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Stark effect on emission spectra of carbon monoxide Fisher, Nina Jo-Anne 1972

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STARK EFFECT ON EMISSION SPECTRA OF CARBOR WUIMOXIDE by NINA JO-ANNE FISHER B.Sc., University of British Columbia, 1969. A THESIS SUBMITTED IN PARTIAL FUi-FILwENT OF THE REQUIREMENTS FOR THE DEGREE OF RASTER OF SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER, 1972. In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my Department o r by h i s r e p r e s e n t a t i v e s . I t is u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f 7 The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8 , Canada ABSTRACT The electronic emission spectra of the CO molecule in an applied electric field of 53-8 ^ilovolts/cm nas been oDserved. The electric field was determined from the Star* Effect on the Hy line at 43^0A. The spectra were produced in the nign field region of a low pressure glow discharge using carbon monoxide gas and water vapour. The electric dipole moment of tne CO molecule nas been determined for the BlZ*state using the P(l) transition of the Angstrom ( 0 , 0 ) band. The effect observed is a second order effect in the B 1 .Testate and it has. been deduced that tne dipole moment of the A1?/ state is very small or zero. The dipole moment of cne B 1 Z fstate is 1.6l debye 4-iii TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1 Footnotes for Chapter 1 4 CHAPTER 2: Theory 6 The Motion of the Nuclei 6 The Motion, of the Electrons 13 Coupling of Nuclear and Electronic Motion 15 Characteristics of the 'Z^and 'Tf States of' CO 19 The Dipole Moment 24 The Effect of an Electric Field Upon the Dipole Moment .24 First Order StarK Effect 25 Second Order Stark Effect 30 Footnotes for Cnapter II 33 CHAPTER III: EXPERIMENTAL DETAILS " 34 Electric Discharge Tube .'.....34 Production of the Spectra 38 Observation of the Spectra 39 Determination of the Electric Field Strength 42 Footnotes for Chapter III 48 CHAPTER IV: EXPERIMENTAL OBSERVATIONS ' 49 Analysis of the Spectra 49 Measurements 53 Computations * 55 Determination of the Dipole Moment of une B 'Z + State of CO 62 Footnotes for Cnapter IV c4 CHAPTER V: CONCLUSION AND SUGGESTIONS FOR FURTHER STUDY LIST OF TABLES TABLE I: First and Second Order Stark Coefficients for and '7f States (in cm"1) 32 TABLE II: Conditions for Production of the CO Stark Spectra 41 TABLE III: Stark Effect Coefficients for H(4340A) 44-TABLE IV: Calculation of the Stark Shift of the Components of H(4340A) 47 o TABLE V: Measurements of selected lines of the Angstrom (0,0) hand in the region of maximum electric field (M) and zero electric field(Z) 54 TABLE VI: Method 1: The difference between measurements taken in maximum electric field and in zero electric field 56 TABLE VII: Method 2: The difference between P(1) and each measured line in zero field, and in the maximum field A ^ 57 TABLE VIII: Values obtained for P(1) (in microns) 59 TABLE IX: Calculation of Plate Dispersion 61 vi LIST OF FIGURES Figure 1: Rotation in two particle system ana in center of mass system 8 Figure 2: Vibration in two particle system and. in center of mass system II Figure 3: Vector diagram of Hund's case (a)'. 16 Figure Vector diagram of Hund's case (D). 17 Figure 5: Vector diagram of Hand's case (a) 18 Figure 6: Energy level diagram snowing Angstrom and Herzberg transitions 20 Figure 7: Transitions between I f and f states of CO 23 Figure 8: Classical derivation of the first order Stark Effect 28 Figure 9: First Order Stark Effect on 1 Z r and 1 Tf states of CO 29 Figure 10: Gas Discharge Tube 35 vii LIST OF PLATES Plate 1: Stark Effect on Hydrogen(4340A) 43 Plate 2: Stark Effect on CO Angstrom (0,0) band at 451 OA 50 Plate 3= Stark Effect on CO Herzberg(0,3) band at 4380A 52 Plate 4: C0+(0,1) Band of Baldet-Johnson' System 66 viii AC KNOtfLEDGEfoEriTS I would like to thank Professor F.W. Daiby for nls patient encouragement and criticism during the four summers wnicn i nave worked in his laboratory. I would also liKe to thanx my husband and my parents i for their moral support during the writing of tnis tnesis. CHAPTER I INTRODUCTION When an external electric field, is applied to an atom or molecule, shifts and splittings are observed in cue spec era. This phenomenom, known as the Star a Effect, proviues a wetnoa of determining the electric dipole moment of a molecule and therefore gives some information about the distribution of electric charge within the molecule. This study is concerned with the electric dipole moment of CO in. the A ana B states. The theory of the StarK Effect in molecules nad been discussed in the 1930's by W.G. Penney 1 and J.H. Van Vlecx 2; and has been treated more recently by Jon H. Shirley3 ana Jonn R Lombardi^. In addition, Guderova and Posdeev-5 nave pubiisned analytical expressions for the matrix elements on trie oasxs of an asymmetric top model and suggest methods of calculation suitable for computer application. On the experimental side-,* even though the Star a Effect on atomic hydrogen had been observed as earxy as 1913 by StarK° and LoSurdo?; by the 1930's only molecular hydrogen nad shown a Stark Effect. One of the molecules studiea rather intensively during this period was CO. In an exhaustive review of the literature and spectroscopic data on CO, C0^> anci C 0 2 + up to 1965, Paul H. Krupenie states: "All experimental attempts to observe the S tar a ki'lect in the electronic spectra of CO and CO* have yielded negative results because of insufficient resolution. Svensson a observed no splitting in the B-A bands of CO in fields up to 115kv/cm using a dispersion of 4A/mm. Steubing failed to observe splitting in the C 0 + B-X bands with fields up to ° c 67 kv/cm, and dispersion of 5-9A/mm. Rave observed no shift in fields up to 250kv/cm for the 4- ° 8 A-X bands(CO ) with dispersion of 1OA/mm." The main difficulty lay in the small Stark Effect predicted for molecular spectra combined with the limitations of low resolving power. q Theoretical calculations by R.C. Sahni^ in 1955 predicted a dipole moment of 1.00 debye for the ground state. The calculation is extremely sensitive to the electronic contribution to the total moment and a change of only 2% in this value gives a large change in the predicted value for 10 the dipole moment. More recent theoretical calculations yield values ranging from .061 debye to .69 debye depending upon the type of calculation and the assumed polarity of 11 the CO molecule. In a calculation by Stevens and Karplus in 1968, the value J U U = .14 debye was obtained assuming the polarity C~0 +. 12 In 1958, C.A. Burrus measured the dipole moment of the ground state (X'Z. ) of CO. Using microwave techniques and fields up to 12,800 volts/cm., he obtained a dipole moment .112 + .005 debye. 17> In 1962, Raoul Kopelman and William Klemperer ^ of Harvard reviewed the experimental work done on CO and C 0 + in the 1930's and estimated limits for the dipole moments of 3 several excited states. Tne values wnicn they give are: Molecule State Dipole Moment (debye) (upper limit) CO k'TT .15 B ' Z + .30 CO X 2 Z * .2 kz7T - 2 At the end of the article they comment: t "The low values of the dipole moment of tnese states of CO and CO* are somewnat surprising. The common explanation a> b 0 f tne low value of the dipole moment of ground state CO is tnat the polarity of the CO bonding electrons is cancelled by the lone pair electrons on carbon. Since it is one of the lone pair electrons waicn changes orbital in going to either of the two o states of the Angstrom bands and also in forming CO1", the lack of a dipole moment in these states seems puzzling." The only measurements of an excited state dipole moment of CO have been made on the &}7f state. Both measurements 1^ yielded values of jlA, ~ 1.38 debye. In the summer of 1966, F.W. Dalby and A.E. Douglas working at U.B.C. obtained a single Stark Effect spectrum of CO with a field of approximately 60,000 volts/cm. and a dispersion of 1 A /mm. The present worK 'was undertaken in tne summer of 19?0 to provide confirmation of the spectrum obtained by Dalby and Douglas. 4 Footnotes for Chapter I 1. W.G. Penney, Phil, Mag. 11. 6 ° 2 ( 1 9 3 D -2. J.H. Van Vleck, The Theory of Eleotrio and Magnetic Susoeptibllltles (Oxford University Press, London, England, 1932), p. 147 - 155. 3. Jon H. Shirley, J. Chem. Phys. 38, 2896 (1963). 4. John R. Lombardi, J. Chem. Pnys. ^+8, 348 ( 1 9 6 8 ) . 5. L.N. Gunderova and N.M. Posdeev, Opc. and Spec. 22., 132 (1970). 6. J. Stark, Ann. Physik 41, 965 (1914). 7. A. LoSurdo, Rend. Accad. Linoei 22, 665 (1913) - cited in D. Phelps, Doctoral Thesis U.B.C. (1966), p.5. 8. Paul H. Krupenie, The Band Spectrum of Carbon Monoxide (National Standard Reference Data Series, National Bureau of Standards - 5; Washington, D.C. p 1966), p.33* a. B. Svensson, Z. PhysiK 21, 450 ( I 9 3 D . b. W. Steubing, Physiic Z. 26, 915 (1925). c. W. Rave, Z. Physik 2i> 72 (1935). 9. R.C. Sahni, Trans. Faraday Soc. 42., 1246 (1953). 10. H. Lefebvre-3rion, C. Moser, R.h,. Nesbet, w. Yamazaxi, J. Chem. Phys. 38, 2311-L (1963). Sheldon Green, J. Chem. Phys. 54, 82? (197I). 1 1 . R.M. Stevens and M. Karplus, J. Chem. Pnys. 42., 1094 ( I 9 6 8 ) 1 2 . C.A. Burrus, J. Chem. Phys. 28, 427 (1958). 1 3 . Raoul Kopelman and William Klemperer, J. Cnem. Pnys. 36, 1693 (1962). a. W.E. Moffitt, Proc. Roy. Soc. (London) A I 9 6 , 524 (1949) 5 b. R.C. Sahni, Trans. Faraday Soc. 42, 1246 (1953). Richard C. Stern, Richard H. Gammon, hichael E. Lesx, Robert S. Freund, William A. Klemperer, J. Chem. Phys. $2, 3 W (1970). R.H. Gammon, R.C. Stern, M.E. Lesk, B.G. Wic-ice, W. Klemperer, J. Chem. Phys. 2136 (1971). CHAPTER II THEORY The energy associated with a diatonic molecule may be conveniently separated into two parts: 1. the energy due to the motion of the nuclei 2. the energy due to the motion of the electrons. Associated with each'of these motions is a number of quantized states which will be described following the general pattern of Herzberg^. The Motion of the Nuclei The nuclei of a diatomic molecule have two modes of motion, namely the rotation of the nuclei about tneir center of mass and the vibration of the nuclei along tne internuciear axis. Since it is difficult to treat the exact motion of the nuclei mathematically, it is common to consider mecnanicai models wnicn approximate the motion and to successively modify tne results obtained from these models in order to conform witn experimental evidence. These modifications are generally an order - of-magnitude smaller. It is also matnematically convenient to convert from a two particle system to a single particle system, usually the center of mass system. Thus, tne system consisting of two masses mi and m2 separated by a distance r is replaced by a system with one particle of m a s s ^ a t a distance r from cne center of mass of the system. The two systems are related since the reduced mass^/tis equal to mi012 + m2 7 The mechanical model used as an analogy to the rotation of the nuclei is the rotating dumbbell wnicn consists of two point masses and m 2 separated by a massless rod of lengtn r. In the center of mass system, the dumbbell consists of a single particle^rotating at a distance r from the center of mass. These two systems are shown in Figure 1. The energy of rotation Is given by the formula: E r = p 2 21 where P is the angular momentum of the system about tne center of mass and I is the moment of inertia in tne center of mass system. In classical mechanics tne rotational energy could assume amy value but in quantum mechanics tne angular momentum, P, is quantized such that iPl - h i/J(Jc 1) • • -2 IT where J is the rotational quantum number and taKes integer values Q,t i 2, Substituting this value for P into the classical energy expression gives E r = h2 J(J+1) 8 It is customary to express the result in units of cm" 1, obtained by dividing the energy expression by he. The result is called a term value and the rotational term vaiue is> F(J) = BJ (J 1) where B is called the rotational constant and is equal to h 8 ttzQX B is constant for a given rotational state and is inversely proportional to the moment of inertia. iROTATfOM IN T W O - P A R T I C L E SYSTEM:: C E N T E R OF M A S S R O T A T I O N IM C E N T E R ~ O F - M A S S S Y S T E M C E N T E R O F M A S S FIGURE 1 Q In the presence of an external eleotric field a state of rotational angular momentum J will split into J + 1 components of slightly different energy such fcnafc the space quantization number Mj has the values |j| , £|j - l| , ... . Tnis is consistent with the classical behaviour of a particle in a field. The particle precesses about the field sucn tnat tne angular momentum describes a cone about the field direction with a constant component in the direction of the field. However, while in the classical case any angle oetween the field direction and the angular momentum is permitted, in the quantum mecnanical case only those angles wnich satisfy tne requirement ivij rjj|f±|j-i are permitted. So far the treatment of the rotational motion nas assumed that the molecule is completely rigid. Tnis is a property of the dumbbell model and not of the molecule itself. In fact, the molecule is free to stretch along tne internuclear axis, something which It is bound to do due to its rotation and the ensuing centrifugal force. In otner words, the rotational constant B is actually a function of J since tne moment of inertia will increase with J due to the centrifugal stretoning. When this effect is included, the rotational term value Decomes: F(J) = BJ(J +1) - DJ2(J+1)2 where D = 4b3 a na d is very much.smaller tnan B. To a first approximation, the atoms of a diatomic molecule can be considered to vibrate in simple narmonic motion along the internuclear axis. As in the case of rotation, some mathematical simplicity is achieved by transforming to the center 10 of mass coordinate system. This transf orination is shown in Figure 2. The motion of the single particle system is represented by the mechanical model of the harmonic oscillator. By definition of simple harmonic motion, the restoring force acting on the partiole/*is directly proportional to tne displacement of the particle from its equilibrium position, r - r e. Thus the force is given by tne equation F = -k(r - re) and the potential energy of the particle is P.E. = 1 k(r-re)2 f where k is the force constant. Suostituting tnis potential energy term intc the wave equation gives the vibrational energy levels: •p — Vl \ I I \TJL i ^ —Y ~ " x ' ' " ' where v is the vibrational quantum number wnicn taxes integer values and Vis the classical oscillation frequency. The corresponding vibrational term values are G(v) = 7J (v+t) c However, If the potential energy term were to be applied to all values of r, then the restoring force would increase with Increasing distance from equilibrium, and tne two atoms of m BR A T ! 0 & I; N' - f -TWO ^ PAR'T ICL ^ 'SYSTEM V I B R A T f ON m C E M T E R - O E - M A S S . . . . S Y S T E M C E N T E R O F M A S S F IGURE 2 12 the molecule would never be able to separate. That is, this type of a potential would preclude the dissociation of tne molecule and thus contradict experimental evidence. Tnerefore, it is necessary to include in tne potential energy term the information tnat the atoms can separate-in wnicn case tne force between them becomes zero and the potential energy acnieves a constant value. A particle which moves unaer tne influence of such a potential is called an annarmonic osciiiator. Tne anharmonic oscillator is represented by a potential of the form P.E. = f(r-re)2 - g(r-r e)3 + which yields the following vibrational term values: G(v) = We(v+i) - ttexe( v+|)2 * with ^ » ^ x e » ^ y e being a condition required for the solution of the wave equation. p For the CO molecule the values in units of cm" are . A 1 Tf C i x + Up to this point the rotation ana vibration of the nuclei have been treated as independent motions for tne purpose of introducing the models and the mathematics associated witn them. It is clear however that tne nuclei might simultaneously rotate and vibrate and a more appropriate model would be a vibrating rotator. If the molecule vibrates as it rotates, then the internuclear distance changes and since the rotational e ' <<4ye 1515.61 17.2505 2182 50 2180 16.8 13 constant B is proportional to 1/r , then B becomes a function of the vibrational quantum number, V . Furtnermore, since tne value of the internuclear distance is generally larger due to the anharmonicity of the vibration, tne new vaxue for tne rotational constant, B v , can be expected to oe sligntiy smaller than the equilibrium value, B e . To a first approximation tne coupling of the vibration with rigid rotation gives: B v =• B e " where % is a constant and B e since (r-r e) < r e . Similarly the centrifugal stretching term, D, woula also be a function of the vibrational number and to a first approximation: D y = D e - p e M ) where j?e < D e and D e is the same as given previously. However since the centrifugal stretching term is already of tne oraer 1 0 " 6 of the rotational constant, this modification is negligible, .or the CO molecule, the appropriate values in units of cm" are:^ U e & Al<fl- 1.6116 .02229 B 1 X + 1.961 .027 6.1x10-6 c 1 Z + 1.0536 .020 5.7xio~6 In summary, the interaction of vibration and rotation of tne nuclei gives the following term value for the vibrating rotator: T = G ( v ) f F v ( j ) = . ^ X e ( v 4 ) 2 ^ ...ByJ(J-el)_ u v j 2 ( j + 1 ) 2 > The Motion of the Electrons In a diatomic molecule the electrons associated witn tne molecule move in an electric field established by tne two nuclei. This field is symmetric with respect to the internuclear axis and, 14 as in the classical case, the electron orbital angular momentum vector precesses about the field direction (i.e. the internuclear axis) such that only its component in tne direction of tne internuclear axis remains constant in time. The vector wnicn represents the component of the electronic orbital angular momentum along the internuclear axis is given tne symbol A and has magnitude A(h/2 ^ ). The quantum number A can nave values A = 0,1,2, and the corresponding electronic states of the molecule are a assigned the names: 7T, A , £ , ... In addition, the electron spins comoine to form a resultant spin vector "S* with a corresponding quantum number S. The quantum number S is integral if tne total number of electrons in the molecule is even, and half-integral if tne total number of electrons is odd. As a result of the orbital motion of tne electrons, an internal magnetic field is created along tne internuclear axis. The spin vector ^precesses about the field direction (ie. tne internuclear axis) witn a constant component along tne direction of this axis. The vector wnicn represents tne component of tne electronic spin angular momentum along the internuclear axis is given the symbol I and the corresponding quantum number Z can have the values: — S, S—1, S—2, ... —S. That is, the multiplicity of Lis 23+-1. The multiplicity is added to the electronic term symbol as a left superscript. 15 The total electronic angular momentum about tne inter-nuclear axis is the vector sum of the orbitai and spin angular — » momenta and is given tne symbol XL. That is: SI = i - A + Z.1 and for a given value of JL {£ 0),n has a 2S+1 fold multi-plicity due to the values of H . Coupling of Nuclear and Electronic Motion Thus far the motions of the nuclei and the electrons have been treated independently, In the actual diatomic molecule these motions occur sumultanecusly and it is necessary to consider now they influence each other. The different angular momenta in a molecule form a resultant which is always called J, the total angular momentum. The various ways in which tne angular momenta may comoine to form this resultant are designated Hund'scase (a), (b), ... etc. We are interested only in cases (a), (b), and (d). 16 Hund's case (a). — > • If both the electronic orbital angular momentum L ana the electronic spin angular momentum 3 precess very rapialy around the internuclear axis,then the .electronic motion is strongly coupled to the internuclear axis anai2= A + Z is a good quantum number to describe tne states. In tnis case SI tne total electronic angular momentum, and if, tne nuclear rotational angular momentum, form tne resultant vector J wnicn is constant in magnitude and direction and has SI and ft slowly rotating about it. For a given vaxue of n , J taxes the values J = XL, -TL+1, -CLf 2,.. . and is integral whenXl is integral, and half-integral wnen JTL is half-integral. Figure 3: Vector diagram of Hund's case (a). 17 Himd's case (b). If the electronic spin vector S is omy weakly couplea to the internuclear axis, then the electronic orbital angular momentum, , and the nuclear rotation vector, N, form a —y resultant, K which can tase the values: K = J l , - A f l , Jit- 2, .... The spin vector S and the vector h tnen comoine to form the — » total angular momentum J which has possible' values: J = (Ki-S), (K>S-1) |K-S | . The precession of K and S about J is slow compared to the nutation of the figure axis - which is just the rotation of the nuclei in the caseA=0. S N Figure 4: Vector Diagram of Hund's case (d). 18 Hund's case (d). — > If the electronic orbital angular' momentum L is not strongly coupled to the internuclear axis, it may oe coupled — > instead to the nuclear rotation axis R, which is then quantized having quantum number R ana integer values. The angular momenta ~R and ~L combine to give K wnicn then combines with the spin S to form the total angular momentum J. The quantum number K which denotes the angular momentum apart from spin can have the values: K » R+L, R+L-l, ... |R-L|. This is the usual quantum number used since the coupling between K and "s is so small that J can be disregarded. L Figure 3: Vector diagram of Hund's case (a). 19 With increasing rotation of tne molecule, an interaction occurs between the rotating nuclei and tne electronic oroital angular m o m e n t u m T h i s effect is calledA-douoling and can be interpreted as a transition towards Hund's case (d); tnat is, the uncoupling of L from the internuclear axis and its subsequent coupling with the nuclear rotation. The interaction removes"the two fold degeneracy oiA. and splits each J value into two components. The splitting increases with increasing J but Is usually less than 1 cm-1. > The formula for the splitting as given oy Kovacs^ is: AF c d(J) = (B0-Bd)J( J+l) where Bc and B d are the effective rotational constants of tne _A-doubled levels. Characteristics of the 1?T and ltL+ States_o_f_GQ The Angstrom and Herzberg transitions in CO are snown in Figure 6. These transitions snare the same lower state, the A17T state and Doth have "'"states as tneir upper states. In the C 1^! """and B 1 Zl^states, _/\_=0. Since tnere is no component of the electronic orbital angular momentum along the internuclear axis and hence no magnetic field in tnat direction, there could be no coupling of tne spin S to tne internuclear axis. Moreover since the states are ooth singlets, then S=0; that Is, tnere is zero net electron spin. — > Therefore, the vectors J and K are identical and the quantum number J is used to identify the states. 20 ioor 9 0 80 7 0 6 0 -5 0 4 0 3 0 20 10 X ' 2 + © igure 6: Energy level diagram snowing Angstrom ana Herzoerg transitions. 21 Since J = (KtS) , U+3-1), ... and K = J l , A -t-1 while JL = 0 and S - 0 it is apparent that the rotational quantum number ta-tces the values: J = 0 , 1 , 2 , 3 j . « « . for both the C 1 Z + and B s t a t e s of CO. In the A1??*state, -A. - 1 since it is a 7fstate and again the net spin S = 0 since the multiplicity is 1. —V -j The vectors K and J are identical, so for the A /7"state J x 1 > 2 , 3 > . . . . since J = K = .A, _/L«-l, ... and A . = 1 Since S = 0, the distinction between Hund's cases (a) and (b) might appear pointless. However, as a result of the analysis of the perturoations of the A state by other states of CO, it has been concluded that the A17f state is in intermediate coupling close to case (b)^ In addition, since-A^ 0, this state is subject toA-doubling which gives two components for each value of J. The splitting between these components is expected to be very smali since the state is close to case (b) coupling. The allowed transitions between the ^ZL* and 177 states of CO are shown in Figure 7. These transitions are governed 22 by the selection rules for electric dipole transtition: 1. A J = o, i 1 j = o ^ > J = o 2. •«- > - + + ; - *+> ~ 3. U - o, tl k. A s = o n P(l) P(2) P(3) Q(l) Q(2) Q(3) R(l) R(2) R(3) 1 1 1 r V I — ] I ) Figure 7: Transitions between 1Z. * and 'V states of CO 24 There are additional selection rules which nave oeen omitted nere because they do not apply to the states of CO which are under investigation. The transitions involving cnanges in J have been individ-ually named: A J = is called tne R brancn A j - 0 is called the Q. brancn A J r -1 is called the P Drancn where J = J1 - J" and " refers to tne lower state while ' refers to the upper state. The Dipole Moment . An electric dipole is formed whenever two equal and opposite charges are separated by a small distance. Since the centers of positive and negative charge do no coincide for diatomic molecules which consist of unlike atoms, sucn molecules must nave a permanent electric dipole moment along the internuclear axis. The electric dipole moment is given the symbol JlZ. Since the dipole moment depends upon tne separation of charge, it is apparent that j Z is a function of tne internuclear distance and therefore of the electronic state of tne molecule. Measurements of the dipole moment are used to deduce information about the distribution of the electric charge in tne molecule. The Effect of an Electric Field Upon the Dipole Moment An electric field causes a force to be exerted on charged particles - with positive charges being pusned in tne direction of the field and negative charges in tne opposite direction. Tnus 5 the positive and negative parts of a molecule are displaced from their equilibrium positions by the presence ox an electric field. As a result of the polarization of the molecule, tne electric dipole moment changes in the presence of an electric field. We shall investigate how the energy of tne electric aipole is affected by the presence of an external electric field. First Order Stark Effect If the center of positive charge is taken as the origin of the system, then the change in energy of the i°n electron due to an electric field is: A = -ervj_ • T where e is the electronic charge —> t~ h r 1 is the position of the electron from the center T~.no 1 hi iro r» ha E is the electric field strength Since the molecule is axialiy symmetric, only the component of tne position vector along the internuclear axis will contribute to the expression AW^. Thus, where ri_int is the component of the vector rj_ along tne inter-nuclear axis. But er^_illfc is just the contribution of tne i t n electron to the electric dipole moment which lies along the internuclear axis. So, The total change in the energy of the molecule due to tne presence of the electric field is the sum of the cnanges from eacn electron 2b In the molecule. Thus, W = = f ( - / V E ) —* — - -/c-E since = M-t the electric dipole moment. Thus the energy of a state in the presence of an electric field is given by W = w e -jiL Ecos O t where W0 is the energy in the absence of a field and cose is the angle between the dipole momentyOand the electric field E . For a molecule with a permanent electric dipole moment in a state, the dipole moment, which is along the internuciear axis, is perpendicular to the total angular momentum J and tnere-— fore -^j, the component of the dipole moment in tne direction of J is also zero. Thus, the time average ofy^j processing about the field direction, is also zero. In other words, there is no first order Stark Effect in a ^ state. However for a diatomic molecule in a'Estate, there is a component of the electric dipole moment in the direction of J and — * . — * therefore a component in the direction of E also since J will precess about E . In order to determine the magnitude of tne first order Stark splitting, it is necessary to find tne time average of y^. Since the state of GO under consideration is a 1 7T state, we will assume S = 0 in the following development. Since the nutation of.Aabout J taxes place very rapidly in -v comparison to the precession of J about the field direction, we proceed by first finding ^j, the time average of the component of ju, in the direction of J, and then taking its component in the direction of the field. (see Figure 8) MJ = ^ c o s L / t / J ) — - yU. cos(VL , J) ^U. VL //J(J+1) = ^ j C o s ( e , J 1 C O S ( e Y j ) j+D /J(J^I) /tAM J(J+1) Thus for the first order Starve splitting in tne ^ state we nave ^ W 1 = - M-A/ffi J(J+1) A diagram of the first order Stark Effect and tne allowed transitions is shown in Figure 9. 28 N vJ Figure 8: Classical derivation of the first order Star* Effect 2-9 J = 0 + |m| 0 INCREASING E L E C T R I C F I E L D |m| Figure 9: First Order StarK Effect on ' Z ^ a n a ' V states of GO -3.0 Second Order Stark Effect The second order StarK Effect tar.es into account tne effect of the electric field upon the molecular wave functions. In general the change in energy is calculated from tne term: Z 4 w 2 = z yCL , nn E 2 W_, - W / n n where W n is the energy of the undisturbed state Wn' is the energy of any state perturbed by tne electric field is the z-component of the dipole moment matrix nn For the rotating dumbbell which cnaracterizes tne 1JE state, the second order energy change as calculated by Van VlecK is A w 2 = knr2-I^2e2 f J(J«-i) - 3M2 1 h 2 lj(j«-l) C 2J-1) ( 2J+3> I When this expression is written in terms of the rotational constant B and expressed in units of cm""1 w e have: AW2(cm--1) = JA~Z E 2 / j(jfi) - 3M2 2Bc2h2 IJ(J*1) (2J-1) (2J+3) The case J=0 is a special case for wnich A W 2 (cm-1) = - ^ 6 2 E 2 6BC 2 H 2 For a symmetric top model, wnicn is the model used to describe the ^-Tf state, the second order energy cnange as given by Van Vleck is8: A W 2 = 47r2i^.2E2 r(j2_M2) (j2_A2) _ [(j+l)2 -W2][(J.l)2 _ A z ] h2 j3( 2J-1) (2J+1) (J-»-l)3( 2J^i) In units of cm-1 and In terms of the rotational constant B, tnis expression becomes: A W 2 - M.2E2 f (J2-K2) (J2-l) - [(JfI)2 -M2! [(JJhUj-=l2. / 2 B c 2 h 2 [ J 3 ( 2 J - 1 ) ( 2 J * 1 ) ( J > 1 ) 3 ( 2 J + ! ) U J + 3 ) -3 where A = 1 has been substituted for the 1 V state. In Table I, the coefficients of the term for the , Oil first order effect; and E 2 for the second order effect 2Bc2h2 are shown for J = 0,1,2 in the 1 ^ state and J « 1,2 in the 17f state. These coefficients sncw tnat the maximum star* Effect is to be expected for the states with lowest J values witn the effect decreasing rapidly for increasing J values. It snould •u ^  ,-> v- a. A f'hot-. h h a ri 1 n nlft moment will generally be different u i i . w v N - / ' ^ . •«• — —• x - — for the two different states. Table I First and Second Order Stark Coefficients for 1Z.* and 17f states, (cm"1) State J M First Order Coefficient Second Order Coefficient o f v t t E Of > g 2 E 2 ch 2Bc2n2 1 2 ] * o o o -1/3 1 0 0 • +1/5 ±1 0 -1/10 2 0 0 *1/21 0 + 1 / 4 2 12 0 -1/21 17T 1 0 0 -l/io n - 1 / 2 * - 3 / 4 0 2 0 0 t.i/^ 2 -1 " i / 6 m / 1 5 1 2 1 2 - 1 / 3 - 8 / 1 8 9 ro 3 Footnotes for Chapter II. 1. G. Herzberg, Molecular Spectra and molecular Structure, 1. Spectra of Diatomic nolecules (Van iMostrand Kelnnola Company, New YorK, 1950, 2 n d edition), Chapters I-V. 2. Paul H Krupenie, The Band Spectrum of Carbon i-ionoxiae (National Standard Reference Data Series, National Bureau of Standards - 5; Washington, D.C. 1966), p.38a. 3. Ibid., p.38a. Istvan Novaes, Rotational Structure in the Spectra of Diatomic Molecules (American Elsevier Publishing Company Inc., New York, 1969), p.59. 5. Paul H.Krupenie, The Band Spectrum of Carbon Monoxide. P. 23. 6. C.H.Townes and A.L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955), p. 250. 7. J.H. Van Vleck, Tne Theory of Electric and Magnetic Susceptibilities (Oxford University Press, London, England, 1932), p. 152. 8. Ibid., p.153. CHAPTER III EXPERIMENTAL DETAILS Electric Discharge Tube The gas discharge tube used to study tne StarK; Effect in CO is shown in Figure 10. It is a modified LoSurdo tube with a direct current discharge. When a potential is applied to tne catnode, most of tne potential difference -occurs in the 1 or 2 millimeter region directly above the catnode. This yields an extremeiy high electric field just above the cathode surface with tne field going to zero both at the cathode surface and in the region beyond the cathode dark space. The type of discharge observed can be classified as a glow discharge according to the characteristics outlined by U 4- /-v 1 a u ^ ^ ^  r-v-P -P ^t.t m i 1 1 1 marovio 14 rr o wnl hn^a a u w a u o u n « T \ is <X y i ^ o o I A A w x c t JL w r» U A 4 . J . A u A > ^ w is applied to the cathode. Initially, a very small current (less than 1 milllamp) flows but there is no ooservable light in tne discharge tube. As the voltage is steadily increased to several hundred volts, there is a sudden increase in the current and tne gas in the discharge tube begins to glow. The discharge has now become self-sustaining and exhibits the following regions^: 1. cathode darK. space 2. negative glow 3. Faraday darK space positive column F I G U R E 10, ELECTRIC D I S C H A R G E TUBE GAS I N L E T > Q U A R T Z T O S P E C T R O G F G R O U N D G L A S S J O I N T G L A S S S T O P P E R Q U A R T Z T U B E - A L U M I N U M C A T H O D E 36 The mechanism through which the discharge is sustained is •probably the secondary emmission of electrons3 tnrougn bombardment of the catncde by positive ions. Tne positive ions introduce a space charge effect^. The positive ions move ratner slowly in comparison to the less massive electrons witn the result that a net positive cnarge builds up around the catnode region. This will tend to distort the electric field produced at tne catnode but the amount of distortion is not Known. In the course of this worx various catnodes were tried; from imm to 1mm diameter Aluminium and from 1mm to 2mm diameter Caroon. The carbon cathodes seemed to be particularly susceptible to instabilities and sudden blow-ups and were therefore not used very often. With the aluminium cathodes, it was possible to acnieve very high intensities with the 2mm size but only by sacrificing a high electric field. For the |-mm size, tne problem was inverted -high fields but low light emaiission. For these reasons, the 1mm aluminium cathode was used for most trials. All catnodes were hand polished. The cathode is tightly fitted into a quartz tuoe of 3mm diameter which is also polished on the cut surface. The position of the cathode inside the quartz tube was varied from 3mm down Inside the tube to even with tne surface of tne tube. When tne cathode was below the edge of the quartz tube, very stable discharges with easily visible high field regions were produced. However the intensity of light emitted from within the nign field region was not sufficient for good photographs, and usually after about 2 hours a darn: ring formed on the inside of the quartz tuoe 37 making it impossible to observe the high field region. In terms of light intensity, the best position for tne catnode was even with the quartz tube. (as shown in Figure 10). Catnod.es were seldom re-usable. The main problem encountered was instability of tne discharge as the cathode voltage was increased. In many cases tne instability would subside if the voltage were raised slowly and allowed to adjust at eacn step. Instabilities' were also introduced by sputtering at the catnode which created pocked, uneven catnoae surfaces. In addition, the phenomenom of streamers-5. from tne anode was occassionaily observed, altnough tne discharge could maintain itself in spite of this effect. There appeared to be several different modes of operation of the discharge; some stable ana some flickering and it was not apparent which mode was most beneficial for tne proauction of tne Stark Effect. The mode is most probably a function of the type of gases being used. The stable discharges always produced a cathode with an evenly hollowed out 'well' in the center; while the unstable discharges usually produced a very uneven catnode surface. Eventually most of the discnarges suffered a breakdown by arcing. This could have been produced by thermionic emmission^ since the cathode becomes heated as the result of the power dissipated on the small surface ar"ea; or by field emission, the possibility of field emission being- enhanced by tne formation of thin layers of oxide or impurity on the-cathode surface. 721 Producfelon of the Spectra Several combinations of gases and liquids were tested before obtaining a reproducible CO spectrum in the region from 410OA to 4525A. These combinations included C02 and H20, formic acid and H20, formaldehyde, CO and H20, CO and H2, and argon and CO. The most successful combination was CO and H20 witn tne water being used both as a stabilizer in the discharge tube and as a source of hydrogen since the StarK Effect on atomic hydrogen is one of the standard methods of calibrating tne electric field. .The system was pumped down to a pressure of less tnan 10 microns before the gases were introduced. The water vapour was introduced first since it produced a stable, reliable discharge and 'prepared' the cathode surface at voltages less then 2 kilovolts. Using water vapour, the discharge had a deep red color in the area immediately above tne catnode. The CO was- added slowly and increased to a maximum pressure of 600 microns. During this time the discharge slowly changed color from red to bluish-white indicating the presence of the CO. When a stable discharge was obtained, the voltage to the catnode was gradually increased. With a surface cathode tne maximum possible voltage was near 6 kilovolts, but with the cathode lowered 1 millimeter inside the quartz tube voltages as nigh as 9 Kilovolts could be obtained. The corresponding currents were .highly variable, seemingly dependent upon the mode of the discharge. Typical current values were 1 - 5 milliamps for both tne.surface and lowered cathodes. The maximum power which could be dissipated in a 1mm cathode was 20 watts. In an attempt to cool the system and thereby allow it to withstand higher voltages and currents, a liquid nitrogen trap was placed on the lower end of the catnoae. With this system a combination of 8.6 xilovolts, 2.9 milliauips was obtained. However, difficulties were encountered with the aeKnotinsity seal on the cathode which cracked at the lower temperatures. This difficulty was temporarily overcome by applying glycerine to tne areas sealed by de Khotinsky - glycerine having tne consistency of a thick paste at the temperature of liquid nitrogen. However, the system was stable for only 2 hours which was not long enough for a good exposure. This idea was eventually aDandoaed. Tne conditions pertaining to the production of the successful spectra are given in Table II. Observation of the Spectra The spectra produced in the discharge tube were photographed on a 3.^ meter Ebert spectrograph with a grating of 30,000 lines per inch. All spectra were photographed in second order at a dispersion of approximately lA/aiai. With a water lens of focal < length 12.2 cms., the cathode darK space was focused on the slit of the spectrograph. A KodaK 0-52 filter was then placed in front of the slit. This filter was used to DIO C K out tne third order o o of the wavelength region 2880A to 3030A wnich includes the Third Positive System of CO ( 266O-382OA ), The First Negative bystern of C0+ (1800 - 3150A ), and the f3 jr.* - 8?7T transition ol Cu ( 2670 - 298OA ). Several types of KodaK plates were used -la-E, ia-0, 103a-0, and lla-0. Since tne intensity of the light was very weak and the cathode lifetime was limited, it would be desiraoie to use a fast plate and therefore cut down on tne required exposure time. For this reason, plate types la-E ana la-0 are preferable. However, these plates have moderately low resolving power and coarse granularity and tne lines of interest were not well resolved. Therefore, tne plate type most frequently used was lla-0 which has both medium resolving power ana medium granularity, though it has the disaavantage of requiring longer exposures. A minimum exposure time of 5 hours was required for a good plate and the two successful plates were eacn exposed for 7i - 8 hours. Photographic details for txiese plates also appear in Table II. Table II: Conditions for Production of•the CO Stark Spectra Plate Number Type of Cathode Postion of Cathode Gases Pressure Voltage Current Plate Exposure Type Time 57 a Carbon 1 mm. lowered 1 mm. CO 600 microns 5.6 xv • 7 ma Kodak 71 lla-0 hours 63b Aluminium surface CO 200 5 . 5 KV 4.0 ma Kodax 8 1 H20 microns 103a-0 hours 1-42 Determination of the Electric Field Strength The electric field was calibrated using one Stark Effect on atomic hydrogen, more specifically the Balmer line Hy at o 4340.468A. The hydrogen was a dissociation product of the water vapour and was photographed at the same time as the GO spectrum. The long exposure times make the hydrogen line extremely diffuse. A photograph of H(4340A) appears in Plate I. The change in energy ( in units of cm"1) of tne hydrogen line in the presence of an electric field can be represented by the formula?: A (cm-1) = raE - bE2 oe3 where E, the electric field strength, is measured in 10° volts per centimeter and a, b, and c are constants. In terms of the electric field strength the formula becomes: E (106 volts) = - + Jb_ A 2 * ( 2 b2 - c ) A 3 cm a ~ — r — - - j r a-> a? ar where A is the change in the hydrogen line in units of cm-1. The coefficients a, b, and c for the Stark Effect components of Hy are given in Table III. From these values, it can De calculated that the factor b is of tne order 10"^, while the a3 factor 2b2 - c is of order 10~12. P L A T E I STARK EFFECT ON HYDROGEN ( 4 3 4 0 A ) Table III Stark Effect Coefficients for H (4340A) Component a b c 2 W 1 2 8 . 7 8 146 ..3 0 . 0 0 3 5 IT 3 2 1 . 9 5 1 4 2 . 2 7 . o 5 12 TT 7 7 2 . 6 8 1 4 2 . 5 1 4 . 9 2 15 7T 9 6 5 . 8 5 1 3 4 . 2 2 2 . 0 4 18 7r 1 1 5 9 . 0 2 1 3 0 . 5 2 9 . 3 0 0 <r 0 1 3 4 . 1 0 0 <r 0 1 4 6 . 3 0 3 <r 1 9 3 . 1 7 1 4 2 . 2 7 . 6 5 10 cr 6 4 3 . 9 0 1 3 0 . 5 lb.00 10 <r- 6 4 3 . 9 0 1 4 2 . 5 1 4 . 9 3 13 <r 8 3 7 . 0 7 1 3 4 . 3 2 2 . 0 4 k'5 Therefore, to a good approximation tne electric field strength can be determined from the simple formula: E ( 1 q 6 volts) = _ A _ (cm" 1) cm a By comparison with a diagram of the relative positions and intensities of the Stark components^, it can De determined that the components present in Plate I are 18 V , 15^*, 13 ^ 10 <r, 3 <r, and 0 <r. Measurements of the H y line were made on a Zeiss comparator of two different occasions. These measurements appear in Table XV. In Plate I, the components 18 V and 3«r- are clear on Dotn sides of the central component and the shift, A (microns)., was calculated in Method 1 of Table IV by the formula Right - Left . 2 However, the components 15 TT, 13*"", and 10cr are obsured on tne longer wavelength side (Right) and so no measuremexits of these components were possible on the right side. In Metnod 2 of Taole IV all shifts, A (microns), were calculated from tne central component 0 C7~. The values for £(microns) were calculated using the a values of 'a* quoted in Table III. The average of all, values of A in Table IV is 9.61 x 10~3 a microns. The average value excluding the 15 IT and 13<T-components from Method 2 is (9«36 + .09) x 10"3 microns. Because of tne difficulty of resolving tnese component.s, the latter vaiue seems preferable since it is more consistent witn tne values ootained by Method 1. The dispersion on Plate I in the region of the hydrogen line is (5-753 * .002) cm^/micron, This yields an electric field of: E(10^ volts) = (microns) x dispersion (cm~l cm a micron = (9.36 ± .09) x 10-3 x ( 5 . 7 3 3 * . 0 0 2 ) t s 53-8 x 10~3 ( + o r , in kllovolts cm E =- 53.8 kv (4- 1%) cm where all values of experimental uncertainty are mean deviations from the mean value. Table IV Calculation of the Stark Shift Method 1 Component 18 7T 3 <r Method 2 Component L18 IT L15 7r L13 <r-L10 <r L 3 <r 0 <r R 3 <r-R18 77" Left Right 32.047 53.859 32.075 . 53-939 41.138 44.718 41.191 44.757 32.075 32.585 34.115. 37.105 41.235 43.051 44.756 53-939 o the Components of H(4340A) A(microns) A x 10"3(microns) Si 10.906 9.41 10.932 9.43 1.790 9.21 1.783 9.23 A(microns) x 1 0 m i c r o n s ) £L 10.976 9.47 10.456 10.83 8.936 10.57 5.9^6 9.23 1 . 8 1 6 9 . 4 0 1.705 10.887 9.48 9.39 4.8 Footnotes for Chapter III 1. A.M. Howatson, An Introduction to Gas Discharges (rergamon Press Ltd., London, 1965), P«3 2. Ibid. p. 81. 3. Ibid. p. 45. 4. Ibid. p. 55. 5 . Ibid. p. 69. 6. Ibid. p. 90 - 92. 7. E.U. Condon and G.H. Shortley, The Theory of Atomic Spectra (Combridge University Press, Cambridge, England, 1935), p. 403. 8. Ibid. p. 403. 9. Ibid. p. 401. CHAPTER IV EXPER IN EN TA L OB ,5 ER VAT 10 wS Analysis of the Spectra The Stark Effect on .the B1^.4" to A 1 TT transition of 00 -the (0,0) band, of the Angstrom transitions - is shown in Plate 2. (Plate 63b from Table II). The lines were identified from tne tables of Schmidt and' Gero and the line of particular interest is P(l). The high electric field region occurs in tne lower part of the photograph and in this region P(l) nas the following characteristics: a. the line deviates toward shorter frequencies (to the right) b. the line broadens c. there is no component which continues undeviated by the electric field d. there is no component wnich deviates towards longer frequencies ( to the left ) On the basis of a first order Star*. Effect, woich would De due solely to the dipole moment of the A1^state, tnree components would be expected. Since they are not observed we might tentatively assume that the dipole moment of the A1 TT state is very small or zero If we consider the second order StarK Effects, and assume that the dipole moments of the two states are equal, tnen tne effect in the upper state would be approximately tnree times larger than the effect in the 177" state, (from tne coefficients in Table I.) However, in the event tnat tne dipole moment of the TJ state is very small or zero, tnen tne second oraer effect 4 3 2 1 R I 23 M l Q 4 3 21 P L A T E 2 STARK EFFECT ON CO ANGSTROM ( 0 , 0 ) BAND AT 4 5 1 0 A 51-would be due entirely to the dipole moment of tne upper state. On the basis of tnis assumption, tne line 1(1) would snow a shift toward shorter frequencies with only one component. Tnis is the observed behaviour of F(l) in Plate 2. The transitions Q(l) from 12L* , J-i — > 17T, J=1 and R(l) from i J=2 77, J=l; share tne same lower J state as the F(l) transition. If the effect is a first order effect in i the 17Tstate, then these transitions should also snow tnree components in the high field region. In Plate 2, R(l) is unaeviated in the high field region and Q(l) does not appear to deviate, though it is obscured by another line. (P2(ll) - hot identified on Plate 2). The Herzberg transitions G 1 ^ +-*• A177" share tne same lower state as the Angstrom transitions and are potentially another method for determining the dipole moment of the 17T state. o A photograph of the (0,3) Herzberg transition at ^380.27A is shown in Plate 3. (Plate 57a from Table II) The rotational structure has been identified using the data of Scnmid and Gero as indicated previously. In tne nigh field region r(l) is very faint but tne P(2) transition, though not very intense either, can be observed to split into two components - one component to shorter frequencies and one component to higher frequencies. Again, this behaviour cannot be explained in terras of a first order Stark Effect in the 177* state, since the '77 , J=2 level would give five components due to M=C>, £i, ±2. However on tne assumption that the dipole moment of the '77 state is very close to zero and the behaviour is due to a second order effect in the P L A T E 3 STARK EFFECT ON CO HERZBERG ( 0 , 3 ) BAND AT 4 3 8 0 A 3 state, then the J=1 level of the upper state would yield two components due to M=0,tl - one component to sxiorter frequencies and one component to longer frequencies as snown in Table I. Measurements Of the two photographs wnich showed appreciable Stark Effects, one was made .with pure GO in tne discharge tube and due to the absence of hydrogen there is no method of calibrating the electric field strength. For this reason, ail of tne following' o measurements are made on Plate 2 wnich snows tne Angstrom transition B 1 2 : + — > A 17 7 " . The measurements were made on a Zeiss comparator on two separate occasions, with two sets of measurements sa^en each time. On each occasion the plate was traversed twice, once in tne region of maximum electric field and once in the region of zero electric field. Several lines which showed no StarA Effect were measured in addition to the P(l) line. The measurements were made in microns and are shown in Table V. Table V Measurements of selected lines of tne Angstrom (0,0) band in tne region of maximum electric field (M) and in zero electric field (Z). Line #1 M Z M #2 Z . M #3 z M #4 z *2<9) 7.9588 7.9521 7.9502 7.9526 0.5232 0 . 5 1 0 0 0.5202 0 . 5 1 3 9 P(3) .09^9 .880 .0814 .0877 9.64b3 9 . 5 5 1 0 9 . 6 5 53 9 . 6 5 5 9 P(7> 6.9576 6.9533 6.9510 6.9533 .5194 .5137 .5207 . 5 1 7 5 P(2) . 7 4 3 1 .7392 .7394 .7417 .3052 . 3 0 4 5 . 2 9 8 8 . 3 0 2 1 ?2(10) .7160 .6124 .6123 . 6 3 1 7 .1800 .1777 .1781 . 1 7 8 9 P( 8) .4361 .4315 .4265 .43 27 8.9953 8 . 9 9 4 7 8 . 9 9 7 4 8 . 9 9 3 5 P(l) .2910 .2542 .2998 .2581 .8516 .8224 .8596 . 8 2 2 2 P 2 ( H ) 5.5649 5-5588 5.5601 5.5622 .1232 .1224 • 1253 . 1 2 8 0 Q( 1) , . 4 7 7 6 .4740 . 4 6 9 8 .4760 .0413 .0421 .0441 .0441 Q(2) . 2 0 7 8 .2023 .2008 . 2 0 6 1 7.7663 7.7583 7.7674 7.7 661 Q(3) 4.7944 4.7859 4.7833 4.7875 • 3532 .3499 .3315 * .3503 P2(12) .5429 .5349 .5342 .5356 .1016 . 0 9 8 3 . 1 0 1 7 .1028 Q(4) . 2 3 7 8 .2318 .2307 .2305 6 . 7 9 8 I 5.7951 6.7992 6.7948 R(l) 3.9^61 3.9341 3.9339 3.9380 .5060 . 5 0 3 4 • 30^7 .50^8 Q( 5) • 5232 .5531 ' .5256 .5380 .0929 . 0 8 8 3 .0888 . 0 9 5 9 P2(13) .4216 .4108 .4113 .4125 5.9647 5.9758 5.97/8 5.9813 Computations Two separate metnods were used for determining tne snli't of P(l) In the region of the maximum electric field. Method 1: The difference between tne measurement in tne maximum field and the measurement in zero field was calculated for eacn line which had been measured. When all measurements except P(l) are averaged, the value obtained is an indication of tne 'shift' due to inaccuracies in the measurements, fnis value can be compared to the shift of P(l) to give an uncertainty reading. In addition, if any line such as R(l), Q(l), Q(2) etc., snows an appreciable difference from tne other lines, then tnat xine can be assumed to have a StarK Effect and can be excluded from tne averaging process. The calculations for Method 1 appear in Tabla VI and a summary of the shift of 1(1) ± the uncertainty appears in Table VIII. Method 2: The difference between eacn line and P(l) was calculated both in the zero field* region, an<* l n t n e maximum field region, The absolute difference oetween these two values, 1^2 ~ » represents the shift of P(l) in tne maximum field region. This value will be already corrected for tne 'shift' due to limitations in the measuring process. Therefore, tne values obtained for AP(l) by Method 2 should be smaller, than those obtained by Method 1. The calculations for Method 2 appear in Table VII, with the average values for AP(1) shown in Table VIII. Table VI Method 1: The difference between measurements taken in maximum field and in zero electric field. electric Line P2(9) P(3) P( 7) P(2) p 2 ( io) P( 8) 1 ( 1 ) P 2 ( l l ) Q(l) ' Q( 2) Q(3) P 2(12) Q(4) R(l) 0.(5) #1 +.0067 +.0069 +.0043 +.0039 +.0036 *.0046 +.0368 ••.0061 •.0036 +.0055 +.0085 +.0080 +.0060 0121 +.0001 +.0108 #2 -.0024 - .0063 -.0023 -.0023 -.0014 -.0062 +.0417 -.0021 -.00b2 -.0053 -.0042 -.0014 r.0002 -.0041 -.00 24 -.0012 #3 +. OO06 -.0033 +.0037 + . 0 0 0 / *.0023 4. . 000b \0292 + . 0008 -.0007 -.•0020 +.0033 T.0033 +.0030 +.0u2b r .004t> >079 + .0 #4 +.0063 -.0000 J-.0026 -.0033 - . 0 0 0 8 +.0039 •.0374 -.0027 +.0000 +.0013 +.0012 -.0011 +.0044 -.0001 ^.0081 -.0035 Table VII Method 2: The difference in zero field, between P(l) A z t and in and each measured line tne maximum field, A ^. Line A z # 1 . A M A - A Z M A z #2 A M A - A Z M P 2 ( 9 > 1 . 6 9 7 9 1 . 6 6 7 8 .0'301 1.6945 1 . 6 5 0 4 . 0 4 4 1 P ( 3 ) 1 . 8 3 3 8 • 1 . 8 0 3 9 . 0 2 9 9 1.8296 1 . 7 8 1 6 . 0 4 80 P ( 7 ) 1.6991 1.6666 . 0 3 2 5 1.0952 1 . 6 5 1 2 . 0 4 4 0 P( 2) 1 . 4 8 5 0 1 . 4 5 2 1 . 0 3 2 9 1 . 4 8 3 6 l .~4396 . 0 4 4 0 P 2 ( 1 0 ) 1 . 3 5 8 2 1 . 3 2 5 0 . 0 3 3 2 i . 3 5 ^ o 1.3125 . 0 4 3 1 P ( 8 ) 1 . 1 7 7 3 1 . 1 4 5 1 . 0 3 2 2 1 . 1 7 4 6 1 . 1 2 6 7 . 0 4 / 9 P 2 ( l l ) 1.6954 1 . 7 2 6 1 . 0 3 0 7 1 . 6 9 5 9 1.7397 . 0 4 3 8 0 ( 1 ) 1 . 7 8 0 2 1 . 8 1 3 4 . 0 3 3 2 1 . 7 8 2 1 1.8300 . 0 4 7 9 Q ( 2 ) 1 . 0 5 1 9 1 . 0 8 3 2 . 0 3 1 3 1 . 0 5 2 0 1.0990 . 04 / 0 Q(3) 1 . 4 6 8 3 1 . 4 9 6 6 . 0 2 6 3 1 . 5 7 0 o 1.5105 . 0 4 5 9 P 2 ( 1 2 ) 1 . 7 1 9 3 1 . 7 4 8 1 .0288 1 . 7 2 2 5 I-. 7 64 6 . 0 4 2 1 Q ( 4 ) 2 . 0 2 2 4 2 . 0 5 3 2 . 0 3 0 8 2 . 0 2 7 6 2 . 0 6 9 1 . 0 4 1 5 R( 1 ) 2 . 3 2 0 1 2 . 3 4 4 9 . 0 2 4 8 2 . 3 2 0 1 2 . 3 6 5 9 . 0 4 5 8 Q( 5) 2.7311 2.7669 . 0 3 5 8 2 . 7 3 0 1 2 . 7 7 4 2 . 0 4 4 1 P 2 ( 1 3 ) 2 . 8 4 3 ^ 2 . 8 6 9 4 .0260 2 . 8 4 5 6 2 . 8 8 8 5 . 0 4 2 9 Table VII Continued # 3 Line A z A M A - A Z M P 2 ( 9 ) 1.6942 1 . 6 7 1 6 . 0 2 2 6 P ( 3 ) 1.8292 • I . 7 9 4 7 . 0345 P ( 7 ) 1 . 6 9 3 3 1.6678 . 0 2 5 5 P ( 2 ) 1 . 4 8 2 1 1 . 4 5 3 6 .0285 P 2 ( i o ) 1 . 3 5 5 3 1 . 3 2 8 4 . 0 2 6 9 P ( 8 ) 1 . 1 7 2 3 1 . 1 4 3 7 .0286 P 2 ( l l ) 1.7000 1 . 7 2 8 4 . 0 2 8 4 0 . (1) 1.7803 1 . 8 1 0 3 .0300 Q ( 2 ) 1 . 0 5 4 1 1.0853 . 0 3 1 2 0 . (3 ) 1 . 4 7 2 5 1 . 4 9 8 4 . 0 2 5 9 P 2 ( 1 2 ) 1 . 7 2 4 1 1 . 7 5 0 0 . 0 2 ^ 9 Q ( 4 ) 2 . 0 2 7 3 2 . 0 5 3 5 . 0 2 6 2 R( 1 ) 2 . 3 1 9 0 2 . 3 4 5 6 .02-^ 6 0.(5) 2 . 7 3 4 1 2 . 7 5 8 7 .02V4 , P 2 ( 1 3 ) 2 . 8 4 5 6 2 . 8 6 6 9 . 0213 ff4 A A A - A Z i"i Z ivi I.09I7 . 1.6b0o .0311 1 . 8 3 4 7 1 . 7 9 6 7 . 0 3 8 0 1 . 6 9 5 4 1 . 0 6 0 6 . 0 3 4 8 1 . 4 7 9 9 1 ' . 4 3 9 2 . 0 4 0 7 1 . 3 5 6 2 1.3165 .0377 1.1713_ 1.1378 .0335 1 . 6 9 4 2 1 . 7 3 4 3 . 0 4 0 1 1 . 7 7 8 1 1 . 8 1 5 5 . 0 3 7 4 1 .0561 1.0922 .0361 1 . 4 / 1 9 ' 1 . 5 0 8 1 . 0 3 6 2 1 . 7 1 9 4 ' 1 . 7 5 7 9 . 0 3 8 5 2 . 0 2 7 4 2 . 0 6 0 4 . 0 3 3 0 2 . 3 1 6 4 2 . 3 5 3 9 . 0 3 7 5 2.7253 2.7708 .0455 2 . 8 4 0 9 2 . 8 8 1 8 . 0 4 0 9 Table VIII Values obtained for A 1(1) #1 #2 #3 #4 AVERAGE Method 1 .0368 1 .0057 .0417 t .0032 .0292 £ .0027 .0374 1 .0035 .0363 r .0035 (in microns) Method 2 .0307 .0448 .0271 .0374 .0350 \G bO In Table VIII, there is good agreement between the values obtained by the two methods ana as predicted tne average Value obtained by Method 2 is smaller than tne average vaiue obtained by Method 1 and is within the uncertainty value obtained Dy Method 1. Taking an average value from all of the data would give: AP(1) (microns) - .0356 i- .0047 where the uncertainty is the mean deviation from the mean value. In order to convert from microns to cm_l it is necessary to calculate the plate dispersion. Several lines were cnosen ana the differences between them were calculated in the zero field region using the measurements numbered 3 ajad- ^  i n Table V. The differences between the lines in units of cm-1 were calculated from the data of Schmid and Ger'o'2. fne plate dispersion in cm-1/niicron was then calculated and averaged. Tne aata ana calculations appear in Table IX. From these calculations, tne average value of the plate dispersion is: (5.059 t .006 ) crn-1 micron where the uncertainty is the mean deviation from the mean. Table IX Calculation of Plate Dispersion #3 #4 Lines A(cm _ 1) A(microns) dispersion A(microns) dispersion (om-l/micron) (cm-l/inicrot) F 2 ( 9 ) - » Q(3) 16.00 3 . 1 6 6 7 5 . 0 5 3 3 . 1 6 3 6 5 . 0 5 8 P 2 ( 9 ) - » Q(5) 2 2 . 4 2 4 . 4 2 8 3 5.063 4 . 4 1 / 0 5 . 0 7 6 ? 2 ( 9 ) - > P ( 8 ) 7 . 6 9 1 . 5 2 1 9 5 . 0 5 1 . 5 2 0 4 5 . 06 P ( 7 ) — ( 5 ) 17-35 3 . 4 2 7 4 5 . 0 6 2 3 - 4 2 0 7 5 . 0 7 2 P ( 7 ) — » Q ( 4 ) 1 3 . 7 5 2.7206 5 . 0 5 4 2 . 7 2 2 8 5 . 0 5 0 P ( 7 ) — > P 2 ( 1 3 ) 1 7 . 8 8 3 . 5 3 8 9 5 . 0 5 2 3 - 5 3 6 3 5 . 0 5 6 6 2 —1 Using the average plate dispersion, the shift in P(1) in cm is: AP(1) = (.0356 + .0047)microns x (5-059 ± .006) cm"1 micron - 1 180 + .024 cm Determination of the Dipole Moment of the State of CO Assuming a second order Stark Effect in the upper state, the shift in energy in units of cm is given by the formula: —'I ? ? A E( cm ) = A S 2 2 6Bc h where ja. is the dipole moment of the B ZL state and is Af(l), for the J=0 to J=1 transition. Solving for the dipole moment: yU = ch ^661(1) E where c = 2.9979 x 10 cm/sec. h = 6.6252 x ID"2? erg-sec. B = 1.9475 cm-1 (see footnote 3) P(1) = .180 cm-1 (+13%) E'= 53.8 x 105 volts/cm = 179 statvol.ts/cm (+1 %) Substituting: ^OL = 2.9979x1010cm x6.62S2x10 27erg-sec ?/6x1.9475cm 1x.1S0cm 1 sec 179 statvolts cm 1 63 which gives: . _18 A^A- = 1.61 x 10 erg-cm (f lty*) statvolt The units of/a can be reduced as follows: erg-cm = erg-cm = statcoulomo - cm. statvolt erg/statcoulomb and since by definitipn, 10~18 statcoulomo-cmf = 1 debye, cnen ^yOL - 1.61 debye (f Footnotes for Chapter IV 1. R. Schmid and L. Gero, Z PhysiK 21, 656 (193^~35). 2. Ibid 3. Paul H Krupenie, The Band Spectrum of Carbon honoxide (National Standard Reference Data Series, National Bureau of Standards - 5; Washington, D.C., 1 9 6 6 } , p.58, Table 3 8 . 65 CHAPTER V: CONCLUSION AND SUGGESTION FOR FURTHER oTUDY The surprising outcome of tnis worx is tne conclusion that the dipole moment of the A^ I T state of CO is very swan ana most probably zero as suggested by Plates 1 and 2. if tms is true, then the fact that the value of 1.61 debye differs so greatly from the value of .30 debye predicted by Kopelman and Klemperer is not too alarming. It would be very helpful to nave further corroborating evidence from the Herzberg (0,3) band at 4380A. Tnis should be possible to do within the limits of the techniques already available. The main problem will undoubtedly be the tendency towards very low light emission in the high field region. The Stark Effect on CO1" is also of some interest and has been sought in vain. On Plate 63b, the (0,1) band of tne Baldet-Johnson System of C0+ was observed and it appears to show some Stark Effects although nothing is well enough resolved for measurements. This band is shown in Plate k and is included at the end of this thesis in the hope of inspiring someone to the study of C0f. P L A T E 4 CO"1" ( 0 ,1 ) BAND OF B A L D E T - J O H N S O N SYSTEM 

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