Download - CHAPTER 6 Complete
-
7/27/2019 CHAPTER 6 Complete
1/31
CHAPTER 6INTRODUCTION TO
SPECTROPHOTOMETRIC METHODS
Interaction of Radiation With
Matter
Add to your notes of Chapter 1
Analytical sensitivity=m/ss
Homework Problems 1-9, 1-10
Challenge 1-12
-
7/27/2019 CHAPTER 6 Complete
2/31
TOPICS
General Properties of Light
Wave Properties of of ElectromagneticRadiation
Quantum-Mechanical Properties ofRadiation
Quantitative Aspects of
Spectrophotochemical Measurements
A. GENERAL PROPERTIES OF ER
ER can be transmitted through vacuum
The behavior/ properties ofelectromagnetic radiations can be fullyexplained only by its dual nature as awave and a particle
-
7/27/2019 CHAPTER 6 Complete
3/31
B. Wave Properties of ER
Beating/oscillating (sinusoidal) electric andmagnetic fields
Magnetic and Electrical Fields are mutuallyperpendicular and perpendicular to thedirection of propagation
Simplified Picture of a Beam of ER
-Plane polarized-Monochromatic (Single Frequency)-Zero phase angle at time = 0
-
7/27/2019 CHAPTER 6 Complete
4/31
B-1 Wave Characteristics Amplitude (A): length of electric vector at the maximum in the wave
Wavelength (): linear distance between any two equivalent pointson successive waves/ distance traveled in one cycle. Period (p): time in seconds required to complete one cycle (time for
passage of successive maxima or minima through a fixed point inspace)
Frequency() = 1/p: number of oscillations of the field per second/number of cycles per unit time. (hertz, Hz = s-1)= 1/p
Velocity of propagation (v) = vi = i x In vacuum (independent of wavelength)
c = x = 2.99792 x 108 ms-1~ 3.00 x 108 ms-1 In medium containing matter: slower due to interactions between
electromagnetic field and electrons in matter In Air (0.03 % less than in vaccum)
181000.3
= mscvair
Effect of matter on Velocity and Wavelength
-
7/27/2019 CHAPTER 6 Complete
5/31
Wave number (cm-1)
k depends on medium
Power of radiation (P): Energy of beam per secondon given area.
Intensity (I) is the power per unit solid angle.
Solid angle: angle formed at a vertex of a cone.
P and I are proportional to the square of the
amplitude of the electrical field.
k
cm==
)(
1
B-2 The Electromagnetic Spectrum
-
7/27/2019 CHAPTER 6 Complete
6/31
Spectroscopic Method, Type of ER, andType of Transition
B-3 Mathematical Description of a Wave
)2sin(
2
)sin(
+=
=
=
=
=
+=
tAy
anglephase
velocityangular
ttimeatfieldelectricofmagnitutey
tAy
-
7/27/2019 CHAPTER 6 Complete
7/31
B-4 Superposition of waves
Effects of wavestraversing thesame space areadditive
)sin( += tAy
:y electric field
:A amplitude: phase angle
: angular velocity of the vector
2=
=y
..)2sin()2sin( 222111 ++++= tAtAy
-
7/27/2019 CHAPTER 6 Complete
8/31
Summing waves of same frequency
Resultant has same frequency
The larger the phase differencethe smaller the amplitude ofthe resultant
Same phase i.e. oo 360/360/021 = n )& same frequency
maximum amplitude = maximum constructive interference
phase difference = 180/ 180+ n x360zero amplitude =maximum destructive interference
Summing waves of different frequencies
Resultant is not a sinfunction
Period of beat
( )12
11
=
=bP
-
7/27/2019 CHAPTER 6 Complete
9/31
Superposition of Waves: Applications
Any periodic function can be described by a sum of simple sine orcosine terms
Applications1) construction of waves of specific shapes
Square wave Fig. 6-6 p.138
2) De-convoluting a complex periodic function
Complex periodic functionFourrier Transformsum of sin or cosfunctions
)2sin
1....10sin
5
16sin
3
12(sin tn
ntttAy ++++=
B-5 Diffraction of Radiation
Bending of a parallel beamradiation as it passes througha narrow opening (slit) orsharp barrier (an edge).
The slits acts like secondarysources
Diffraction is a consequenceof interference of light that isallowed through smallapertures or light that hitssharp edges.
Slit width
Diffraction of monochromatic radiation
Youngs experiment (1800)
-
7/27/2019 CHAPTER 6 Complete
10/31
Constructive interference occur when the difference in path (CF)traveled is an integer multiple of .
CF = BCsin BC = d: distance between the two aperture
n: order of interference
nd =sin
The grating equation
sin
int:
sin
sin
dn
BCd
erferenceorderofn
BCn
u
BCCF
=
=
=
=
==
Constructive interference occurs when the difference in path(CF) traveled is an integer multiple of .
-
7/27/2019 CHAPTER 6 Complete
11/31
Determination of Wavelength
OE
DEBC
OD
DEBCn
insubstitute
ODDE
==
=
)2(
sin
)2(sin BCCFn ==
B-6 Coherent Radiation
Coherent radiation is produced by a set of radiationsources which have identical frequencies constant phase relationships
Incoherent sources Emission of radiation by individual atoms or molecules results in
incoherent light beam: beam of radiation is the sum of individualevents (10-8s) (series of wave trains,)
Because the motion of atoms and molecules is random, thus
phase variation is also random. Coherent sources
Optical lasers
-
7/27/2019 CHAPTER 6 Complete
12/31
B-7 Transmission of Radiation
Propagation of E.R. through a transparent substance.
The velocity of propagation lower than its velocity in vacuum. This observation led to the conclusion that E.R. interacts with
matter.
The velocity of propagation depends on: composition and structure of matter (atoms, ions, molecules) concentration of substance
No frequency change no permanent transfer or energy. Instantaneous (10-14 to 10-15s) dipoles are generated in
substance. (temporary deformation of electron clouds/polarization)
Interaction leads to scattering in the case of large particle
Measure of Interaction - Refractive index at a specifiedfrequency )
i
iv
cn =
Transmission of radiation (Contd)
Refractive is wavelengthdependent!
Dispersion: variation ofrefractive index of asubstance withwavelength
Application: selection ofmaterials for opticalcomponents Lenses (normal)
Prism (near anomalous)
-
7/27/2019 CHAPTER 6 Complete
13/31
B-8 Refraction
Change in direction ofpropagation whenradiation traverses at asharp angle two media ofdifferent density, due todifference in velocity in thetwo media.
Refraction
Snell's law
2
1
1
2
2
1
sin
sin
==
2
12
sin
)(sin)(
vacvac =
2
12
sin
)(sin)(
airair =
airvac 00027.1=
-
7/27/2019 CHAPTER 6 Complete
14/31
Refractive index of materials
For = 589 nm
Substance Refraction index
Vacuum 1.0000
Air (STP) 1.0003
Water (20) 1.33
Acetone 1.36
Fused quartz 1.46
Typical crown glass 1.52
Polystyrene 1.55
CS2 1.63
Heavy flint glass 1.65
Diamond 2.42
A.7.3 Dispersion Spatial separation of E.R. of different wavelengths when refracted due to
change of refractive index of medium of propagation with wavelength. (rainbow) Prism based monochromators exploit this effect. Typical dispersion of susbstances: Normal dispersion region: gradual increase of with frequency Anomalous dispersion region(s): sharp changes in with frequency. Occurs
at freq= natural harmonic frequencies of some part of the molecule, ion,atomabsorption of beam occurs
Important information for the manufacture optical components. For lenses: must be high and relatively constant over the wavelength ofinterest. (Chromatic aberation are minimized)
For Prism: refractive index must be large and highly frequency dependent. (region of interest approaches the anomalous dispersion region
-
7/27/2019 CHAPTER 6 Complete
15/31
B-9 Reflection
Light/ER bounced off theinterface between two media
When the angle of incidence (i)is close to 90 most of the E.R. isreflected.
Fraction of radiation reflected fora beam entering at right angles
2
12
2
12
0 )(
)(
+
=I
Ir
I=1 refl
Air=1
Glass=2 refr=2
refleci =
B-10 Scattering
Nature of interaction between radiation and matter Electromagnetic field "pushes" electrons around. Polarization of electron densities, i.e. change in electron density
distribution. Deformation of electron clouds caused by the alternating
electromagnetic field of radiation Energy is momentarily retained 10-14 to 10-15 s and reemitted= scattered
in all direction. Raleigh Scattering
Size of particles much smaller than lambda Intensity proportional to
1/4
Dimension of particle Square of the polarizability of particles
Scattering by Large Molecules Radiation scattered is broadened (doppler effect) Used to determine size and shape of colloidal particles
Quasi Elastic Light Scattering / Dynanmic Light Scattering / PhotonCorrelation Spectroscopy
-
7/27/2019 CHAPTER 6 Complete
16/31
Scattering
Raman Scattering:scatteredincident Energy transferred is quantized and
corresponds to vibrational energy transitions
B-11 Polarization of Radiation Polarization - confinement of the
electrical vector in one plane Direction of Polarization of a wave is
defined by the direction of the electricalvector (E)
The plane of polarization: defined by theE vector and the direction of propagationof the wave.
An unpolarized wave: can be thought ofas a random superposition of manypolarized wave. Ordinary sources: (incandescent bulb,
Sun). Atoms behave independently andemit waves with randomly oriented planesof polarization about the direction of
propagation From non-polarized to polarized
Use medium that interacts selectivelywith radiation in one plane
Anisotropic crystals selectively absorbradiation in one plane and not theother.
-
7/27/2019 CHAPTER 6 Complete
17/31
Polarized and Unpolarized ER
C. QUANTUM-MECHANICALPROPERTIES OF RADIATION
Photoelectric effect Electrons are dislodged from metallic surfaces when
irradiated with ER of appropriate frequency Explained by Einstein in 1905
Wave model with radiation uniformly distributedcan not explain ejection of electrons, noraccumulation of energy by electrons to produce
instantaneous current observed.
Radiation = discrete packets of energy =photons
-
7/27/2019 CHAPTER 6 Complete
18/31
C-1The photoelectric effect
Millikan (1916) Vacuum phototube
Cathode coated with an alkali metalor its compounds
Radiation electron ejected withdifferent kinetic energies (KE)
With a negative potential at anode,only electrons with sufficient KE willget into the circuit, and current isobserved (photocurrent)
Stopping voltage: negative voltagerequired to annul photocurrent (V)corresponds to the Kinetic energy ofmost energetic electron KE = e x V
Expt: measure V for differentsurfaces and at different frequency.
Relationship between Voltage applied and
Frequency of radiation Observations
Photocurrent is proportional to intensity of light atlow applied voltages when is constant. Morephotons more electrons.
Stopping voltage depends on frequency for thesame photocathode. Radiation must possessenough energy to dislodge electron and impartkinetic energy.
Stopping voltage depends on composition of
coating on the photocathode. The stopping voltage is independent of the intensityof the incident radiation. Meaning it depends onlyon the frequency.
-
7/27/2019 CHAPTER 6 Complete
19/31
E=h=eV + KEm=h-h= 6.62 x 10-34Js = minimum
binding energy ofelectron
The photoelectric effect
C-2 Energy States of Chemical Species
Max Planck (1900) german physicist
Two postulates:
Chemical systems exist only in certain discreteenergy states and change in energy states occurwhen atoms, ions, moleculesabsorb or emit anamount of energy exactly equal to the differencebetween the states.
The frequency of radiation emitted or absorb isrelated to the difference in energy of energy states.
chhEE == 01
-
7/27/2019 CHAPTER 6 Complete
20/312
Quantization of
Energy States of Matter Atoms, Ions
Electronic states Origin of energy of atoms and ions:
motion of electrons around positive nuclei
Ground state: lowest energy state (room temp. energystate)
Excited states: higher energy states
Molecules
Electronic states Vibrational states Rotational states
-
7/27/2019 CHAPTER 6 Complete
21/312
C-3 Interactions of Radiation and Matter Molecules, ions, atoms can be
stimulated by adding Electrical energy Thermal energy Radiant energy Chemical energy
Absorption of energy can be followedby emission
Amount and type of energy ()absorbed and emitted reflect theamount and the energy states,respectively, of the analyte.
Spectrum: representation of type andamount radiation absorbed or
emitted . Spectrum provide information aboutthe analyte and its concentration
Absorption and Emission
-
7/27/2019 CHAPTER 6 Complete
22/312
Luminescence
Fluorescence- excitation to short lived Singlet excitedstate (singlet)
Phosphorescence long lived excited state (triplet) Photoluminescence excitation by radiant energy
Chemiluminescence excitation by chemical energy
C-4 Emission
Methods of Excitation
bombardement with electrons X-ray
electrical ac spark, flame, furnace, dc arc UV, Vis, or IR
electromagnetic radiation fluorescentradiation
Exothermic chemical reaction
chemiluminescence Types of spectra produced Line
Band
Continium
-
7/27/2019 CHAPTER 6 Complete
23/312
Types of emission spectra
Line Spectra
Produced by individualatomic particles in gaseousphase
Narrow, width of lines ~ 10-4
Origin of line spectra: pureelectronic transitions
Source of the line spectrum(Uv-vis) of Na ([Ne]3s1)contrasted to molecularemission (E1 and E2vibrational states omitted)
Source of X-ray linespectra:excitation ofinnermost electrons Example: X-ray emission
spectrum of Mo metal
-
7/27/2019 CHAPTER 6 Complete
24/312
Band spectra
Molecular emission Origin: numerousquantized vibrational androtational levels (omittedin fig.) in the groundstate.
Excited vibrational statesare short lived (10-15s):relaxation via collisionsto lowest vibrational stateof the excited state.
Relaxation via collisionsto electronic state isslower
Continuum spectra
Produced by hot objects
Produced by heating of solidsto incandescenceblack-body radiation
Spectrum produced ischaracteristic of thetemperature of the emittingsurface. High temperaturehigher energy radiationemitted
-
7/27/2019 CHAPTER 6 Complete
25/312
C-5 Absorption of Radiation
Absorption of radiation indicates excitation of theabsorbing species from the room temperature groundstate to higher electronic, vibrational or rotational state
The absorption spectrum informs on the nature andamount of absorbing species
The appearance of the spectrum depends on the type ofabsorbing species, the physical state and theenvironment of the absorbing species
Atomic versus Molecular Absorption
Type ofabsorbingspecies,physical stateandenvironmentdetemine theappearance of
the spectra.
3s 3p
fig 8.1
-
7/27/2019 CHAPTER 6 Complete
26/312
Atomic Absorption
Monoatomic species
Few well definedfrequencies
Only electronic transitionsinvolved.
UV and Visible radiationcan cause transition of theoutermost electrons only
X-ray radiation can causetransition of electronsclosest to the nuclei of
atoms
Transition from 3s to 3p
nm
Molecular Absorption
Molecular absorption spectra are more complex dueto the multiplicity of energy states in a molecules
UV and visible radiation causes electronic transition ofbonding electrons
Electronic transitions are coupled to vibrational androtational transitions
In condensed phase: solvent effects broaden the
signals Pure vibrational absorption (IR)
Pure rotational spectra in gas phase (ground-state rot.States) (microwave) (0.01 to 1cm)
rotationallvibrationaelectronic EEEE ++=
-
7/27/2019 CHAPTER 6 Complete
27/312
Absorption Induced by a Magnetic Field
Applied magnetic field interact with the magneticmoments of electrons and nuclei leading toadditional quantized energy levels
Method of excitation of nuclei: Radiowaves: 30 MHz (= 1000 cm ) to 900MHz or
33.3 cm ) NMR- most common range: 200 MHz (= 150 cm) to
600 MHz (= 50 cm )
Excitation of electrons magnetic moments:
by microwaves ~9500 MHz (= 3.16 cm) ESR: electron spin resonance EPR:electron paramagnetic resonance
-
7/27/2019 CHAPTER 6 Complete
28/312
C-6 Relaxation Processes
The lifetime of an excited state is generally very short,
because several mechanisms for relaxation are availableto the system which mediate the return to the groundstate
Categories of Relaxation Processes Non-radiative:
loss of energy in small steps via collision
Radiant energy converted to kinetic energy
Radiative: fluorescence and phosphorescence
Fluorescence and Phosphorescence
Fluorescence
From excited singlet state
Average lifetime: ~10-8s.
resonant (atoms in gaseousstate)
non-resonant (molecules ingaseous state and in solution)
Stokes shift: shift of thefluorescence emission to lowerfrequencies relative to theexcitation frequency
-
7/27/2019 CHAPTER 6 Complete
29/312
Phosphorescence
From meta-stableexcited state (tripletstate)
Average lifetime:~10-5s and longer
C-7 The Uncertainty Principle Werner Heisenberg (1927) The uncertainty on the
measurement of the energy of aparticle or system of particles is atleast equal to h/t
h: Plancks constant t= duration of measurement The longer t is the higher the
precision
Application: be aware of naturallimitations when trying to makeimprovements to better theprecision of measurements
htE =
-
7/27/2019 CHAPTER 6 Complete
30/313
D. Quantitative Aspects ofSpectrophotochemical Measurements
Signal transduced: radiant power = P Signal measured (S): voltage or current
S = kP + kd.
kd: dark current (current detected in absence ofradiation)
kd is compensated for in all modern instruments S = kP + kd
Absorption Methods
The attenuation of the beam that is related to the concentration
Transmittance
0P
PT=
:0P power of incident beam
:P power of transmitted beam
Absorbance
P
PTA 010 loglog ==
Beer's Law
A = abc for monochromatic radiation
a: proportionality constant = absorptivityb: thickness of absorbing medium
A= bcc: concentration in moles per literb: thickness of absorbing medium in cm
(M-1
cm-1
): molar absorptivity
-
7/27/2019 CHAPTER 6 Complete
31/31
Emission, Luminescence, and Scattering Methods
S= kC
C: concentration