Atomic and Laser Spectroscopy

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L-E B, OL, MOV 83 Atomic and Lasr Spctroscopy Th aim of this xrcis is to giv an ovrviw of th fild of lasr spctroscopy and to show modrn spctroscopic mthods usd in atomic, molcular and chmical physics.

Lasr Inducd Fluorscnc on molcular iodin Dtrmination of th molcular vibrational constants and th Mors potntial function of th molcular iodin, I X Σ ground stat. By using th HN 543.

1 L-E B, OL, MOV 83 Atomic and Lasr Spctroscopy Th aim of this xrcis is to giv an ovrviw of th fild of lasr spctroscopy and to show modrn spctroscopic mthods usd in atomic, molcular and chmical physics. In this laboratory charactristics of th iodin molcul will b studid by lasr spctroscopy. I. Lasr Inducd Fluorscnc on molcular iodin Dtrmination of th molcular vibrational constants and th Mors potntial function of th molcular iodin, I X Σ ground stat. By using th HN nm lasr lin xcitation of molcular iodin, containd in a small glass cll, can b prformd and lasr inducd fluorscnc (LIF) can b dtctd by using a small monochromator obsrving th fluorscnc. Th HN lasr lin will produc a progrssion of fluorscnc lins causd by transitions from th xcitd B 3 Π stat to diffrnt vibrational stats of th X Σ ground stat.. A synthtic spctrum of I fluorscnc, xcitd by a nm H-N lasr. Intnsity wavlngth / nm Fig.: synthtically gnratd spctrum of molcular iodin in th 53-8 nm wavlngth rgion; th intnsity pattrn of this spctrum is slightly diffrnt from th xprimntal on.

2 Aftr analysis of th spctrum, th molcular vibrational constants ω and ω x can b dtrmind. Th dissociation nrgy, D, of th X Σ ground stat can b dtrmind and th Mors potntial function can b calculatd.. Thory: th vibrational structur of diatomic molculs. Th Harmonic Oscillator Using classical mchanics and Hook's law on can discuss th vibrations of a diatomic molcul by applying a simpl modl: d x F kx m dt whr x is th displacmnt from th position of quilibrium and k is th forc constant. Th solution to this quation is a sinus function: x x sin(nft + φ) with f π whr f is th vibrational frquncy, x o is th vibrational amplitud and φ is a phas constant dpnding on th initial conditions. Th potntial nrgy of th harmonic oscillator is V(x) kx /. If w solv th Schrödingr quation for this potntial nrgy considring th rducd mass µ of th systm and with th quilibrium distanc btwn th two masss as r w nd up with th following nrgy ignvalus dpnding on th vibrational quantum numbr v: k µ E h k hf π µ ( v + / ) ( v / ) v + whr f π k µ This is th frquncy obtaind from a systm with mass µ attaind to a string with forc constant k vibrating around its quilibrium position. Th vibrational quantum numbr is v with th possibl valus,,,... Th zro point nrgy is hf / with v. Thus, th molcul is still vibrating though th vibrational quantum numbr is v. This is also th fact according to th Hisnbrg uncrtainty rlation. W can now dfin th vibrational nrgy G(v) in th following way: G( v) E! ( )! ( v +/ ) hc f c v +/ whr ω dnots th vibrational frquncy in cm - and v is th vibrational quantum numbr. In Fig.5, potntial nrgy diagram is givn showing both th vibrational nrgy lvls as wll as th potntial curv.

3 Fig. 5. Th vibrational nrgy lvls of a diatomic molcul. If w hav a transition btwn two vibrational stats within th sam lctronic stat th wavnumbr σ /λ for th corrsponding radiation is givn by: Ev' Ev" σ G(v') G(v") hc hc v and v ar th vibrational quantum numbrs for th uppr and lowr vibrational lvls.. Th Anharmonic Oscillator. Th dscription of molculs by using th harmonic oscillator is mrly a first ordr approximation of a mor gnral cas. If for instanc th bond btwn th atoms is strtchd thr coms a point whr it will brak - th molcul thn dissociats into atoms. Thus, for largr amplituds of th xtnsion of th bond a mor complicatd dscription has to b applid. A purly mpirical xprssion, which fits this curv to a good approximation, is th Mors function: V ( r) D a( r r) [ ] whr a is a constant for a particular molcul and D is th dissociation nrgy. If w now apply this nrgy function and us it in th Schrödingr quation th vibrational nrgy lvls ar found to b: G(v) ω (v + /) - ω x (v + /) + ω y (v + /) 3 ( v,,,...) Th so calld zro-point nrgy can b obtaind by putting v. Thus w obtain approximatly G() ω / as th nrgy of th v lvl. This point lis ω / units abov th lowst part of th potntial nrgy curv. In this xrcis, w us a lasr lin of th HN lasr (543.5 nm). This wavlngth accidntally coincids with th nrgy of th vibrational lvl u 6 of th xcitd stat B 3 Π of iodin. Th fluorscnc spctrum is collctd whn this stat rlaxs to th ground stat. Th xcitd stat s vibrational lvls ar also found to b: 3

4 F(u) T + ω (u + /) - ω x (u + /) + ω y (u + /) 3 (u, ) with diffrnt vibrational constants ω, ω x, ω y. Fig. 6: Mors potntial of both xcitd and ground stats of th iodin molcul. Whn th xcitd stat u 6 dcays to any vibrational lvl of th ground stat, th nrgy diffrnc σ can b xprssd as: σ v F(u 6) - G(v) So, if w tak th diffrnc btwn two adjacnt fluorscnt missions: σ v - σ v+ (F(u 6) - G(v)) (F(u 6) - G(v+)) G(v+) - G(v) Lt us now calculat this xprssion to obtain th vibrational constants of an unknown spctrum: ΔG(v+l/) G(v+l) - G(v) ω - ω x (v + ) + ω y (3v + 6v + 3/4)

5 In a spctrum whr a vibrational progrssion can b sn, th sparation btwn two adjacnt vibrational lins is approximatly givn by: σ v - σ v+ G(v+l) - G(v) ω - ω x - v ω x As ω >> ω x, th sparation is roughly around ω. Not that this xprssion is a linar function of v. Th plot of σ v - σ v+ vrsus v is calld a linar Birg-Sponr xtrapolation. If w incras th quantum numbr v w will rach a point whr th diffrnc ΔG(v+/) btwn two succssiv lvls bcoms vry small, i.. at th nrgy qual to V ( ). Th summation of th combination diffrncs will giv D ΔG(v + / ) v Birg and Sponr gav a graphical mthod to obtain this summation as is shown in Fig.6. v 8 Fig.6. Linar Birg-Sponr xtrapolation. Th ara undr th curv givs th valu of D, which is in our cas approximatly qual to D. Whn using th linar xprssion of ΔG(v+/) making th summation, on obtains th following xprssion: D ω 4ω x Evaluation of this constant can thn b usd in ordr to obtain th Mors potntial function dscribd arlir: V( r) D a( r r) [ ] This is just on of svral mpirical formula proposd to giv th molcular potntial curv. If w simply xpand th potntial as a Taylor sris in (r r ), th following xprssion is obtaind: r r! r r 3! V (r) V (r ) + (r -r ) V (r ) + ( ) ( ) V"( r ) + V ( r ) 3 5

6 Classically w can compar this with th rsult obtaind from th harmonic oscillator whr Hook s law F - k (r - r ) givs ( r r ) V ( r) k By comparing th xprssions w s that th forc constant k V"(r). Taking th drivativs of th Mors quation w obtain at r r V(r ) ; V (r ) a D This lads to th following quation ha ω x 6π cµ whr µ is th rducd mass, h Planck s constant and c th spd of light From th litratur w can tak th rotational constant B to obtain th quilibrium distanc r by using th xprssion: B h 8π cµ r Thus w can driv th Mors potntial function knowing th xprimntally drivd constants ω, r and D. 6

$In ordr to gt good spctra, choos diffrnt xposur tims of th monochromator-ccd stup. For som filtrs it is possibl to s also th scond ordr diffraction pak.$

7 . Exprimntal part: task during th xrcis Calibration Calibrat th spctromtr systm by using 4 Hg filtrs and th light from th roof lamps. Us th mirror and th lns to focus th light into th spctromtr. In ordr to gt good spctra, choos diffrnt xposur tims of th monochromator-ccd stup. For som filtrs it is possibl to s also th scond ordr diffraction pak. Rmmbr that diffraction is govrnd by th Bragg s law n λ d sinϑ whr n is th ordr of th intnsity maximum, d is th lattic constant and ϑ is th angl at which occurs th maximum. Whn th spctrum looks nic, tak th valu of th pak channl (first and scond ordr diffraction pak), using th PEAK command: writ ths valus in a tabl with th corrsponding filtr wavlngths, plot wavlngths vrsus channls and prform a linar last squars fit (you can us Excl or MatLab on th computr in th lab, or whatvr othr programs you hav). Th bst fit quation givs you th calibration of th spctromtr. Fig.. Ovrviw of th st-up ndd in ordr to calibrat th spctromtr. Lasr Spctroscopy Th HN grn lasr is usd to xcit molcular iodin (I ) from th X Σ ground stat to th B 3 Π xcitd stat. Th grn HN lasr lin at nm coincids (by accidnt) with a branch of th B 3 Π - X Σ I transition. A monochromator quippd with a linar diod array consisting of 48 diods is usd to rcord th spctra.. Switch on th lasr by turning th ky of th powr supply and lin up th optics. OBS!: th HN lasr light has th powr of.5 mw and can caus damag on th y if you look dirctly into th lasr.. Put th iodin cll blow th lasr and align th fluorscnc light mittd by th gas into th ntranc slit of th monochromator. 7

8 3. Us a pic of papr in front of th spctromtr to chck if th fluorscnc light is corrctly alignd. In ordr to gt good spctra it is ncssary to us background subtraction and avrag svral spctra (s blow). 4. Rcord th channl numbr for ach lin of th I LIF spctrum and thn dtrmin th wavlngths using th calibration quation; calculat th corrsponding wavnumbrs σ in cm - and Δσ ij /λ i /λ j btwn two adjacnt lins. Not that ach spctrum lin corrsponds to a particular vibrational quantum numbr ν. OBS!: th I spctrum lis btwn 5 nm and 9 nm and it is ncssary to rcord up to 3 lins in ordr to hav good rsults. 5. Plot Δσ as a function of vibrational quantum numbr ν. Prform a linar last squars fit (Birg-Sponr xtrapolation) and dtrmin ω and ω x. Calculat also th dissociation nrgy D in cm -. Compar your valus of ω and ω x with th thortical ons you find on th NIST wb pag (s blow How to us th NIST chmistry wbbook pag ). Obsrv that your D valu is not th sam as th D givn at NIST wb pag. Thr, D is th distortion constant for rotational nrgy. It cannot b dtrmind in th prsnt xprimnt. 6. Calculat th molcular constant a using th formula for ω x, and th quilibrium distanc r from th rotational constant B. You find th valu of B on th NIST wb pag. Dtrmin and plot th Mors potntial function. 8

9 How to us th NIST Chmistry WbBook pag... First you go to th NIST link: And lt s say you ar sarching for th quilibrium intrnuclar distanc r of th hydrogn (H ) molcul in th xcitd stat C Π u pπ. So In th sarch options, click on formula. In th pag, fill itm with H. You ar sarching for somthing that blongs to th constants of diatomic molculs part, so that s what you slct in th itm 4. In th following pag a lot of data will appar, and whn you scroll down you will s a tabl that looks lik this: Stat T ω ω x ω y B α γ D β r Trans. ν n 3 Π u 5pπ m 3 Σ u + 4fσ Richardson, 934; Dik, 958 (937) 8 [.3].57 n a [457.] 6 m a Richardson, Yarrow, t al., 934 s 3 Δ g 4dδ r 3 Π g 4dπ s c Richardson, 934; Fostr and Richardson, 953; Dik, r c Richardson, 934; Fostr and Richardson, 953; Dik, 958 OK Hr you hav to sarch for th stat you want (C Π u pπ), and tak not of th valu you want. BUT, you hav to b carful: th symbols may diffr to th ons you us, or th units. So how do you chck this out? If you look carfully in th initial pag ( you will s a titl that says Documntation. A fw links ar on display, among thm A Guid to th NIST Chmistry WbBook. Click on it. A lot of links will appar aftr th titl Contnts. In part iv. Data Availabl is th itm k. Constants of Diatomic Molculs. This is what you ar sarching for. Whn you click on it, an xplanation of ach symbol maning will appar, somtims with units. Th symbols that do not hav units, ar in th standard units, for xampl th nrgy and th wavnumbr is in cm -. In this cas, you sarch for Intrnuclar distanc in Å, r. So, in th pag of th data of th hydrogn, you hav to go to th tabl, sarch for th nam of th stat and find th valu givn aftr r, in this cas th answr is:.37 Å. If you want, you can us also Nam and fill itm with hydrogn.

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum