chapter 6 complete

7/27/2019 CHAPTER 6 Complete

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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


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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


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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


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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


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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


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Spectroscopic Method, Type of ER, andType of Transition

B-3 Mathematical Description of a Wave

)2sin(

2

)sin(

+=

=

=

=

=

+=

tAy

anglephase

velocityangular

ttimeatfieldelectricofmagnitutey

tAy


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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


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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


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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)


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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 .


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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


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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)


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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=


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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


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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


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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.


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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


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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.


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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


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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


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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


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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


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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


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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


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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


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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 ++=


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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


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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


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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 =


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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


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Emission, Luminescence, and Scattering Methods

S= kC

C: concentration

chapter 6 complete

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