chapter 6 part i 1h
TRANSCRIPT
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CHAPTER 6INTRODUCTION TO
SPECTROPHOTOMETRIC METHODS
Interaction of Radiation With
Matter
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Announcements
• Add to your notes of Chapter 1
• Analytical sensitivity
– γ=m/ss
• Homework
– Problems 1-9, 1-10 – Challenge Problem (?)1-12
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TOPICS
• General Properties of Light
• Wave Properties of Electromagnetic
Radiation
• Quantum-Mechanical Properties of
Radiation
• Quantitative Aspects ofSpectrophotochemical Measurements
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A. GENERAL PROPERTIES OF ER
• ER can be transmitted through vacuum
• The behavior/ properties of
electromagnetic radiations can be fully
explained only by its dual nature as a
wave and a particle
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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 (λ): 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 forpassage of successive maxima or minima through a fixed point inspace)
• Frequency(ν) = 1/p: number of oscillations/cycles of the field persecond. (hertz, Hz = s-1)
• Velocity of propagation (v) = vi = λi x ν – In vacuum (independent of wavelength)
• c = λ x ν = 2.99792 x 108 ms-1~ 3.00 x 108 ms-1
– In medium containing matter: slower due to interactions betweenelectromagnetic field and electrons in matter
– In Air (0.03 % less than in vaccum)
181000.3 −×=≅ mscvair
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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 persecond on given area.
• Intensity (I) is the power per unit solid angle.
• P and I are proportional to the square of the
amplitude of the electrical field.
ν
λ ν k
cm==
)(
1
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Spectroscopic Method, Type of ER, and
Type of Transition
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B-3 Mathematical Description of a Wave
)2sin(
2
)sin(
φ πν
πν ω
φ
ω
φ ω
+=
=
−=
−=
−−−−−−=
+=
t A y
angle phase
velocityangular
t timeat field electricof magnitute y
t A y
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B-4 Superposition of waves
• Effects of wavestraversing the
same space are
additive
)sin( φ ω += t A y
: y electric field
: A amplitude:φ phase angle
:ω angular velocity of the vector
πν ω 2=
= y
..)2sin()2sin( 222111 ++++= φ πν φ πν t At A y
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Summing waves of same frequency
• Resultant has same frequency
• The larger the phase difference the smaller the amplitude ofthe resultant
• Same phase i.e. oo 360/360/021 ×=− nφ φ )& same frequency
maximum amplitude = maximum constructive interference
• phase difference = 180°/ 180° + n x360° zero amplitude =
maximum destructive interference
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Summing waves of different frequencies
• Resultant is not a sinfunction
• Period of beat
( )12
11
ν ν ν −=
∆=bP
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Superposition of Waves: Applications
• Any periodic function can be described by a sum of simple sine orcosine terms
• Applications
1) 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 t n
nt t t A y πν πν πν πν ++++=
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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 ≅ λ
Diffraction of monochromatic radiation
Young’s experiment (1800)
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The grating equation
θ λ
θ λ
θ
θ λ
sin
int:
sin
sin
d n
BC d erferenceorderof n
BC n
u
BC CF
=
=
=
=
==
•Constructive interference occurs when the difference in path
(CF) traveled is an integer multiple of λ.
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Determination of Wavelength
OE
DE BC
OD
DE BC n
insubstitute
OD DE
==
−−
=
λ
θ
)2(
sin
)2(sinθ λ BC CF n ==
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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, thusphase 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 withmatter.
• 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 =
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Transmission of radiation (Contd)
• Refractive is wavelengthdependent!
• Dispersion: variation of
refractive index of a
substance with
wavelength
• Application: selection of
materials for opticalcomponents
– Lenses (normal)
– Prism (near anomalous)
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B-8 Refraction
• Change in direction ofpropagation when
radiation traverses at a
sharp angle two media of
different density, due to
difference in velocity in the
two media.
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Refraction
Snell's law
2
1
1
2
2
1
sin
sin
υ
υ
η
η
θ
θ ==
2
12
sin
)(sin)(
θ
θ η vac
vac =
2
12
sin
)(sin)(
θ
θ η air
air =
air vac η η 00027.1=
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B-9 Reflection
• Light/ER bounced off theinterface between two media
• When the angle of incidence (θi)
is close to 90° most of the E.R. is
reflected.
• Fraction of radiation reflected for
a beam entering at right angles
2
12
2
12
0 )(
)(
η η
η η
+
−=
I
I r
θI=1 θrefl
Air=1
Glass=2 θrefr=2
refleci θ θ =
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B-10 Scattering
• Nature of interaction between radiation and matter – Electromagnetic field "pushes" electrons around.
– Polarization of electron densities, i.e. change in electron densitydistribution.
– Deformation of electron clouds caused by the alternatingelectromagnetic field of radiation
– Energy is momentarily retained 10-14 to 10-15 s and reemitted= scatteredin all direction.
• Raleigh Scattering – Size of particles much smaller than lambda
– Intensity proportional to• 1/λ4
• 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:
– νscattered ≠νincident
– Energy transferred is quantized and
corresponds to vibrational energy transitions
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B-11 Polarization of Radiation
• Polarization refers to theconfinement of the electrical vectorin one plane
• Direction of Polarization of a waveis defined by the direction of theelectrical vector (E)
• The plane of polarization: definedby the E vector and the direction ofpropagation of the wave.
• An unpolarized wave: can bethought of as a randomsuperposition of many polarizedwave.
• From non-polarized to polarized – Use medium that interacts
selectively with radiation in oneplane
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Polarized and Unpolarized ER