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The Iodine Spectrum Revisited

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Pls complete "3.4 Discussion" in "Chapter 3.pdf" file. Since you have been solving 3.3, it must be quite straightforward for you. I also upload a paper (Ref. 7) that you might need in solving Problem 1. Pls be advised that I uploaded a paper (Ref. 5) needed to solve Problem 7. It appears you didn't need to refer to Ref. 7. Also, it is not quite clear whether you provided all the answers. For example, in problem 2, it asks to assign v' and verify v'' assignments, but you just gave v'/v'' in the first column of your solution table. I uploaded some queries regarding your solution for 3.3 here as well. pls check your answers carefully. Thank you.;Attachments Preview;Queries for 3.3.docx Download Attachment;The Iodine Spectrum Revisited.pdf Download Attachment;The Iodine Spectrum Revisited;R. B. Snadden;Heriot-Wan University, Riccarton, Edinburgh EH14 4AS. Scotland;An excellent undergraduate experiment in molecular;ipertroscopy involves the study of the absorption spectrum;of iodine vapor in the visible region.' The normal procedure;focusesatwntion on linesoriginatingat thelowest vihrationa1 level of the ground electronic state. The convergence of;vibrational levels in the upper excited electronic state then;permits a comolete analvsis to be made of the iodine molecule in its excked state k i t h values being obtained for the;fundamental oscillation freauencv. the force constant of the;bond (k),the anharmonicit,. c o n k k t (x), and the dissociation enerev (DO).;While this is-in itself of considerable interest, similar data;for the iodine molecule in its nronnd electronic state is of;even greater interest but cannot be obtained following the;above procedure without additional information being made;available. The normal method for obtaining such data is to;excite the iodine molecule with monochromatic radiation;and analyze the resulting fluorescence ~ p e c t r u m.Howev~,~;er, handling an emission spectrum is complicated both ex~erimentallv analvticallv.;and;* This;outlines an alternative procedure for analyzing;the ground electronic state of the iodine molecule by using;information provided by "hot" bands, observed in the absorption spectrum of iodine vapor.;The hand spectrum of iodine vapor in the risible region of;the spectrum as obtained by a spectrograph is shown in;Figure 1.;The spectrum arises because iodine molecules absorb "visible" nhotous and are therebv nromoted from the s o u n d;electrdnic state to an upper exiitkd state. From about1500 t o;545 nm the spectrum is uncom~licated lines within this;and;region are known t o originate from the u = 0 vibrational level;in the ground electronic state to all values of u in the upper;excited electronic state.;Beyond 545 nm the spectrum becomes more complicated;due to the appearance of "hot" bands, that is, bands originating from u = 1and u = 2 in the ground electronic state.;Because of this complication the standard undergraduate;experiment focuses attention on the spectral region 500 to;545 nm. Treatment of the results within this reeion can lead;to the complete analysis of the iodine molecnle~n excited;its;state. Such an analysis requires information additional to;that provided by the actual spectrum.;However, if attention is concentrated on the "hot" bands;the ground state properties of the iodine molecule can be;obtained without recourse t o anv additional data. If a spectroscope is used it is very difficnit to "unscramble" the fines;originating from u = 0, u = 1, and u = 2. The use of a;spectrograph improves things slightly but greatly increases;the time spent on the experiment. However, modern spectrophotometers of high resolution can now be obtained at;relatively little cost. Using one such instrument (Shimadzu;UV 240), an iodine spectrum can be obtained of such clarity;that no difficulties arise in the identification of the hot;bands because we can now emwlov line intensities to "unscramble" the data as is made ciea, in Figure 2.;Thus the series of lines from 500 to 543.2 nm orieinate a t u;= 0, their intensities are clearly seen to diminish beyond;543.2 nm. A new band beains to appear at 545 nm and;increases in intensity u p toabout 563nm beyond which i t;decreases. This new hand, absorbing at higher wavelengths;Figure 1. Band spectrum o iodine vapor in the visible region (adapted from;f;Barnard, A. K., Mansell, A. L. Fundamentalsof Physical Chemistw McGrawHill: London. 1966: p 87).;Figure 2. The use of line intensities to "unscramble" the spectrum.;and hence corresponding to transitions of lower energy, ir;the "hot" hand originating at u = 1. Finally a further "hot;hand, wrresponding to still lower energies and originating at;u = 2. makes its a~uearance t about 569 nm.;a..;Transitions responsible for the three bands are shown in;of;Fieure 3. Com~arison the information in Figures 4(a) and;Each of the above differences represents the energy difference (exnressed as a wave number) between the vibrational;0;levels'u, and u = 1in the ground electronic state.;Now the pattern of allowed vibrational energy levels given;by the Schrodinger equation for the Morse potential energy;function is approximately;E, = h d u + '1s) - x h d u;+ lid2;where w = oscillating frequency in hertz. The energy difference between the u = 0 and u = 1states is therefore;Expressing this energy difference in spectroscopic units of;cm-' gives;Levilt. 0. P.. Ed. Findlay's Practical Physical Chemistry, 9th ed.;Longman: London, 1973: p 183.;Verma, R. D. J. Chem. Phys. 1960, 32,738.;Shoemaker. D. P., Garland, C. W., Steinfield,J. I. Experiments in;Physical Chemistry, 3rd ed., McGraw-Hill: London, 1974, p 474.;Volume 64;Number 11 November 1987;919;Wave Numbers of "Llnes" in the lodlne Spectrum;Lines" originating at v = 0;Line" No.;3cm-;1;2;3;4;5;8;7;8;9;10;11;12;13;14;15;18559.7;18484.5;18408.3;18330.5;18246.5;18162.0;18075.8;17987.6;17898.2;17810.2;17717.8;17621.9;17524.2;17425.3;17323.5;Lines" originating at v = 1;Line" No.;Zcm-;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;Lines" wlglnating at v = 2;Line" No.;Tfcm-;18350.7;18275.2;18195.4;18115.1;18029.7;17948.0;17863.9;17777.7;17688.9;17598.2;17504.3;17407.0;17309.6;17211.7;17108.6;31;32;33;34;35;36;37;38;17569.6;17477.1;17387.1;17292.4;17196.9;17098.4;16999.2;16985.8;Atl,o/cm-;209.0;209.3;212.9;215.4;216.8;214.0;211.9;208.9;209.3;212.0;213.6;214.9;214.6;213.6;214.9;M a n = 212.8;X = 213.8cm-'.;Ai2,~lcm-;208.1;211.8;211.1;211.9;210.1;211.2;212.5;212.8;Mean = 211.2;Y = 211.2 em-'.;Similarly, comparison of the information in Figures 4(b);and 4(c) yields;Here each of the above expressions represents the energy;difference between the vibrational levels u = 1 and u = 2 in;the ground electronic state.;Knowing X and Y, eqs 1and 2 can be solved simultaneously to obtain values ofZ and x. The determination of the force;constant of the bond (k) and the dissociation energy (Do);follow for they are related to ij and x by the equations;k = 4r2ij2C2p;Figure 3. Transillans responsible for the three bands observed in the Iodine;spectrum.;where p = reduced mass.;Returning now to the actual iodine spectrum. The problem is to match a particular line originating at u = 0 and;terminating at u' with a line originating a t u = 1and terminating a t the same 0', similarly for lines originating a t u = 1;and u = 2. For this purpose each of the lines is identified by a;serial number. Lines originating a t u = 0, u = 1,and u = 2 are;identified respectively by the numbers 1-15,1630, and 3138 (Fig. 4). The wave numbers of the lines are tabulated in;the table such that matching data are aligned horizontally.;From the table, the energy difference (in cm-I) between;the u = 0 and u = 1vibrationallevels of the ground electronic;state is seen to fluctuate about a mean of 212.8 cm-'. Hence;from eq 1;212.8 = O(1- 2x) = 0;-2 G;(3);That this is the only correct match can be confirmed by;obtaining diagonal values of AT from the table. Such values;do not fluctuate about a mean but either steadily increase or;decrease.;Similarly the energy difference (in em-') between the u =;1and u = 2 vibrational levels of the ground electronic state;fluctuates about a mean of 211.2 cm-I. Hence from eq 2;Equations 3 and 4 can now be solved simultaneously to;obtain values of Z and x equal to 214.4 cm-' and 0.0037;respectively. These compare favorably with literature values;920;Journal of Chernlcal'Educatlon;Figure 4. Allocation of Jerial numbers to Identify lines.;of 214.50 cm-I and 0.0029, re~pectively.~ force constant;The;and the dissociation energy can then be calculated to be 172;N m-I and 173 kJ mol-'. This latter result is about 15%;higher than the literature value. The main reason for the;discrepancy is that the Schrodinger equation for the allowed;levels contains only one anharmonicity constant. In fact a;more precise expression requires cubic, quartic,...terms in;(u - %) with additional anharmonicity constants y, z,...;These terms become important a t large values of u and hence;in the determination of dissociation enerm.;As a final exercise the student can justify the existence of;hot" bands by determining the relative populations (N) a t;room temperature (293 K) in the u = 0, u = 1, and u = 2 states;from the calculated spacings. Thus the spacing between the;u = 0 and u = 1 levels is 212.8 cm-I. From the Boltzmann;distribution;N"=I;AE = ex{-- exp[-;Nu=;AEhe = e;x;-;-1;Xhc;kT;Similarly the spacing between the u = 1and u = 2 levels is;211.2 cm-I.;that is, the population of the u = 1 and u = 2 states are;significant.;In summary, using all the information provided by the;absorption spectrum for iodine vapor it is possible to determine i m ~ o r t a n toarameters of the iodine molecule in its;ground elertrunir srate without employing any extraneous;data. The loss of ilcwrars inherent in this method is acretx.;able and is more than compensated for by the experimental;simplicity.;Volume 64;Number 11;November 1987;921

 

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