Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule using constnt devition spectrometer Apprtus Constnt devition spectrometer, trvelling microscope, polrimeter tube, iodine crystls, cndle, mercury vpour lmp. Principle of the experiment Absorption spectrum of I 2 molecule One of the most redily observed bnd spectrum of I 2 is the visible bsorption bnd system which is responsible for the violet color of the iodine vpour. The system cn be obtined by pssing continuous spectrum light through iodine vpour nd then dmitting it into spectrogrph. It is found to be composed of very lrge number of nrrow bnds extending from the fr red to the bsorption limit t bout 5000 Å. The electronic trnsition involved is 1 Σ + g (ground stte) O + u. 0.25 0.2 Excited stte Energy 0.15 0.1 0.05 0 0.05 A exc n conv Electronic ground stte D" D 0 0 0.1 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 intertomic distnce Figure 1: Energy digrm for trnsition between the ground stte nd excited stte of the I 2 molecule. Ech electronic stte consists of mny vibrtionl levels. Dissocition energy of I 2 molecule D 0 = Dissocition energy of the ground stte = 1.5422 ev D 0 = Dissocition energy of the O + u stte = 0.5502 ev Excittion energy of trnsition is 7598 cm 1.
Wvenumber n = 1/λ. In our cse n = Dissocition energy of the ground stte 1eV = 8068cm 1 10 8 λ(inåunits) cm 1. D 0 = (n conv A exc )cm 1 D 0 = 1 8068 (n conv 7598)eV. Dissocition energy of the excited stte D 0 = (n conv n oo )cm 1 D 0 = 1 8068 (n conv 15598.3)eV. n conv = convergence limit = 20399.8 cm 1 (for exmple) This is obtined from the experimentl grph. Constnt Devition Spectrometer Prism tble Constnt devition prism Collimtor length Telescope objective Slit of mesured width Drum clibrted in wvelength Eyepiece Figure 2: Constnt devition spectrometer. A constnt devition spectrometer is shown in the figure. It consists of Hrtmnn slit diphrm, collimtor tube, specilly shped constnt devition prism, nd microscope to view the spectrum. The prism tble cn be rotted using drum which is cllibrted. By rottting the drum prticulr line of the spectrum cn be brought t the pointer, nd then the wve-length of the line cn be red out from the drum (provided the drum hs been ppropritely cllibrted). In this mnner, the wvelength of ll the lines of spectrum cn be found out.
Eqution (4) tells us tht if we plot λ versus 1 x x 0, we should get stright line. The slope of this line would be equl to, nd the intercept on the y-xis would give you λ 0. Thus, the other two constnts cn be determined from the grph. Hrtmnn Dispersion Formul When nrrow bem of white light psses through prism, it gets refrcted nd thus chnges direction when it comes out. More importntly, the extent of refrction depends on the wvelength of light. When this emerging refrcted light is mde to fll on flt screen, it forms vrious nrrow spots corresponding to different wvelength. Now it turns out tht even if the wvelengths present in the incident light re uniformly seprted from ech other, the resultnt spots on the screen re not uniformly seprted. In other words, dispersion does not follow liner reltionship with the wvelength. In fct, dispersion follows reltionship with the wvelength which is given by the Hrtmnn Dispersion Formul, which goes s x = x 0 + λ λ 0, (1) where x is the position of the line with wvelength λ, on the liner scle, nd x 0, nd λ 0 re undetermined constnts. This reltion cn be verified by using modified setup by putting trvelling microscope in plce of the eyepiece of the spectrometer. Determintion of unknown constnts Hrtmnn dispersion formul contins three unknown constnts, so we would need three independent equtions to determine them. Suppose we hve mde three observtions by mesuring the positions of the resultnt lines of three known wvelengths: Wvelength λ (Å) Line position x (cm) λ 1 x 1 λ 2 x 2 λ 3 x 3 Putting them in the Hrtmnn formul (1), we get Solving these, one obtins: x 1 = x 0 +, λ 1 λ 0 x 2 = x 0 +, (2) λ 2 λ 0 x 3 = x 0 +. λ 3 λ 0 x 0 = x 3(λ 3 λ 2 )(x 1 x 2 ) x 1 (λ 2 λ 1 )(x 2 x 3 ) (λ 3 λ 2 )(x 1 x 2 ) (λ 2 λ 1 )(x 2 x 3 ) (3) The other two constnts λ 0 nd cn lso be clculted, but we will be stisfied with one constnt for the time being. Now, eqution (1) cn lso be cst in the form: λ = λ 0 + x x 0, (4)
λ 1/(x x ) 0 Procedure Prt 1 Setup the CD spectrometer in front of the mercury lmp. Fix the drum t 5000 Å nd it should not be disturbed fter tht. djust the trvelling microscope so tht you cn go from one end of the spectrum to the other, using just the horizontl motion screw of the microscope. Once this is chieved, djust the trvelling microscope so tht cross-wires lie on the violet line of the spectrum. Note the horizontl scle reding of the trvelling microscope. Turn the horizontl motion screw until the next line comes on the cross-wires. Note the horizontl scle reding. Repet this procedure for ll the lines, until you rech the end of the spectrum. Once this is done, the cllibrtion of the spectrometer is possible. Prt 2 Next, replce the mercury lmp by n ordinry lmp. Put the tube contining iodine crystls between the light source nd the slit, so tht the light pssing through the tube flls on the slit. This might require bit of lignment. The result will be continuous spectrum rnging from red to violet. Het the tube uniformly using cndle or better, spirit lmp. At this stge the bsorption spectrum should be viewble through the microscope in its full glory. Study the spectrum crefully nd djust the slit width so s to increse the contrst of the drk bnds, nd to mke them shrp. Note the position of s mny bnds s possible, using the horizontl motion screw of the trvelling microscope. Cre should be tken to get s mny vlues s possible in the region where the bnds come closer to ech other. This region is crucil for getting the vlue of the dissocition energy. The region where the bnds come very close to ech other is the region of tht wvelength of light which, if bsorbed, dissocites the I 2 molecule.
Observtions nd clcultion Hrtmnn Dispersion Formul 1 λ (Å) Line position x (cm) x x 0 (cm 1 )(fter clculting x 0 ) Violet1 (4046.56) 2.888 0.221061 Violet2 (4077.83) 2.822 0.224334 Indigo (4358.33) 2.215 0.259698 Blue (4916) 1.402 0.329204 Green (5460.74) 0.885 0.396727 Yellow1(5769.60) 0.660 0.435611 Yellow2(5790.66) 0.647 0.438092 The constnt x 0 cn be clculted using the formul x 0 = x 3(λ 3 λ 2 )(x 1 x 2 ) x 1 (λ 2 λ 1 )(x 2 x 3 ) (λ 3 λ 2 )(x 1 x 2 ) (λ 2 λ 1 )(x 2 x 3 ) (5) Using the three lines with wvelengths 4047, 4358 nd 5461 we clculte x 0 : x 0 = 1.63562 Clculte 1/(x x 0 ) for ll the lines. Plot λ versus 1/(x x 0 ) for ll the points except the two yellow lines. Drw visul best fit line through these points, so tht the line intersects the y-xis. 6500 6250 6000 5750 5500 5250 λ 5000 4750 4500 4250 4000 3750 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 1/(x-x 0 ) Clculte the slope of the line, which will give you. You cn use the vlues of x 0, nd ny one reding to clculte λ 0. Alterntely it cn lso be red out s the intercept of the line. λ 0 = 2272Å = 8034Åcm Red out the wvelengths of other known lines from the grph nd note wht is the error.
Iodine bsorption spectrum Bnd no. x Wvelength (clculted from x) n (cm 1 ) (cm) λ (Å) 1.. 5750 1.739 10 4 2.. 5730 1.745 10 4 3.. 5700 1.754 10 4 4.. 5670 1.764 10 4 5.. 5640 1.773 10 4 6.. 5620 1.779 10 4 7.. 5580 1.792 10 4 8.. 5550 1.802 10 4 9.. 5520 1.812 10 4 10.. 5490 1.821 10 4 11.. 5470 1.828 10 4 12.. 5450 1.835 10 4 13.. 5430 1.842 10 4 14.. 5410 1.848 10 4 15.. 5390 1.855 10 4 16.. 5370 1.862 10 4 17.. 5350 1.869 10 4 18.. 5330 1.876 10 4 19.. 5320 1.880 10 4 20.. 5310 1.883 10 4 21.. 5300 1.887 10 4 22.. 5290 1.890 10 4 23.. 5280 1.894 10 4 24.. 5270 1.898 10 4 Now plot grph between the bnd number (on the x-xis) nd the wve-number n (on the y-xis) nd extrpolte the curve till the point where it becomes completely flt. This will give you the convergence limit n conv. 2 1.95 1.9 Wve number X10 4 1.85 1.8 1.75 1.7 0 5 10 15 20 25 30 35 40 45 50 Bnd number Figure 3: Plot between the bnd number nd its wvenumber.