1
© Dr. Nidal M. Ershaidat
Phys. 645: Environmental Physics
Physics Department
Yarmouk University
Chapter 2 Chapter 2 Elementary SpectroscopyElementary Spectroscopy
http://ctaps.yu.edu.jo/physics/Courses/Phys645/Chapter2
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Outline
2-1 The Solar Spectrum2-2 Light-Matter Interaction2-3 Biomolecules, Ozone and UV LightAppendix: The Ozone Hole
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Spectroscopy: Generalities 1
Measurements in environmental physics result generally in a spectrum.
The variation of the intensity (of light) with some variable (frequencies of this light) I = f(νννν) is called a spectrum.
Spectroscopy = Study of spectra.
Spectroscopist = physicist or scientist specialized in spectroscopy.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Spectroscopy: What is a spectrum?
Example 1Example 1: �When we represent the RADIANCY of a black body as a function of the frequencies emitted by this BB we obtain a “black body spectrum”
TT/2
Figure 2-1
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Black Body - Definition
The Black Body radiation was one of the important problems in the physics of the 20th century.
A Black Body is an object which emits and absorbs perfectly all wavelengths of the electromagnetic spectrum.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Black Body Spectrum
The light emitted or absorbed of a black
body is very characteristic.
TT/2
2
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Spectroscopy Example 2Example 2:
When we represent the INTENSITY of X-rays emitted by an element as a function of the frequencies we obtain the “X-ray spectrum”
Figure 2-2
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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2-1 The Sun Spectrum - Generalities
� Light reaching the earth from the sun
is essential for life.
� The detailed balance between the
inflow and the outflow of solar energy
establishes the temperature of the
earth’s surface.
� The solar light is absorbed by
photosynthetic organisms & energy
is conversed into chemical free energy
for later use
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The Sun Spectrum vs. Earth
This is also true for Light re-emitted by the earth’s surface and atmosphere
Light arrives on the earth’s surface and it is composed of a wide range of frequencies characteristic of:
1) The emitter (the sun)2) Specific elements of the solar surface 3) The composition of the atmosphere responsible for the transmission of light to the earth’s surface
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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2-1 The Sun Spectrum & Ozone (O3)
Ozone absorbs all light with a wavelength less than 295 nm, the UV region.
� if the ozone layer decreases then, not only, UV will reach the earth’s surface but all shorter wavelengths.
And this is very dangerous for life.
�Biomolecules such as the DNA (carrier of genetic capital) and proteins are sensitive to photons
2-1 The Solar Spectrum
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Figure 2-3: Absorption spectrum by various pigments
IR
The Sun & photosynthesis
UV
Pigment absorption
Wavelength (nm)
3
13
Pigment Absorption of the Sun light
Chlorophyll-a
• major pigment of higher plants, algae &
cyanobacteria• absorbs red and blue lightIn association with carotenoids they provide plants with their green color
Figure 2-3
Pigment absorption
Wavelength (nm)
Pigment is the�� the natural coloring matter of animal or
plant tissue.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Pigment Absorption of the Sun light
Pigment absorption
Wavelength (nm)
Bacteriochlorophyll-a & Bacteriochlorophyll-b are the major pigments absorbing in the near infrared region of the spectrum
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Earth is an emitter (a black body: T=288K)
The earth does not only absorb and reflect light. It also emits light, and the emission can be considered as that of a Black Body at
T=288K. Its spectrum is in the far infrared.
The energy balance is based on the emission and partial absorption of this infrared light and any changes in any of these processes may disturb the balance.In particular, changes in CO2, known for its few strong absorption bands in the IR, may alter the mentioned above balance.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Environmental Physics &
Atomic and Molecular Spectroscopy
The goal of this chapter is to see how Atomic Spectroscopy and Molecular Spectroscopy are related to Environmental Physics
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Spectroscopy gives answers
We need answers to several questions:
1- Why are specific colors of the light emitted
or absorbed by atoms and molecules?
2- Can we quantify the amount of absorption?
3- “Thickness” of an absorption band and its
implication?
4- Quantification of changes in the
atmospheric transmission spectrum due to
changes concentrations of CO2 and O3.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Answering the questions
Requires:
1- Basic understanding of the interaction of
light and matter (paragraph 2)
2- Knowledge of the terminology of
spectroscopy
4
2-2 Light-Matter Interaction
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Introduction
In all these processes energy may be absorbed or released.
Interaction of Light with Matter = Interaction of an electromagnetic wave with matter.
When light enters a medium, it interacts
with the atoms and molecules of the medium and several processes may
occur.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The Frame: Quantum Mechanics
� Einstein Coefficients,� Optical Density & Lambert-Beer’s Law,�Application to the Ozone Layer.
Quantum Mechanics is the frame Quantum Mechanics is the frame
necessary to study such an necessary to study such an
interaction.interaction.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The Perturbation Theory
2-2-1 The Transition (Electric) Dipole Moment
Consider a quantum system, atomic or Consider a quantum system, atomic or
molecular system, with discrete energy levels molecular system, with discrete energy levels
EEkk and wave functions and wave functions 0
kψψψψ
are the unperturbed solutions of the timeare the unperturbed solutions of the time--
independent Schrindependent Schröödinger equation dinger equation
0
kψψψψ
00
0 kkkEH ψψψψψψψψ ==== 2-1
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The Hamiltonian H0
For simplicity we shall consider that the
eigenvalues of H0 (i.e. Ek) are not
degenerated
The eigenstates of H0, are stationary. (((( ))))0
kψψψψ
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Applying a time-dependent perturbation
At this instant At this instant tt, The state of the system will be, The state of the system will be
ΨΨΨΨ t
H1(t)will mix with H0, and the total hamiltonian
at an instant t is:
H(t) = H0 + H1(t)
Consider now that a timeConsider now that a time--dependent dependent
perturbation is applied on the system and that perturbation is applied on the system and that
the perturbation hamiltonian is the perturbation hamiltonian is HH11((tt))..
When the perturbation is applied, starting from
t=0, the system evolves.
Generally, the eigenstates are no more
eigenstates of the hamiltonian H(t).
(((( ))))0
kψψψψ
5
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Transition Probability
Calculation of the probability Pkn that the
system be in some stationary state (((( ))))0
nψψψψ
is called the matrix element
ΨΨΨΨψψψψ tn
0
Transition Probability & Schröödinger
To calculate Pkn we need and this
means that we need to solve the Time-
dependent Schröödinger equation
(TDSE)
ΨΨΨΨ t
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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(((( ))))(((( ))))
ΨΨΨΨ++++====∂∂∂∂
ΨΨΨΨ∂∂∂∂ttHH
t
ti 10�
Time-dependent SchrSchröödinger equation dinger equation
verifies the TDSEverifies the TDSE
verifies the initial condition: verifies the initial condition:
ΨΨΨΨ t
00
kt ψψψψ========ΨΨΨΨ
is a unique solution of is a unique solution of Eq. 2Eq. 2--22..
ΨΨΨΨ t
ΨΨΨΨ t
2-2
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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in the eigenfunctions basein the eigenfunctions base
can be written as a linear combination of can be written as a linear combination of
the base of eigenfunction the base of eigenfunction
ΨΨΨΨ t0kψψψψ
(((( )))) �/tEi
k
k
kketct
−−−−ψψψψ====ΨΨΨΨ ∑∑∑∑
0
ΨΨΨΨ t
(((( ))))
ΨΨΨΨΨΨΨΨ==== ttckk
0
2-3
2-4
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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���� h s of TDSE
(((( ))))
(((( ))))
(((( ))))∑∑∑∑
∑∑∑∑
∑∑∑∑
−−−−
−−−−
−−−−
ψψψψ++++
ψψψψ
∂∂∂∂
∂∂∂∂====
ψψψψ∂∂∂∂
∂∂∂∂
k
/tEi
k
k
/tEi
k
/tEi
k
kk
k
kk
k
kk
etcE
etct
i
etct
i
�
�
�
�
�
0
0
0
2-5
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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���� h s of TDSE by
(((( )))) �/tEi
kk
kkn
ketcE
−−−−∑∑∑∑ ψψψψψψψψ++++00
(((( ))))
(((( ))))
ψψψψψψψψ
∂∂∂∂
∂∂∂∂====
ΨΨΨΨ∂∂∂∂
∂∂∂∂ψψψψ
∑∑∑∑−−−−
k
/tEi k
knk
n
etct
i
tt
i
��
�
00
0
0
nψψψψ
2-6
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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2-7
r h s of TDSE
(((( ))))(((( )))) (((( ))))
(((( ))))
(((( )))) (((( ))))[[[[ ]]]]
ψψψψ++++
ψψψψ
====
ψψψψ++++
∑∑∑∑
∑∑∑∑
∑∑∑∑
−−−−
−−−−
−−−−
n
/tEi
k
/tEi
k
k
/tEi
n
nn
k
kk
k
kk
etHtc
etcE
etctHH
�
�
�
0
0
0
1
10
6
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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r h s of TDSE by
(((( ))))(((( )))) (((( ))))
(((( ))))
(((( )))) (((( ))))(((( )))) (((( ))))∑∑∑∑
∑∑∑∑
−−−−
−−−−
ΨΨΨΨψψψψ++++
ψψψψψψψψ
====ΨΨΨΨ++++ψψψψ
n
/tEi
k
/tEi
k
n
nn
k
knk
n
ettHtc
etcE
ttHH
�
�
1
0
00
10
0
n
0ψψψψ
(((( )))) (((( ))))tcWetct
i nnkn
t
k
nk∑∑∑∑
ωωωω
====∂∂∂∂
∂∂∂∂ i
�
Multiplying by Multiplying by �/tEi ne
−−−−
2-8
2-9
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Finding ck(t)
wherewhere
(((( )))) (((( ))))tcWei
tct
nnkn
t
k
nk∑∑∑∑
ωωωω−−−−====
∂∂∂∂
∂∂∂∂ i
�
�
nknk
EE −−−−====ωωωω0
1
0
nknk HW ψψψψψψψψ====
2-10
2-11andand
We can also use the notation:We can also use the notation:
nHkW nk 1==== 2-12
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Using initial conditions
Taking Taking
Then at Then at tt = 0= 0
cc11(0) = 1(0) = 1 and and cckk(0) = 0(0) = 0 (for (for kk >1>1) )
Then for a time Then for a time tt sufficiently short sufficiently short
cc11((tt) ) ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ 11 and and cckk((tt) ) ≈≈≈≈≈≈≈≈ 00 (for (for kk >1>1) )
(((( )))) 0
10 ψψψψ========ΨΨΨΨ t 2-13
34
Computing ck(t)
Integrating Eq. 2-10 in these conditions*:
yields:
(((( )))) (((( ))))tcWei
dt
tdcnnk
n
tk nk
∑∑∑∑ωωωω
−−−−====i
�
(((( )))) tdWei
tc k
t t
k
k ′′′′−−−−==== ∫∫∫∫′′′′ωωωω
1
0
1i
�
where 11
0
11
0
1HkHW kk ====ψψψψψψψψ====
(((( ))))�
1
1
EEkk
−−−−====ωωωωand
2-14
2-15
2-16b
*Note that Eq. 2-14 is an ODE and no more a PDE.
2-16a
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Probability of “the excited state k”
The probability of finding the quantum system
in an excited state k, thanks to the absorption
of a quantum of energy is (((( )))) (((( ))))2
tctkk ====P
This probability is related directly
2
1
2
11HkWk ==== 2-17
36
An incident light, (a light source is switched on) i.e.
an incident electromagnetic wave, with frequency
ωωωω will “perturb” the system, and a perturbation
hamiltonian H1 will mix with the hamiltonian of
the system H0.
Interaction of Light with Matter=Perturbation
The atomic or molecular system is considered at the origin of the coordinates system, and being globally neutral it will interact with the electric
component of the em wave through a moment µµµµ.
for simplicity we shall consider a linearly polarized light and neglect the magnetic component of the em wave (Why can we do that?).
(((( )))) tcosEtE ωωωω==== 0
7
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Perturbation = A linearly polarized light
The perturbation hamiltonian is:
(((( )))) (((( ))))tEtH��
••••µµµµ−−−−====1 2-18
∑∑∑∑====µµµµi
i ii rq��
where is the electric dipole operator: µµµµ�
The sum is taken over all electronic charges qi at position ir
�
(((( )))) θθθθωωωωµµµµ==== costcosEtH01 ⇒⇒⇒⇒ 2-19
(((( ))))0E,��
µµµµ====θθθθ^
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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PPkk
(((( )))) tdWei
tct
k
ti
k
k ′′′′−−−−==== ∫∫∫∫′′′′ωωωω
0
1
1
�
θθθθωωωωµµµµ====→→→→
costcosEkWk 011
∫∫∫∫ ′′′′′′′′ωωωωθθθθµµµµ−−−−
====′′′′ωωωω−−−−
→→→→ tti
tdtcosecosEki
k
0
1
01
�
(((( )))) (((( ))))
(((( ))))2
1
12
1222
02
21
1
2
ωωωω−−−−ωωωω
θθθθµµµµ====
====
ωωωω−−−−ωωωω
k
tk
kk
sincosEk
tctP
�
�
⇒⇒⇒⇒
2-20
2-21
2-22
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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ComputingComputing
(((( ))))∫∫∫∫ ′′′′′′′′ωωωω
′′′′ωωωω−−−−′′′′ωωωω====
tkk
tdtcostsinitcos
0
11
2
∫∫∫∫ ′′′′′′′′ωωωω′′′′ωωωω−−−−
tt
ki
tdtcose0
1
∫∫∫∫ ′′′′′′′′ωωωω′′′′ωωωω−−−−
tt
ki
tdtcose0
1
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The probability that the system (atomic or
molecular) which was initially (at t = 0) in the
state 1 be in the state k at t is thus proportional to the (square of the matrix element )
Transition dipole momentTransition dipole moment
(((( ))))22
11
µµµµ====µµµµ∝∝∝∝ ktkk
P
(((( ))))2
11
2µµµµ====µµµµ kt
k transition dipole momenttransition dipole moment
For an isotropic solution or a gas, we should average all over the angles θ θ θ θ
2-23
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Transition dipole moment rateTransition dipole moment rate
The transition probability peaks sharply around ωωωω = ωωωωk1
For a non monochromatic light, one should average over a “frequency band” and this leads to the rate of population of level k:
(((( )))) (((( )))) (((( ))))ωωωω≡≡≡≡ωωωωµµµµεεεε
ππππ==== WBW
dt
tdkk
k1
2
1
03 �
P2-24
W(ωωωω) = Time averaged energy density of the incident em field at frequency ωωωω.
The Einstein CoefficientsLambert-Beer’s Law
8
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Einstein CoefficientsEinstein Coefficients
In this expression we have averaged over all possible angles between E0 and µµµµ
2
1
0
1
3kk
B µµµµεεεε
ππππ====
�
Bkk11 is the Einstein Coefficient for absorption and stimulated emission is directly related to the extinction coefficient measured in an absorption experiment.
(((( )))) (((( )))) (((( ))))ωωωω≡≡≡≡ωωωωµµµµεεεε
ππππ==== WBW
dt
tdkk
k11
2
03 �
P
W(ωωωω) = Time averaged energy density of the incident em field at frequency ωωωω.
2-25
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Einstein CoefficientsEinstein Coefficients
Here, we shall establish a simple relation between the rates of absorption, stimulated emission and spontaneous emission in an atomic or molecular system
Consider a quantum system, and two energy levels E1 & E2. Consider that the population of
these 2 levels are respectively N1 & N2.
Radiative Processes
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Transitions between 2 energy levelsTransitions between 2 energy levels
3 possible transitions (called radiative
processes) are possible between E1 & E2.
Absorption: Level 1 absorbs incident light (frequency ωωωω) and the system
“transits” to level 2.
B12 W(ωωωω)AbsorptionLight is ON
E2, N2
E1, N1
Figure 2-4-a
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Stimulated emissionStimulated emission
Stimulated emission: Level 2 emits light (frequency ωωωω) and the system “transits”
to level 1.
StimulatedemissionLight is ON
E2, N2
E1, N1
B21 W(ωωωω)
Figure 2-4-b
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Spontaneous emissionSpontaneous emission
Spontaneous emission: Level 2 emits light (frequency ωωωω) spontaneously and
the system “transits” to level 1.
SpontaneousemissionLight is OFF“Dark Process”
E2, N2
E1, N1
A21 W(ωωωω)
Figure 2-4-c
9
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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BB1212 = = BB2121 & & AA2121 = = aa BB2121
The rate of population of level 1 is given by:
For a steady state (((( ))))01 ====
dt
tdN
(((( ))))(((( ))))
2112
21
21 BNNB
AW
−−−−====ωωωω
(((( ))))221
1
212112NANWBNWB
dt
tdN++++++++−−−−====
Light is off
2-26
2-27
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Ratio Ratio NN11//NN22
Tke
N
N ωωωω==== �
2
1
In the absence of an external radiation field
and for a system in thermal equilibrium the
ratio N1/N2 follows Boltzmann Distribution:
eVeV.Tk40
10250 ====≈≈≈≈
k = Boltzmann constant = 1. 38 x 10-23 J K-1
and for T = 300 K (Room Temperature):
2-28
2-29
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The energy density The energy density WW((ωωωωωωωω))
The energy density W(ωωωω) is given by Planck’s radiation law
(((( ))))1
132
3
−−−−ππππ
ωωωω====ωωωω
ωωωω TkecW
�
�
The 2 expressions are identical and this gives:
(((( ))))(((( )))) 1
2112
2121
−−−−====ωωωω
ωωωω TkeBB
BAW
�
2-30
2-31
We have seen (eq. 2-27) that:
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Relation between Einstein CoefficientsRelation between Einstein Coefficients
B12 = B21
12
21
32
3
21
21
B
A
cB
A====
ππππ
ωωωω====�
2
21
0
32
21
0
3
3
2133
µµµµππππ
µµµµωωωω====µµµµ
εεεεππππ
ωωωω====
ccA
2
21
0
21
3µµµµ
εεεε
ππππ====
�B
12
00 ====µµµµεεεε cusing
2-32
2-33
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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||µµµµµµµµ1212||22 determines the rates of determines the rates of
all radiative processesall radiative processes
Major conclusion:
||µµµµµµµµ1212||22 determines the rates of all radiative determines the rates of all radiative
processes and consequently common processes and consequently common
selection rules apply to these processesselection rules apply to these processes
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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LambertLambert--BeerBeer’’s Laws Law
How are the macroscopic quantities (we measure) related to the “quantum”
Einstein coefficients and µµµµ12?
10
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Macroscopic absorptionMacroscopic absorption
A classical absorption measurementA light of intensity (flux) I with “band width” dωωωω falls on a sample of thickness dz.
Light is absorbed especially when the
light is weak and the atoms / molecules
of the absorber are in their ground state
N1 >> N2 (except in the case of laser where
it is amplified)
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The rate of transitions between states 1 & 2
This rate is given by: (No stimulated emission)
(((( )))) (((( )))) 21
1
2112NANWB
dt
tdN++++ωωωω−−−−====
B12N1 W(ωωωω) = A21 N2
For a steady state(((( ))))
01 ====dt
tdNLight is off
2-34
2-35
Eq. 2-35 is the rate at which energy is removed
from the incident beam or the Intensity loss rateIntensity loss rate.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Classical Macroscopic absorptionClassical Macroscopic absorption
Light passes through a thickness dz. (The total volume of the absorber is V)
dωωωωI dωωωω
dz
∂∂∂∂
∂∂∂∂++++
z
II
W dωωωω Area a
Figure 2-5
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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““Energy lossEnergy loss””
Because of attenuation W is a function of z
The amount of energy in the frequency interval [ωωωω, ωωωω+dωωωω] through the slice (a dz) is W dωωωω a dz. (J. s-1)
The rate at which the beam’s energy decreases is:
(((( ))))dzad
t
tWωωωω
∂∂∂∂
∂∂∂∂−−−−
131
3
−−−−−−−−−−−−
==== sWattmss
mJ
2-36
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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All atoms do not absorb at the same frequencyAll atoms do not absorb at the same frequency
First we should take into account the fact that the atoms/molecules of the system do not absorb light at exactly the frequency ωωωωk.
(((( )))) 1====ωωωωωωωω∫∫∫∫ dF
We define the fraction of transitions that occur in the interval [ωωωω+dωωωω]: F(ωωωω)
dωωωω with the normalization condition:
2-37
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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(((( ))))dzad
t
tWωωωω
∂∂∂∂
∂∂∂∂−−−−====
(((( )))) (((( )))) ωωωωωωωωωωωωωωωω dFV
dzaWBN �121
Energy balanceEnergy balance
The rate of decrease of the beam energy = the rate at which the light energy is removed from the beam by absorption. This implies:
From (Eq. 2-35)
11
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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LambertLambert--BeerBeer’’s Laws Law
(((( )))) (((( ))))ωωωωωωωω
ωωωω−−−−====∂∂∂∂
∂∂∂∂⇒⇒⇒⇒ F
VWBN
t
W �121
In other words:
z
I
t
W
∂∂∂∂
∂∂∂∂−−−−====
∂∂∂∂
∂∂∂∂−−−−
Energy entering the slice (adz) - Energy leaving it per time unit = rate of decrease of beam energy.
2-39
2-38
Where is the change in intensity (in W.m-2) of
the beam upon passage through the slice a dz
z
I
∂∂∂∂
∂∂∂∂−−−−
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W(W(ωωωωωωωω) and the optical properties of the absorber) and the optical properties of the absorber
The energy density distribution W(ωωωω) according to optics equals:
nc
IW ====
n is the index of refraction for the absorber
2-40
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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LambertLambert--BeerBeer’’s Laws Law
I(z) = I0 e- K z Lambert-Beer’s Law
Integrating eq. 2-41 gives:
(((( ))))IKI
ncV
FBN
z
I====
ωωωωωωωω−−−−====
∂∂∂∂
∂∂∂∂ �121
K is the (linear) absorption coefficient [K] = L-1
(((( ))))ncV
FBNK
ωωωωωωωω====
�121
2-41
2-42
2-43
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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(((( )))) (((( )))) (((( ))))ωωωω≡≡≡≡ωωωωµµµµεεεε
ππππ==== WBW
dt
tdkk
k11
2
03 �
P
B21 is given by (F(ωωωω) is normalized) :
∫∫∫∫ωωωω
ωωωω−−−−====
band
dK
N
ncVB
�12
Computing Einstein Coefficients
Integrating K, which is the quantity we measure in an absorption experiment, over the
absorption line gives B21 and consequently B12
and A21 and |µµµµ12|2
2-44
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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I = I(0) 10-OD
OD = Optical Density = εεεε C l
εεεε = molar extinction coefficient (in dm3 mole-1 cm-1 )
C = concentration of the absorber sample(in mole dm-3)
l = pathlength (in cm)
Optical DensityIn practice, the dependence of I on passage through a
material of length l is expressed as follows:
2-45
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Optical Density for chlorophyll a
C = concentration = 10-3 mole-1 dm3
l = pathlength = 0.02 cm
At its absorption maximum, λλλλ = 680 nm
(red light), chlorophyll a has:
εεεε = 105 dm3 mole-1 cm-1
OD = 2
12
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Chlorophyll a absorbs red light
OD = 2 gives a reduction of the intensity of light
of the order of 100!!
All red light is absorbed by a leaf of chlorophyll a
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The transition dipole moment
2
1
0
1
3kk
B µµµµεεεε
ππππ====
�
From the relation between the transition dipole moment and Einstein coefficient B21
The most important result
∫∫∫∫ωωωω
ωωωω
εεεε
ππππ====µµµµ
band
dK
N
ncV
��0
2
123
∫∫∫∫ωωωω
ωωωωεεεε××××====µµµµ −−−−
band
d.
612
12 10011
Check this!
2-46
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For a single molecule, the absorption cross section is given by:
σ σ σ σ = ππππ r2 P
r = radius of the moleculeP = Probability that the photon is
absorbed by the surface ππππ r2
The extinction coefficient ε ε ε ε
30323032
2
.
Nr
.
N AA ππππ====
σσσσ====εεεε See Chapter 4
NA is Avogadro’s number.
2-3 Biomolecules, Ozone & UV Light
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• Absorption of UV light in biological molecules
• Importance of the ozone layer
• Effects of the deterioration of the Ozone layer and Lambert-Beer’s Law
Section 2-372
• Biomolecules
The most sensitive to UV are:
The Spectroscopy of Biomolecules
•Nucleic Acids DNA & RNA
DNA (Deoxyribonucleic acid) is the carrier of the genetic code. It is responsible of Reading and translating the genetic code
• Essentially proteins: such as the αααα-
crystallin which is the major protein of the eyelens.
13
73
The UV region
• UV-A (near UV region)
320 nm < λλλλ < 400 nm
• UV_B (mid UV region)
290 nm < λλλλ < 320 nm
• UV-C (far UV region)
200 nm < λλλλ < 290 nm
Absorption of Light by Biomolecules
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Absorbance - DNA and αααα-crystallin
Figure 2-6: Absorption spectra of DNA (- • • • • - • • • •) and αααα-crystallin (--) in
the wavelength region 240-340 nm.
DNA
Solar spectrum
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Absorption of Light by DNA
For DNA, The spectrum peaks at λλλλ = 260 nm with
a maximum extinction εεεε = 104 dm3 mole-1 cm-1
Fig. 2-6 shows the UV solar spectrum and the absorption by DNA and αααα-crystallin
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Aromatic DNA bases
Absorption of light by DNA is due to the aromatic DNA bases: guanine, thymine, cytosine and adenineThe electronic transitions which contribute to the absorption in the range 220-290 nm are predominantly oriented in the plane of the DNA base!
For a typical cell, the absorption of solar UV due to protein would be about 10% of the absorption of nucleic acids.
See paragraph 2, page 24, for eventual absorption of light in the near UV region by proteins
Comparison
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Comparing to the DNA absorption spectrum, the action spectrum is greater in the region
λλλλ=320 nm. Other absorbers exist but the most sensitive is the DNA.
How damage is done?
It is the chromophores of DNA that form the prime target in the process that leads to the photodamage.
Interaction of light with thymine, or a cytosine-thymine pair produces the pyrimidine (photo product) which alters the reading and translation of the genetic code!
14
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Quantifying the Photodamage
The damage done to a biological system by solar UV can be calculated from the action spectrum!
E(λλλλ) has a large negative slope, I(λλλλ) has a
positive slope.
D is sensitive to even slight changes in I(λλλλ).
(((( )))) (((( ))))∫∫∫∫∞∞∞∞
λλλλλλλλλλλλ====0
dIED 2-47
22--33--3 The Ozone filter3 The Ozone filter
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The Ozone Filter
aa-- What is the Ozone
layer?What is th
e Ozone layer?
bb-- How is Ozone form
ed?How is Ozo
ne formed?
cc-- How does Ozone f
ilter the solar
How does Ozone filte
r the solar
spectrum?spectrum?
dd-- What damages the
ozone layer?
What damages the o
zone layer?
The Ozone holeThe Ozone hole
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� O3 forms a thin layer in the stratosphere.
� Most atmospheric Ozone is in the
stratosphere, about 15-30 km.
� The maximum concentration is found
between 20 & 26 km above the earth’s
surface.
a-What is the Ozone layer
�A concentration of ozone molecules in the atmosphere of the earth. The amount of O3corresponds to a layer of 0.3 cm under NTP.
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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a-What is the Ozone layer
�Ozone
Figure 2-7© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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The Earth’s Atmosphere
�The Troposphere:
- The lowest region. It extends from the
earth’s surface up to about 10 km in altitude.
- All human activities occur in the troposphere.
It is divided in several layers
�The stratosphere:
- continues from 10 km to 50 km.
- Commercial airline traffic occurs in the lower part of the stratosphere.
15
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Mesosphere, Thermosphere & Exosphere
�The mesosphere:
- continues from 50 km to 80 km.
�The Thermosphere:
- continues from 80 km to 600 km.
�The Exosphere:
- continues from 600 km to 1000 km.
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Ozone in the Atmosphere
Figure 2-8
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b- (How is) The Ozone O3 (formed?)
Ozone is a molecule containing 3 oxygen atoms
while normal oxygen (which we breath) is colorless & odorless, Ozone is blue in color and has a strong odor
� O3 is formed through the combination of O2 molecule with an Oxygen atom:
�O2 + O O3
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Ozone is rare in our “air”
Out of 107 molecules of air: 2 million are normal Oxygen for 3 Ozone molecules!!
The ozone layer absorbs the UV-B portion of the sun spectrum.
The Ozone O3 (Properties)
The UV-B is known to be the major cause of skin cancer and cataracts. It is also harmful to some materials and to the marine life!
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Formation and destruction of ozone molecules take place all the time, but its concentration remains relatively stable.
Until recently, the variation (reduction and increase) of the ozone layer, due to sunspots, seasons and according to the altitude, remains nil.
Concentration of Ozone changes!
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c- Formation of the atmospheric Ozone
�Where do O2 molecules and Oxygen
atoms, in the stratosphere, come from?
� The atomic oxygen is formed by photodissociation (dissociation by light) of the oxygen molecules in the 100 km region by wavelengths < 170 nm.
16
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Photodissociation of O2(λλλλ < 175 nm)
�Step 1
� The oxygen molecule in its ground state ΣΣΣΣu-
interacts with the λλλλ < 175 nm photon and transits to the excited state ΣΣΣΣg
- )
�λλλλ < 175 nm
∑∑∑∑−−−−
u
3
∑∑∑∑−−−−
g
3
Figure 2-9a
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Photodissociation of O2(λλλλ < 175 nm)
�O (1D)
�O (3P)�2 eV
� O2 (excited state)
� The excited molecule dissociates to two oxygen atoms, one in the ground state (3P) and the other one in the excited state (1D)
Figure 2-9b
�Step 2
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Photodissociation of O2(λλλλ < 240 nm)
� A much weaker absorption (σσσσ=10-23 cm2 = 10
barn) of light in the λλλλ< 240 nm region occurs and
the resultant oxygen atoms are in the ground state (1P)
Units of cross-section at the nuclear level[1 barn = 10-24 cm2)]
For comparison σσσσRutherford = 1 barn
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What does the Formation of ozone depend on?
The efficiency of formation of ozone by UV
depends on:
1. Availability of oxygen in the stratosphere
2. Changes in the Temperature of the stratosphere and its chemical “contents”
3. Dust from volcanic eruptions
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Characteristics of the Ozone layer
�Because the equator is the region the most exposed to sunlight, ozone above the equator reaches a maximum.
�Ozone diffuses towards the poles where the layer it forms is larger than above the equator.
�Its concentration is highest in late winter and early spring
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c- How does the ozone filter the solar spectrum?
The atmospheric Ozone absorbsessentially all wavelengths below 295 nm
almost 90-95% of solar UV.
17
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The Ozone (absorption) spectrum
Figure 2-10
AppendixThe Ozone Hole
See http://www.theozonehole.com/
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There are two pathways for the destruction of ozone
O + O3 2 O2O3 + O3 3 O2
Ozone depletion reaction
d- The Ozone hole
What destroys the Ozone layer?
These reactions are the net result of more complex reactions catalyzed by various gases and radicals
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Radicals: Cl, NO and OH: The ODS
Chlorine: produced in the volcanic eruptions & in the CFC’s and HCFC’s
ODS = Ozone-Depleting Substance
CFC = ChlorofluorocarbonsHCFC’s = Hydrochlorofluorocarbonsused in refrigerators, as “propellants”and foam-blowing agents (sprays)
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ODS: Hydroxyl radical OH & Nitric oxide
OH results from the breakdown of H2O
vapor
Source: HSource: H22O from supersonic airplanes!O from supersonic airplanes!
NO is formed by photodecomposition of
N2O - used as a fertilizer!-
Cl, NO & OH are responsible for the
destruction of 99% of the stratospheric
ozone!!
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The CFC’s (An ODS)
Figure 2-11
18
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The Ozone tragic cycle
Figure 2-12
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Processes that determine ozone concentration
Figure 2-13
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The aerosol UV absorbent spectrum
TOMS: Total Ozone Mapping Spectrometer
Figure 2-14
© Dr. Nidal M. Ershaidat Environmental Physics - Chapter 2 Spectroscopy
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Is the Ozone depletion dramatic?
10% of ozone depletion will result in 45% increase of solar UV-B reaching the earth’s surface.
That’s why it is so important to monitor the ozone layer and study the “bad”effects of UV on life.
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The Montreal Protocol
� Production of CFC’s is banned since
1995 and fully stopped since 2000
�As for HCFC’s: Production will be banned in 2020.
�(Methyl bromides: 2005)
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Montreal Protocol - Summary of Control Measures
Total phase out by 2005
Total phase out by 201570% reduction by 2000
20% reduction by 200550% reduction by 2001
1995-1998 base level25% reduction by 1999
Freeze in 2002 at averageFreeze in 1995 at 1991 base levelMethyl bromide
Phased out end of 1995Phased out end of 1995Hydrobromofluorocarbons (HBFCs)
Total phase out by 2040Total phase out by 2020
at 2015 base level90% reduction by 2015
Freeze in 201665% reduction by 2010
35% reduction by 2004
Freeze from beginning of 1996Hydrochlorofluorocarbons (HCFCs)
Total phase out by 2015Phased out end of 1995Methyl chloroform
Total phase out by 2010Phased out end of 1995Carbon tetrachloride
Total phase out by 2010Phased out end of 1993Halons
Total phase out by 2010Phased out end of 1995Chlorofluorocarbons (CFCs)
Developing CountriesDeveloped CountriesOzone Depleting Substances
19
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The Kyoto Protocol
The Kyoto Protocol is an international agreement
linked to the United Nations Framework Convention on
Climate Change.
The major feature of the Kyoto Protocol is that it sets
binding targets for 37 industrialized countries and the
European community for reducing greenhouse gas
(GHG) emissions.
These amount to an average of five per cent against
1990 levels over the five-year period 2008-2012. The
Protocol commits industrialized countries to stabilize
GHG emissions.
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The Kyoto Protocol
The Kyoto Protocol was adopted in Kyoto, Japan, on 11 December 1997 and entered into force on 16 February 2005. The detailed rules for the implementation of the Protocol were adopted at COP 7 in Marrakesh in 2001, and are called the “Marrakesh Accords.”
Recognizing that developed countries are principally responsible for the current high levels of GHG emissions in the atmosphere as a result of more than 150 years of industrial activity, the Protocol places a heavier burden on developed nations under the principle of “common but differentiated responsibilities.”
See: http://www.alternate-energy-sources.com/Kyoto-Protocol-summary.html
© Dr. Nidal M. Ershaidat
Chapter 3Energy for Human Use(Core of this course)
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