(expressed in cm-1) for a transition between
two electronic states can be simply expressed by
Iodine is the heaviest common halogen (atomic number=53, atomic mass=127) and exists as a solid at room temperature in sublimation equilibrium with its vapor. Like the other halogens, this vapor consists of a weakly bound diatomic molecule, I2. The homonuclear diatomic has no dipole moment, so the vibrational frequency of this molecule cannot be determined via conventional IR absorption. The vapor has the appearance of a violet gas, indicating a visible absorption. This absorption corresponds to a spin-forbidden transition from the lowest vibrational levels of the singlet electronic ground state to high vibrational levels of a triplet excited state. This transition is stronger and 'redder' for I2 than for the lighter halogen dimers.
Electronic spectroscopy of small molecules provides chemists with the fundamental understanding of the nature of the chemical bond in quantum mechanical detail. We all know that a chemical bond is not infinitely strong, i.e. it has a well defined bond energy. We also know that because the bond is stretchy, the frequency of vibration of the nuclei attached by a chemical bond will be determined by how stretchy or stiff the bond is. The bond has a length, which is characterized by the vibrationally averaged position of the atoms at the end of the bond. To a good approximation, these and all other properties of the bonding between atoms is derivable from the potential energy curve.
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The total energy of a diatomic molecule may be separated into translational energy and internal energy. We are concerned here with the internal energy Eint which can be expressed to a good approximation by
Eint=Eel+Ev+Er (1)
where Eel is the electronic energy, Ev is the vibrational energy, and Er is the rotational energy. This electronic energy Eel refers to the minimum value of the potential curve for a given electronic state. The zero of energy is arbitrarily taken as the minimum in the potential curve for the lowest electronic state (ground state). It is convenient to divide Eq. (1) by the quantity hc, where c is expressed in units of cm s-1, to get the so-called term value, which has units of cm-1. Thus
Tint=Eint/hc=Tel+G+F (2)
where the vibrational and rotational term values Ev/hc and Er/hc
are given their conventional symbols G and F, respectively. The advantage of this change is that the frequency
(expressed in cm-1) for a transition between
two electronic states can be simply expressed by
(3)
where primed (') parameters are properties of the upper state, while the double-primed (") parameters are lower state properties.
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The rotational term difference (F' - F") in Equation (3) will be ignored in the absorption spectroscopy experiment, since rotational structure is not resolved in this experiment.
Fig. 1 Electronic states of the iodine molecule
The transitions that give rise to the absorption spectrum take place between the ground electronic state of the iodine molecule and an excited electronic state. At room temperature, all iodine molecules are in the ground electronic state, and nearly all are in the ground vibrational state (v"=0) as well. For this reason, transitions in the absorption spectrum of iodine all originate in the state v" = 0. Figure 1 illustrates how all the absorption transitions begin in the state v" = 0 and terminate in the upper electronic state in all possible vibrational states; that is, equals anything from 0 to infinity. Since only a single vibrational state is involved in the lower electronic state, the spectrum is simpler than the emission spectrum that arises from transitions between all possible vibrational levels in both electronic states.
In Figure 1 you can see some of the transitions that give rise to the absorption
spectrum of molecular iodine. In practice, not all the transitions are observed because electronic transitions
take place much more quickly than the period of a molecular vibration (Franck-Condon Principle). Furthermore,
one would expect that absorption transition would originate in the state v" = 0,
where the probability is a maximum that is, where y02
is a maximum. This is shown in Figure 1 for the v' = 0 state. In addition, the most intense transition
terminate in upper-level states, where there also is a region of high probability; that is, where yv'2
is a maximum. The B electronic state of the iodine molecule is positioned so that vertical lines (transitions)
drawn from the vibrational state v" = 0 to v' vibrational states intersect the B state in a way that the
most intense transitions are, for the upper-level vibrational numbers, from about v' = 20 to v' = 50, or
nearly to the convergence limit. Lines drawn from the v" = 0 state tend to miss the upper-level
vibrational state of low values of v'. For this reason, these transitions are weak or not observed, as shown
in Figure 1. The nomenclature used in Figure 1 follows Herzberg [1], except that
is used instead of w. It might be helpful to notice again that primed (')
parameters are properties of the upper state only, while the double-primed (") parameters are lower state
properties. Most values with no prime at all correspond to energy differences between states. It is customary
to use the wave number (cm-1) as a unit of "energy" for both states and transitions
between them. With this nomenclature in mind the upper G'(v') and lower G"(v") state energies
are written:
(4)
(5)
Note that T"=0 for the ground state. The absorption transition between these sets of energy levels are given by
(6)
When v" is equal to zero Equation (6) becomes an expression for the
absorption spectrum (we ignore here the second order anharmonicity constant 
)
(7)
that is for all possible transitions between v"=0 and v'=anything. As already pointed out, not all of these transitions may be sufficiently intense to be observable.
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Of special interest are the spacings between vibrational energy levels, and
you can see by examining the transitions drawn in Fig. 1 that
absorption spectrum can give us some information about these spacings. For example, in the B state, the
spacing 
between the v' = 0 state and the v' = 1 is given by G'(1)-G'(0).
In general the spacing can be obtained from Eq. (4) - (6) and again ignoring second order anharmonicity
constant we obtain:
(8)
Equation (8) is the equation of a linear Birge-Sponer extrapolation. The values
of are experimentally accessible, since they are just the differences in
energy (cm-1) between adjacent pairs of absorption bands. Also, v' is the upper-state
vibrational quantum number of the lower energy member of the pair. Remember that the
are just the vibrational energy level spacings in the B electronic state. Equation (8) shows that the spacings
are a linear function of the vibrational quantum number. If is
plotted against (v' + 1), the result is a straight line, the slope of which equals 
and
the intercept of which equals 
. The plot is called a
Birge-Sponer extrapolation. It is linear if second-order anharmonicity constants are sufficiently small, and
they often are. The plot is shown in Figure 2a for the case where and
higher anharmonicity constants are negligible, and in Figure 2b where they are not negligible.
Fig.2 The Birge-Sponer extrapolation
In addition to , and 
,
the dissociation energies D'0 and D'e be determined from the Birge-Sponer extrapolation.
In Figure 1 compare D'0 with the spacings between the
upper-state vibrational energy levels. The sum of all the spacings is exactly equal to D'0. Since
many spacings fall between the state v' = 0 and the convergence limit at v' = infinity, you can replace the
summation sign with an integral:
(9)
This area is the total area of the triangle in Figure 2a. Even if the
Birge-Sponer extrapolation is nonlinear, as it is when the higher anharmonicity constants are not negligible,
the area under the curve can still be measured-for example, by Simpson's method. Thus, in this case, the
dissociation energy D'0 can be determined. So far, we have determined three important upper-state
parameters, , and ,
and D'0. Examination of Figure 1 reveals that the difference between D'0 and D'e
is just 
, the zero point energy. Consequently you can easily
determine D'e
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Because the intensities of the absorption transitions fall off at high upper state quantum numbers, it is not possible to observe the convergence limit directly for the iodine spectrum. How examination of Figure reveals that
(7)
where 
, is the energy in cm-1
of the absorption band at which the extrapolation is begun and A' is the area under the Birge-Sponer curve
from v'b to v'c. The vibrational quantum number at convergence is v'c,
and v'b is the vibrational quantum number at .
The shaded area in Fig 2a equals A'. The total area under the curve (shaded and unshaded areas) equals D'0,
the upper-state dissociation energy. The convergence limit E* is given by Equation (7).
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The He-Ne laser which is used in LIF experiment is inexpensive, simplest-to-operate, and most common laboratory laser. It generates radiation with wavelength l=632.82 nm. The laser is rather monochromatic Dl=0.002 nm. It allows us to resolve the rotational structure of the transition.
The rotational energy of rigid rotator Er is given by
where I = mRe2 is the moment of inertia, and J - rotational quantum number. Here m is the reduced mass of the iodine molecule and Re is the equilibrium distance between atoms. In term values
F(J)=BJ(J+1)
where rotational constant B is written
When we consider absorption spectroscopy experiment the rotational energy contribution F'-F" was neglected. Now we need to add to each transition v"-v' also the rotational part F'(J')-F"(J"). The following selection rule is valid for electronic transition in iodine molecule
DJ=±1. This selection rule can be understood based on the angular momentum conservation law. Since a photon has one unit of angular momentum, the angular momentum of a molecule must change by a compensating amount after emission or absorption of a photon.
Thus we can expect two series of lines (branches):
R branch R(J) corresponds to F'(J+1) - F"(J)
P branch P(J) corresponds to F'(J-1) - F"(J)
Here the J's are rotational level in the lower state J".
The energy of rotational levels F(J) relatively small, especially for molecules with large moment of inertia ( small B ). Therefore at room temperature many rotational levels (how many?) are populated. The number of transitions is twice that number of populated levels. We can not resolve these lines in absorption experiment. However monochromatic laser will excite only one or several rotational transitions. There are coincidences between He-Ne laser radiation and two different rovibrational electronic absorption transition in I2. The laser can excite v"=3, J"=33 of the ground state to v'=6, J'=32 of the B electronic state, and also v"=5, J"=127 of the ground state to v'=11, J'=128 of the B state. These two transition are referred here as P(33)6<-3 and R(127)11<-5. After excitation of the v'=6, J'=32 and v'=11,J'=128 energy levels of the B state, the electronically excited molecules fluoresce back to the ground electronic state. The fluorescence obeys rigorous DJ=±1 rotational selection rule, but the initially excited states can radiate to any vibrational level of the ground states. The relative intensity of the fluorescence signals terminating on different v" levels are determined by Franc-Condon factors.
For each fluorescence transition from the excited v',J' level two transitions are possible to the level v". One with J"=J'+1 and other with J"=J'-1. The difference in the wavenumber for this two transition
=F"(J'+1)-F"(J'-1)=B"(J'+1)(J'+2)-B"(J'-1)J'=2(2J'+1)B".
For R(127)11<-5 transition J'=128 and therefore =514B".
Thus these two lines can be easy resolved and rotational constant (and therefore bond length) can be measured.
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A. Measure the absorption spectrum of iodine molecule with highest resolution possible. Use wavelength range from 500 to 600 nm. Usually you can obtain a spectrum even at room temperature, but it will be better to heat it up to ~40 0C.
B. In order to obtain more accurate results, calibrate monochromator using known emission spectrum (hydrogen or mercury).
C. Tabulate the experimental values of the absorption maxima in nm and cm-1 . Between 500 and 550 nm, all observed transitions originate in the state v"=0. At wavelength longer than about 550 nm some "shoulders" appear on the absorption bands arising from the v"=0 to v' transition. These shoulders are "hot" band arising from the v"=1 and v"=2 to v' transitions and are not used in this experiment. They can, however, cause some confusion in deciding which band arise from the ground state. Fig. 3 shows how the changing intensities can be used to determine which peaks arise from the v"=0.
Fig.3 Using band intencities to determine lower state vibrational quantum numbers in molecular iodine.
D. Another problem is correct assigning of the v' numbers to the different absorption peaks. It is really serious problem, because the transition v"=0 - v'=0 is too weak to be observable, and therefore numbers can not be obtain by simple counting. It is interesting that in spite of that the iodine spectrum was measured for the first time in the beginning of century the correct v' assignment was reported only in 1965 by Steinfeld et al. [2]. You can use for correct assignment the results of that work. You can use the fact that v"=0 -v'=27 transition located close to 541.2 nm, and v"=0 - v'=29 transition at 536.9 nm.
E. Prepare a Birge-Sponer
extrapolation. Calculate and compare with literature data ,
and , D'0 , D'e and E*. You can
use mathcad document for this goal.
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A. Heat the fluorescence cell up to ~80oC.
B. Produce different scans of spectrum with different slit sizes from 585 up to 800 nm. Try to obtain good low resolution spectrum which allow vibrational analysis. Try to assign observed transition. For correct assignment use Franck-Condon factors from table 1 which describe relative intensities for fluorescence signal.
|
P(33)6<-3 |
R(127)11<-5 |
|||||
|
Dv |
v' |
v" |
FCF |
v' |
v" |
FCF |
|
-5 |
11 |
0 |
2 |
|||
|
-4 |
11 |
1 |
20 |
|||
|
-3 |
6 |
0 |
0 |
11 |
2 |
68 |
|
-2 |
6 |
1 |
0 |
11 |
3 |
120 |
|
-1 |
6 |
2 |
3 |
11 |
4 |
100 |
|
0 |
6 |
3 |
21 |
11 |
5 |
20 |
|
1 |
6 |
4 |
55 |
11 |
6 |
9 |
|
2 |
6 |
5 |
100 |
11 |
7 |
68 |
|
3 |
6 |
6 |
120 |
11 |
8 |
68 |
|
4 |
6 |
7 |
83 |
11 |
9 |
2 |
|
5 |
6 |
8 |
2 |
11 |
10 |
33 |
|
6 |
6 |
9 |
0 |
11 |
11 |
65 |
From this table you can see that all anti-Stokes lines (with Dv<0) is from v'=11 transition. Dv=1 and Dv=4 signals are dominated by fluorescence from v'=6. Dv=2 and Dv=3 signals contain significant contribution from both excitations, and Dv=5 and Dv=6 signals are dominated by emission from v'=11.
C. Produce high resolution short scans of different Dv lines, especially originated from v'=11, where separation between transitions to J"=127 and J"=129 can be easy resolved.
D. From vibrational analysis using Birge-Sponer
extrapolation calculate and compare with literature data 
and 
,
D"0 , D"e . From these data and the data obtained for B state calculate energy
of excitation of iodine atom and compare with literature.
E. From the high resolution spectra calculate B" and bond length of the iodine molecule.
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1. The literature value of Re for the ground electronic state of Iodine molecule is 266.6 pm. Calculate the moment of inertia for Iodine molecule, rotational constant B, and the difference in energy (in cm-1) for transitions from J'=128 to J"=127 and J"=129.
2. The vibrational wavenumber of the oxygen molecule in its electronic ground state X is 1580 cm-1, whereas that in the first excited state B to which there is an allowed electronic transition is 700 cm-1. If the separation in energy between the minima in their respective potential curves of these two electronic states is 6.175 eV, what is the wavenumber of the lowest energy transition in the band of transitions originating from v"=0 vibrational state of the electronic ground state to this excited state? Ignore any rotational structure or anharmonicity.
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2. J.I.Steinfeld, R.N.Zare, L.Jones, M.Lesk, W. Klemperer, Spectroscopic constants and vibrational Assignment for the B state of Iodine. J. Chem. Phys. , 42, 25 (1965)
Shoemaker, D.P.; Garland, C.W.; Nibler, S.W. Experiments in Physical Chemistry,
J.S.Muenter , The Helium-Neon Laser InducedFluorescence Spectrum of Molecular Iodine., J. Chem. Educ., 73 , No.3, 576 - 580 (1996)
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You can use a Mathcad program to solve some of the problems which can be
proposed in the quiz or for processing of the results.
If you do not have this program you can download Mathcad
explorer to see Mathcad documents. It is free.
If you are not familiar with Mathcad you can use this file as a tutorial.
In this experiment you can use the following Mathcad documents:
If you do not have Mathcad you can read these documents in PDF format:
Iodine spectroscopy
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on diffraction grating This page was last updated on 14/03/04 15:19