandaccesstoUVregion(extendedλrange=240to
2500nm).LongerlifetimeasthesublimeWreactswithI
2toformWI
2which
redepositandthendecomposeonthefilamentstoleavetheWbackonthefilament
Deuterium/Hydrogenlamps(D
2/H
2lamps)
ContinuumradiationintheUVregion
Make-up:cylindricaltube,containingdeuteriumatlowpressure,
withaquartzwindow(UVTransparent)
Electricalexcitationapplyingabout40Vbetweenaheated
oxide-coatedelectrodeandametalelectrode.
H
2 + E
eH
2*
H
2* Ὴ+ H`
`+hυ
E
e= E
H2* = E
Ὴ+ E
H`+hυ
ThesumofE
ῊandE
H`canvaryfromzerotoE
H2*
andsodoestheenergyofphoton(hυ),thuscontinuous
emission(λ=160nmtoabout375nm)
Lifetime:2000hours
http://www.photron.com.au/.assets/brochures/deuterium_lamp.pdf
Continuum Sources in the IR region
ThecontinuumsourcesforIRradiationare
normallyheatedinertsolids.AGlobarsource
consistsofasiliconcarbiderod.Infrared
radiationisemittedwhentheGlobarisheatedto
about1500
o
Cbythepassageofelectricity.
ANernstGlowerisacylinderofzirconiumand
yttriumoxideswhichemitsIRradiationwhen
heatedtoahightemperaturebyanelectric
current.Electricallyheatedspiralsofnichrome
wirealsoserveasinexpensiveIRsources.
High
Pressure
Mercury
Lamp
Mercury vapor lamps
Mercury vapor lamps are probably the
most common and emit intense light
at 253.7 nm (and certain other
wavelengths). Because of the limited
emission spectra of the lamp wavelengths
are not adjustable.
Becauseoftheintensityofthe
radiation,fixedwavelengthdetectors
canbeupto20timesmoresensitive
thanvariablewavelength
detectors.
49
Douglas A. Skoogand James J. Leary, Principles of Instrumental Analysis,
Saunders College Publishing, Fort Worth, 1992.
Hollow Cathode Discharge Tube
Apply ~300 V across
electrodes.
Ar
+
or Ne
+
travel toward the
cathode.
If potential is high enough
cationswill sputter metal off
the electrode.
Metal emits photons at
characteristic atomic lines as
the metal returns to the
ground state.
Effective bandwidth-the width of the band of
transmitted radiation in λunits at half peak
height.
For monochormators EBW = few 10
th
of a nm
For absorption Filter EBW = 200 nm or more
Transmittance at nominal λ
nominal λ
Wavelength Selectors
Filter (discontinuous)
Monochromators (continuous)
Absorption
filter
Interference
filters
1-sharp-cut off
short λ-selectors
(orange filter)
2-sharp-cut off
long λ-selectors
(Blue-green filters)
3-Band pass filters
Prism
Monomoch.
Grating
Monomoch.
Filtersaresimple,rugged,cheapbutcannotbe
usedforλscanning
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Electronic_Spectroscopy/Electronic_Spectroscopy%3A_Application
http://micro.magnet.fsu.edu/primer/java/filters/absorption/index.html
Filters
Filterspreventpassageofradiationatallλ
sexceptinafixedλregion
AbsorptionFilters
Absorption filters limit radiation by absorbing certain portions of thespectra.
Usefulfor visibleregion
They are made primarily from colored filter glass or dyes suspended in
gelatin and sandwiched between two glass plates
Effective bandwidth =30‒250 nm
Advantages: simplicity, ruggedness, low cost.
Disadvanatage: Theycannotbeusedfor λscanning(isolateonebandofλ
sonly)
Types:
1-Cut-off filters
2-Band pass filters
Band Pass orCombination Filters
AbandpassfilterisconstructedbycombiningspectrallyoverlapingGreenand
Orangecut-offfilters.
Radiationistransmittedthroughthecombination(bandpass)onlyinthe
spectralregionwhichcanbetransmittedbybothfilters
Maximum%T=25%ofincidentradiation
Interferance Filters
2d = m λ
2d n = m λ
λ=2d n/ m
n = ref.index
d =1/2, 1. 3/2 ofλ
(m = 1,2,3)
White radiation
The central wavelength of the transmitted band is controlled by
areful construction of the filter with a proper d-value
Comparison of bandwidths of interference and absorption filter
λ
2 < λ
1
Refraction occurs at both faces of the prism and radiation is thus dispersed
Dispersed radiation is focussed onto a curved surface containing exit slit
Radiation of desired wavelength can be caused to pass the exit slit by rotataion of the prism
Refractive index (n) of the prism materials depends on λ. As λincreases,ndecreases
Refracation depends on nand ndepends on λ; shorter λ, more refraction
Used in UV, visible and IR region
dQ/dn
Geometriccomponente
dn/dl
Dispersion
depends on Prism
material,
(See next slide)
depends on Prism
geometry,
e.g., apex angle (α)
and B/b ratio
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley-VCH Verlag GmbH,
Weinheim, Germany, 1998, vol. 1.
Dispersion = slope = dn/dλ
Prism material
Glass = visible region
Quartz = UV region
NaCl, KBr, CSI = IR region
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley-VCH Verlag GmbH,
Weinheim, Germany, 1998, vol. 1.
Dispersion: Refractive index-wavelength curves
The dispersion of the prism material
depends on the slope of the refractive
index vs wavelength curve:
Grating monochromator
Byrotatingthegrating,differentwavelengthscanbemadetopassthroughanexitslit.Theoutput
wavelengthofamonochromatoristhuscontinuouslyvariableoveraconsiderablespectralrange.
Thewavelengthrangepassedbyamonochromator,calledthespectralbandpassoreffective
bandwidth,canbelessthan1nmformoderatelyexpensiveinstrumentstograterthan20nmfor
inexpensivesystems.
The output of a grating monochrmomator
λ
2 < λ
1
Path Diference = CA-BD = nλ
Constructiveinterferanceoccurswhenthediffreneceinthedistancethatis
travelledbythediffractedradiationfromeachsurfaceofthegroovetothe
wavefrontisanintegralnumberofwavelength:
The Grating Equation
R. D. Braun, Introductiontoinstrumental analysis, 1987, p 166-169
The in-phase radiation can be foucussed at the exit slit using lennese
300-2000 groves/mm (UV-Vis)
10-200 groves/mm (IR)
The Grating Equation
Path Diference = CA-BD = nλ(1)
r +BDC + CDA = 90°(2)
i + r +BDC = 90° (3)
Solving equation 3 for BDC and
substiuting its value in equation 2 gives:
i = CDA (4)
Furthermore, it can be shown that
sin CDA= Sin i = CA/d
CA = d sin i (5)
Similarly,
negativesignisusedasr(refelectedangle)is
ontheoppositesideofthenormal
Puttin 5 and 6 in equation 1:
d sin i –(-d sin r) = nλ
d (sin i + sin r) = nλ
BD=-dsinr(6)
It is the ability of a monochromator to seprate adjacente wavelengths
For example, If a monochormator seprates two adjacente peaks at 207.3 and 215.1 nm
It will have a resolution:
R = λ/Δλ λ= mean wavelength
R = 211.2/7.8 = 27
What resolution of a monochrmoator is required to seprate Na lines 589.0 and 589.5nm?
R = 589.25/0.5 = 1178.5
Resolution (R) of a monochromator
Detecting and Measuring Radiant Energy
Toobtainspectroscopicinformation,theradiantpowertransmitted,fluorescedor
emittedmustbedetectedinsomemannerandconvertedintoameasurable
quantity.
Adetector(alsocalledtransducer)isadevicethatindicatestheexistenceofsome
physicalphenomenon.
Thetermtransducerisatypeofdetectorthatconvertsvarioustypesofphysical
andchemicalproperties(e.g.,lightintensity,pH,mass,andtemperature)into
electricalsignals(voltage,charge,current)thatcanbesubsequentlyamplified,
manipulated,andfinallyconvertedintonumbersproportionaltothemagnitude
oftheoriginalsignal.
Properties of Radiation Transducers
HighSensitivity: Respondsrapidlytolowlevelsofradiantenergyovera
broadwavelengthrange.
LinearResponse:Theelectricalsignalproducedbythetransducerbe
directlyproportionaltotheradiantpowerPofthebeam
G=KP+K’
Lowbackgroundnotice:Producesanelectricalsignalthatiseasilyamplifies
andhasalowelectricalnoiselevel(K’~0)
G=electricalresponseofthedetector
inunitsofcurrent,voltage,orcharge.
K=proportionalityconstantthat
measuresthesensitivityofthedetector
intermsofelectricalresponseperunit
ofradiantpowerinput.
K’=Asmallconstantresponseknown
asadarkcurrent,evenwhenno
radiationstrikestheirsurfaces.K’=0
as instrumentautomatically
compensatebyusingacountersignal
sothatG=KP
P= k G
P
0
= k G
0
(for sample solution)
(for solvent or blank)
A= log P
0
/ P= log kG/kG
0
A= log G
0
/G
Thus we measure absorbance in terms of
electrical signal
Photomultiplier Detector
•The type is commonly used especially for low
radiant powers.
•The detector consists of a photoemissive cathode
(coated with cesium oxide) coupled with a series
of electron-multiplying dynode stages.
•The primary electrons ejected from the photo-
cathode are accelerated by an electric field so as to
strike onto the first dynode and then the e emitted
from 1
st
dynodes are directed onto the 2
nd
dynodes
and so on.
•Amplification = n
d
where d is the number of dynodes and n is the
no of electrode emitted per dynode. Usually 10
6
to10
7
e are emitted per photon
Photomultiplier Detector
Photovoltaic or Barrier Layer cell
Barrier Layer/Photovoltaic Detector
•This device measures the intensity of photons by means of the voltage
developed across the semiconductor layer.
•Electrons, ejected by photons from the semiconductor, are collected by
the silver layer.
•The potential depends on the number of photons hitting the detector.
•Mostly used in the visible region with maximum sensitivity at 550 nm
•Advantage: Useful for simple portable low cost filter instruments,
requires no external power supply, provides readily measured response
at high intensity of EMR
•Disadvantages includes difficulty of amplification of output due to
low internal resistance, low sensitivity at low illumination intensity
and fall off of response upon prolong illumination.
Silicon photodiodes
•They consists of reverse biased pnjunction formed
on a silicon chip.
•The reverse bias creates a depletion layer that
reduces the conductance of the junction to nearly
zero.
•If radiation is allowed to fall on chip, holes and
electrons are formed braking the junction.
•Produces a current that is proportional to radiant
power
•More sensitive then vacuum tube but less sensitive
than photomultiplier tubes
Silicon photodiodes
Heat responding detectors
•In IR region photons are lack the energy to
cause photoemission of electrons. Thus thermal
detector are employed in IR region
•The radiation impinges upon are absorbed by a
blackbody, and rise in temperature is measured.
•These includes
•Thermocouples, Bolometer, Pyroelectric
detectors
Diode Array Detectors
The photo diode array detector passes a wide spectrum of light through
the sample. The spectrum of light is directed to an array of photosensitive
diodes. Each diode can measure a different wavelength which allows for
the monitoring of many wavelengths at once.
-Peak Purity
-Quantify a peak with an
interfering peak
Compound Identification
Monitor compounds with
different UV max.
83
Photoconductivity Detectors
•Most sensitive detector for near IR region. It can be used up to far IR
region by cooling to suppress the noise arising from thermal induced
energies. The resistance decrease when thy absorb radiation.
•A crystalline semi conductor are formed from sulfides some metals
like Pb, Cd, gallium and indium
•Absorption of radiation by this material promotes there bounded
electrons in to an energy state in which they are free to conduct
electrical current. The resulting change in conductivity can then be
measured with a circuit.
•Lead sulfide is the most widely used photoconductive material
Signal Processor and Readout
•The signal processing include amplification of the
electrical signal. Alteration of signal from dc to ac etc.
•They are also called to perform mathematical
operation on signal as differentiation, integration or
conversion to a logarithm.
•Read out unit convert electrical signal to readable
form.
•Read out devices include digital meters, scales of
potentiometers, recorders and cathode ray tubes
•It also include fiber optics or light pipes to flow the
light from one part to another.
Single and Double Beam Spectrometer
•Single-Beam: There is only one light beam or optical path
from the source through to the detector.
•Double-Beam: The light from the source, after passing
through the monochromator, is split into two separate
beams-one for the sample and the other for the reference.
16/9/2006 8:28 Deokate U.A. 87
FIGURE 6-19 Emission spectrum of a brine sample obtained with
an oxyhydrogen flame. The spectrum consists of the supenmposed
line, band, and continuum spectra of the constituents of the sample.
The characteristic wavelengths of the species contributing to the
spectrum are listed beside each feature. (R.Hermann and C. T" J
Alkemade, Chemical Analysis. by Flame photormetry, 2nd ed., p.
484. New York: Interscience, 1979.)
Douglas A. Skoog, F. James Holler, Stanley R. Crouch Principles of Instrumental Analysis sixth
edition 2006, p-150-155
FIGURE6-21Energy-leveldiagramsfor(a)asodium
atomshowingthesourceofalinespectrumand(b)a
simplemoleculeshowingthesourceofabandspectrum.
Douglas A. Skoog, F. James Holler, Stanley R. Crouch Principles of
Instrumental Analysis sixth edition 2006, p-152