Atomic Emission Spectra Using a UV Vis Spectrophotometer and an Optical Fiber Guided Light Source


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1 Atomic Emission Spectr Using UV Vis Spectrophotometer nd n Opticl Fiber Guided Light Source Mnuel E. Mins d Piedde Centro de Químic Estruturl, Complexo I, Instituto Superior Técnico, 096 Lisbo Codex, Portugl Mário N. BerbernSntos Centro de QuímicFísic Moleculr, Complexo I, Instituto Superior Técnico, 096 Lisbo Codex, Portugl The study of tomic emission spectr in the undergrdute lbortory hs been suggested for mny yers to illustrte quntum mechnicl principles (e.g., the ide tht microscopic mtter exists in quntized sttes) nd the reltion between the electronic structure nd spectrl observtions ( ). Becuse of the simplicity of its spectrum, hydrogen is by fr the element of choice in published experiments in tomic spectroscopy ( 5, 8, 0, ), but experiments involving other elements such s lkli metls hve lso been reported (6, 7, 9). Severl types of pprtus hve been used to record the spectr, including n tomic bsorption spectrophotometer (), spectroscopes ( ), spectrogrphs (5 8) nd UV vis spectrophotometers (9 ). In ll pprtuses of the ltter type, the light source is either prt of the spectrophotometer (deuterium lmp), yielding only few s (), or when not prt, is plced inside the instrument (9, 0) nd is therefore difficult to interchnge. This mkes imprcticl the study of more thn one element in lbortory session. As shown in the present pper, the use of n opticl fiber to guide the light from n externl source onto the monochromtor of the spectrophotometer enbles fst sequentil use of severl light sources, irrespective of their size nd shpe. This setup hs been in use in our undergrdute physicl chemistry lbortory to study the emission spectr of hydrogen, sodium, nd helium in fourhour session. The experiment cn be redily extended to other elements (e.g., Hg, Li, K, Xe, Ne) or modified to obtin moleculr spectr from dischrge tubes nd lmps (e.g., N, D, H ) nd tomic nd moleculr spectr in flmes (e.g., lkli metls, C ), provided the pproprite light sources re vilble. Apprtus The pprtus used consists of PerkinElmer Lmbd 5 spectrophotometer, plstic opticl fiber with dimeter of 3.0 mm from Lser Components GmbH (PGRFB3000 Plstikfser), nd light source. In the cse of hydrogen nd helium light source from ElectroTechnic Products, Inc., including Spectrum tube power supply SP00 (5 kv, 0 ma) nd n interchngeble gs dischrge lmp ws used. The spectrum of sodium ws recorded using Bellinghm+ Stnley Ltd. sodium lmp unit removed from polrimeter. The opticl fiber is introduced into the spectrophotometer through preexisting hole on the housing bottom nd fixed by clmp support ner the entrnce of the monochromtor. Another clmp support is used to djust the position of the fiber ner the externl light source. The hydrogen nd helium light sources re plced t distnce of c. 0.5 cm from the tip of the opticl fiber in order to void dmge to the fiber by the het generted t the source lmp. In the cse of the much more intense sodium lmp, longer distnce (c. 8 cm) is required to prevent photomultiplier sturtion. Recording the Spectr The PerkinElmer Lmbd 5 spectrophotometer is operted in the singlebem mode ccording to the mnufcturer s instructions. A preliminry scn is mde t scn speed of 0 or 0 nm min, to djust the bndpss nd gin so tht the intensity of the stronger s observed in the spectrum does not exceed c. 00. To conveniently detect the weker s it my be necessry to record other spectr with incresed bndpss nd/or gin. In the cse of sodium, for exmple, fter the preliminry scn nd the selection of convenient bndpss nd gin, globl spectrum, without resolved doublets, is recorded. Then, slow scns t 7.5 nm min nd bndpss = 0.5 nm re mde in the ner rnge of ech unresolved detected in the previous spectrum. It is then possible to observe firly resolved doublets (well resolved only for the longer wvelengths, c. λ 568 nm). The typicl wvelength rnges covered in the experiment re nm for hydrogen, nm for sodium, nd nm for helium. The wvelength clibrtion of the pprtus ws checked with mercury lmp from ElectroTechnic Products, Inc. Results nd Discussion Using the pprtus nd experimentl procedure described bove, 8 s (prt of the Blmer series) re observed for hydrogen, t lest 8 doublet s re observed in the cse of sodium, nd minimum of 5 s re observed for helium. Becuse of the intrinsic bsorption of the opticl fiber used, the lowest mesurble wvelength is bout 350 nm. No specil precutions re tken to eliminte the contmintion by mbient light. Spectr obtined t high gins nd with wide bndpsses my, however, show extrneous contributions (e.g., the strong mercury s of fluorescent lmps in the lbortory ceiling). Typicl results obtined by the students for hydrogen re nm (H θ ), nm (H η ), nm (H ζ ), nm (H ε ), 0.0 nm (H δ, h ), 33.6 (H γ, G ), 86. nm (H β, F ), (H α, C ) (see ref for ssignments). Those for sodium nd helium re shown in Tbles nd nd in Figures nd. The intensities indicted in Tbles nd re not bsolute, since the efficiencies of the opticl system nd of the photomultiplier of the spectrophotometer re wvelength dependent. The students re sked to complete tsks described in the following sections. JChemEd.chem.wisc.edu Vol. 75 No. 8 August 998 Journl of Chemicl Eduction 03
2 Tsk Assignment of the s in the obtined spectr by comprison with literture dt nd construction of the Grotrin digrm ( ) showing the energy levels nd the observed trnsitions for hydrogen, sodium nd helium (Figs. 3 nd ). Verifiction of the selection rules l = ± nd j = 0, ± for hydrogen nd sodium, nd l = ± nd L = 0, ±, S = 0, J = 0, ± for helium, where l nd L re the orbitl ngulr momentum quntum numbers, j nd J re the totl ngulr momentum quntum numbers for toms tht cn be considered s mono (e.g., H nd N) nd poly (e.g., He) electron species, respectively, nd S is the totl spin ngulr momentum quntum number ( ). Tsk Clcultion of the Rydberg constnt, H, nd the ioniztion energy, IE, of hydrogen using the following equtions ( ): λ = H n n () IE = H hc () where λ represents the wvelength, n = (Blmer series), n is n integer lrger thn n, h is the Plnck constnt, nd c is the velocity of light. A lest squres fit of eq to plot of /λ vs /n, using n = 3 0 for λ = nm, leds to H = (.098 ± 0.00) 0 5 cm. (All uncertinties quoted throughout this pper correspond to the stndrd devition multiplied by Student s t prmeter for 95% confidence level.) This result is in good greement with the theoreticl vlue H = 09,677.6 cm (clculted from ): Tble. Wvelengths nd Intensities of Atomic Sodium Emission Lines λ / nm (in ir) Intensity/ O bserved Assignment ( ) Devition rbitrry units (6 D5/,3/ 3 P / ) (6 D5/,3/ 3 P 3 / ) (7 S / 3 P / ) 75. (7 S / 3 P 3 / ) ( 5 D5/,3/ 3 P / ) (5 D5/,3/ 3 P 3 / ) (6 S / 3 P / ) (6 S / 3 P 3 / ) ( D5/,3/ 3 P / ) ( D5/,3/ 3 P 3 / ) ( 3 P 3/ 3 S / ) D ( 3 P / 3 S / D ) ( 5 S / 3 P / ) ( 5 S / 3 P 3 / ) ( 3 D 5 /, 3/ 3 P / ) ( 3 D5/,3/ 3 P 3 / ) Unresolved doublet. b Clculted using the verge doublet wvelength. = µe 8ε 0 h 3 c where e represents the elementry chrge, ε 0 is the vcuum permittivity, h is the Plnck constnt, c is the velocity of light, nd µ is the reduced mss of the nucleus + electron system given by (3) Figure. Sodium emission spectrum (see Tble for ssignments nd reltive intensities). The observed doublet structure recorded t 7.5 nm min is shown for selected s. K is the resonnce doublet from potssium impurity. S/ S/ P/ D5/, 3/ µ = m N m e m N + m e () where m N nd m e re the msses of the nucleus nd of the electron, respectively. From the obtined Rydberg constnt, (.098 ± 0.00) 0 5 cm, nd eq it is possible to conclude tht for hydrogen IE = 3.6 ± 0.03 ev, in good greement with the vlue IE = ev recommended in ref 5. It should be noted tht for more ccurte work the conversion of the experimentl wvelengths, mesured in ir, to the corresponding vlues in vcuum must be tken into ccount (8, ). In our cse, however, this correction is well within the experimentl error nd ws therefore neglected. Tsk 3 Clcultion of the Rydberg constnt nd of the ioniztion energy of sodium. Clcultion of the quntum defect corrections for the shrp (S, ns 3p), principl (P, np 3s), Energy / ev nm 65.3 nm nm 66.0 nm 7.9 nm nm 66.6 nm 98.0 nm nm 89. nm 568. nm 88. nm 6 5 Figure 3. Grotrin digrm for sodium showing the trnsitions observed in the lbortory (see lso Tble ). The trnsitions t 66.6, 7.9, 98.0, nd 55. nm correspond to unresolved doublets. 3 0 Journl of Chemicl Eduction Vol. 75 No. 8 August 998 JChemEd.chem.wisc.edu
3 Tble. Wvelengths nd Intensities of Helium Emission Lines λ / nm (in ir) Intensity/ O bserved Assignment ( ) Devition rbitrry units ( 5 P S 0 ) ( 3 3 P,, 0 3 S ) ( P S 0 ) b ( 5 D 3,, 3 P,, 0) 0. b.9. ( 5 S 3 P,, 0) ( 5 D P ) ( D 3,, 3 P,, 0) ( S 3 P,, 0) 0. b ( D P ) 0. 5 b b ( 3 P S 0 ) 0. 5 b ( S 0 P ) ( 3 3 D 3,, 3 P,, 0 D ( 3 ) 0. 7 b D P ) 0. 3 b ( 3 S 3 P,, 0) ( 3 S 0 P ) b Bndpss = nm, gin = 5. b Bndpss = nm, gin = 5. nd diffuse (D, nd 3p) series of sodium. Anlysis of the doublet structure of the sodium s. The nlogue of eq for sodium is the empiricl eqution ( ) λ = N n δ n l n δ n l (5) where N is the Rydberg constnt for sodium, n = 3,, nd 5 for the P, D, nd S series, respectively, n is n integer equl to or lrger thn n, nd δ n l nd δ n l re the quntum defects or Rydberg corrections. The quntum defect is relted to the interction of the electron whose trnsitions produce the spectrum with the inner core electrons; it is pproximtely constnt for levels of different principl quntum number, n, but with the sme orbitl ngulr momentum quntum number, l (i.e., for the sme series) ( ). The vlue of the quntum defect increses with the degree of penetrtion of the corresponding orbitl. It tkes, therefore, the highest vlues for the S series nd is close to zero for the D series (see below). Eqution 5 ws seprtely fitted to the dt of the diffuse nd shrp series shown in Tble, in the form λ = A n B + C (6) where A, B, nd C re the fitting prmeters, given by A = N (7) B = δ n l (8) Figure. Helium emission spectrum (see Tble for ssignments nd reltive intensities). C = N n δ n l (9) Energy / ev S0 P D 3 S 3 S 3 D3,, 50.5 nm 78.0 nm 36.0 nm 396. nm 50. nm 38.6 nm 9.0 nm nm 706. nm.9 nm 7. nm nm 0. nm 6.9 nm nm Figure. Grotrin digrm for singlet () nd triplet (b) helium showing the trnsitions observed in the lbortory. The corresponding wvelengths re given in Tble. The vlues of these prmeters were found by using the Solver tool of MS Excel 7.0 to minimize the sum of the squres of the devitions between clculted nd experimentl wvelengths (Tble 3). The uncertinties of the prmeters re not determined in the cse of this nonr fit. This cn be done by Monte Crlo simultion (6), but the clcultion is beyond the scope of this lbortory experiment. Comprison of the results obtined for H, N, nd He, with the corresponding (more ccurte) literture vlues, however, llows n posteriori estimtion of the ccurcy of the Rydberg constnts nd quntum defects obtined from eq 6. Accurcies better thn % re found for the Rydberg constnts, nd in the cse of the quntum defects two to three exct deciml plces re observed. From the dt in Tble 3 nd eqs 6 9 it is possible to conclude tht for the diffuse series δ n d = 0.000, δ 3p = 0.876, nd N = 0,5 cm. These results re in good greement with those reported by Stfford nd Wortmn, which ssumed tht δ nd = 0 nd used r djustment of eq 5 to /λ vs. /n plot to derive δ 3p = 0.88 nd N = 0,600 cm (9). Note, however, tht the Rydberg constnt obtined in the present experiment, N = 0,5 cm, is too high when compred to its theoreticl vlue N = 09,73.7 cm cl JChemEd.chem.wisc.edu Vol. 75 No. 8 August 998 Journl of Chemicl Eduction 05
4 culted from eq 3. In ddition, the quntum defect for the 3p level, δ 3p = 0.876, is lower thn the vlue δ 3p = recommended in (,, 7). For these resons, constrined djustment of eq 5 to the experimentl dt, with N = 09,73.7 cm, ws lso crried out. A slightly worse fit (mximum devition equl to 0. nm) ws obtined, yielding quntum defects δ nd = nd δ 3p = 0.883, in very good greement with the published vlues δ nd = 0.0 nd δ 3p = (,, 7). For the shrp series, the best fit (Tble 3) gve quntum defects δ ns =.36 nd δ 3p = 0.885, nd Rydberg constnt N = 0956 cm ; but imposing gin N = cm yields quntum defects, δ ns =.36 nd δ 3p = 0.883, in better greement with the literture vlues δ ns =.36 nd δ 3p = (,, 7 ). Note, finlly, tht since not ll the doublets of ech sodium were well resolved in the obtined spectrum, the men wvelength vlue of ech doublet in Tble ws selected for the clcultions. For more ccurte clcultion the wvelengths of just one of the two spinorbit components should be used. The mgnitude of the spinorbit coupling cn lso be evluted for the resolved doublet s. In the cse of the D, for exmple, spinorbit coupling of 7.3 cm is obtined from the experimentl dt in Tble. This result is in good greement with the published vlue of 7. cm (). It is lso interesting to note tht very well resolved doublet from potssium impurity is observed in the spectrum of sodium t wvelengths nd nm. This doublet is the equivlent in potssium of the sodium D. In this cse, spinorbit coupling of 57.6 cm is clculted, in good greement with the published vlue of 57.7 cm (). The strong dependence of the spinorbit coupling on the tomic number Z it increses with Z ( ) is clerly seen by compring the obtined results for sodium nd potssium indicted bove (7.3 cm nd 57.6 cm, respectively). Another possible topic of discussion is the reltive intensity of the two components of the doublet s. For instnce, in the cse of the D, the theoreticl rtio between the intensities of the P 3/ S / nd P / S / components is :; tht is, tht of the sttisticl weights (j + ) of the corresponding upper sttes (). For most commercil lmps the mesured rtio is frequently lower owing to the rebsorption phenomenon (), which is importnt when the concentrtion of the sodium toms is high. In our cse rtio of.3: is observed (Fig. ). If, however, the D doublet spectrum is recorded immeditely fter turning the lmp on (when the concentrtion of N in the vpor is low) the theoreticl rtio of : is indeed observed. The first ioniztion energy of groundstte sodium cn lso be clculted from the spectrl dt ( ). In this clcultion it is ssumed tht the ioniztion process cn be decomposed in two steps: in the first one, groundstte sodium is excited to the 3 P stte (energy required = hν =. ev, where ν is the frequency of the D ); in the second, sodium in the 3 P stte is further excited to the ioniztion limit. The energy required for this second step corresponds to the limit n of eq 5 nd is thus given by the constnt C of eq 6. Conversion of the C vlues in Tble 3 to ev leds to C = 3.0 ev. Thus, IE N = 5.5 ev is derived, in good greement with the recommended vlue, IE N = ev (5). Tble 3. BestFit Vlues of A, B, nd C Prmeters (Eq 6) for Sodium D nd S Series Series A/cm Tsk Clcultion of the Rydberg constnt nd the ioniztion energy of helium. Clcultion of the singlet triplet gp for the P sttes. In the cse of helium singlet nd triplet D series the following empiricl eqution is vlid (): λ = He B C/cm D 0, ,505 S 09,56.359,89 n n δ 3p (0) where He is the Rydberg constnt for helium, n = 3,, nd 5, n =, nd δ 3p represents the quntum defect for the singlet or triplet 3P stte. According to eq 0, plot of /λ versus /n should give stright of slope He nd intercept He /( δ 3p ). Lest squre fits to the results in Tble led to He = 0,000 ± 00 cm nd δ 3p = 0.0 for the singlet series nd He = 0,00 ± 600 cm nd δ 3p = for the triplet series. The corresponding vlues in ref re He = 09,7 cm nd δ 3p = nd for the singlet nd triplet series, respectively. The ioniztion energies of the P nd 3 P sttes cn lso be clculted from the intercepts of the lest squre fits referred to bove. The obtined vlues, 3.37 ± 0.0 ev for P nd 3.63 ± 0.0 ev for 3 P sttes, re in excellent greement with the corresponding vlues in ref, ev ( P) nd 3.6 ev ( 3 P), respectively, nd led to singlet triplet gp of 0.6 ev. As for sodium, the ioniztion energy of groundstte helium cn be clculted by dding the energy of the P S 0 trnsition (.3 ev), which in this cse is tken from the literture (), to the ioniztion energy of the P stte indicted bove (3.37 ev). This leds to IE He =.60 ev, in good greement with the vlue.587 ev recommended in ref 5. Concluding Remrks The experiment described is fst ( fourhour session) nd simple nd yields ccurte results. It illustrtes number of importnt topics in tomic structure nd tomic spectroscopy tht re covered in ll undergrdute physicl chemistry courses but often not studied in the lbortory owing to the lck of pproprite equipment. The required pprtus is ssembled with common instruments (polrimeter or refrctometer sodium lmp nd UV vis spectrophotometer), the dditionl equipment required being only plstic opticl fiber, lowcost hydrogen nd helium dischrge tubes, nd pproprite power supply. It cn lso be used to obtin moleculr spectr from dischrge tubes or lmps (e.g., N, D, H ) nd 06 Journl of Chemicl Eduction Vol. 75 No. 8 August 998 JChemEd.chem.wisc.edu
5 tomic nd moleculr spectr in flmes (e.g., lkli metls, C ). Finlly, the present lbortory experiment cn motivte the discussion of more dvnced topics in tomic spectroscopy, such s the hydrogen fine structure (, 8) nd Rydberg sttes (, 9), nd of the working principles of spectroscopic components, such s dischrge tubes (0), opticl fibers (), monochromtors (8, ), nd photomultiplier detectors (8). Literture Cited. Dougls, J.; von NgyFelsobuki, E. I. J. Chem. Educ. 987, 6, 55.. Compnion, A.; Schug, K. J. Chem. Educ. 966, 3, Reiss, E. J. Chem. Educ. 988, 65, 57.. Shields G. C.; Ksh, M. M. J. Chem. Educ. 99, 69, Rppon, M.; Greer, J. M. J. Chem. Educ. 987, 6, McSwiney, H. D.; Peters, D. W.; Griffith, W. B., Jr.; Mthews, C. W. J. Chem. Educ. 989, 66, Miller, K. J. J. Chem. Educ. 97, 5, Shoemker, D. P.; Grlnd, C. W.; Nibler, J. W. Experiments in Physicl Chemistry; McGrwHill: New York, Stfford, F. E.; Wortmn, J. H. J. Chem. Educ. 96, 39, Hollenberg, J. L. J. Chem. Educ. 966, 3, 6.. Guiñón, J. L. J. Chem. Educ. 989, 66, Kuhn, H. G. Atomic Spectr; Longmns: London, Softley, T. P. Atomic Spectr; Oxford Chemistry Primers Series; Oxford University Press: New York, 99.. Hken, H.; Wolf, H. C. The Physics of Atoms nd Qunt, 5th ed.; Brewer, W. D., trnsl.; Springer: Berlin, Hndbook of Chemistry nd Physics, 7th ed.; Lide, D. R., Ed.; CRC: Boc Rton, Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flnnery, B. P. Numericl Recipes, nd ed.; Cmbridge University Press: Cmbridge, Slter, J. C. Quntum Theory of Atomic Structure, Vol. I; McGrw Hill: New York, Powell R. E. J. Chem. Educ. 968, 5, Silvermn, M. P. And Yet it Moves Strnge Systems nd Subtle Questions in Physics; Cmbridge University Press: Cmbridge, Lewin, S. Z. J. Chem. Educ. 965,, A65.. MellirSmith, C. M. J. Chem. Educ. 980, 57, 57.. Guiñón, J. L, GrciAnton, J. J. Chem. Educ. 99, 69, 77. JChemEd.chem.wisc.edu Vol. 75 No. 8 August 998 Journl of Chemicl Eduction 07
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