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Dipole moment of HCI+ determined from optical observations of Stark effect Wong, Shung Yam 1966

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THE DIPOLE MOMENT OP HC1 + DETERMINED PROM OPTICAL OBSERVATIONS OP STARK EFFECT by SHUNG YAM WONG B.Sc, University of B r i t i s h Columbia, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1966 In presenting t h i s thesis i n p a r t i a l f u lfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia,, I agree that the Library s h a l l make i t f r e e l y available for reference and study., I further agree that permission, for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. The Uni v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada ABSTRACT This experiment was aimed at the determination of the dipole moment of the diatomic molecule HC1+ (in the V state). The method was to observe the Stark splitting optically by using a 3.4 meter Jarrell ash spectrograph. The charged diatomic molecule was obtained by passing HCl gas through a LoSurdo discharge tube in which a high electric field was applied; optical plates were obtained from the spectrograph and analysed. Dipole moment of HC1+ in the Vx state was found to be smaller than 0.8 debye. ACKNOWLEDGEMENTS I would like to thank Dr. P. W. Dalby for his guidance and encouragement and Dr. D. Phelps for his help during the various stages of the experiment. i i i TABLE OF CONTENTS Page Introduction 1 Theory 2 Perturbation and mathematical representation of Stark s p l i t t i n g .. 3 The change i n energy due to Stark effect assuming Hund's coupling case a .. 4 Lambda doubling and i t s th e o r e t i c a l representation 6 Spectra of HC1 + ..... 7 Experimental set-up arid techniques 8 Experimental d e t a i l s and d i f f i c u l t i e s 12 To show that state belongs to Hund's coupling case a 15 Determination of e l e c t r i c f i e l d strength from He 3614A by a comparator 16 The evaluation of p-type doubling using combination relations ... 20 The cal c u l a t i o n of r o t a t i o n a l terms of the 0-0 band of HC1 + i n z £ + state . 21 The evaluation of A-doubling from combination relations 23 Conclusion 26 In the analysis of the HC1 + spectrum 27 An improvement f o r the experiment 28 Bibliography 29 Appendix 30 LIST OP FIGURES Page 1. Stark s p l i t t i n g 3 2. Vector diagram f o r Hund's coupling'-case (a) . 4 3. P o t e n t i a l gradient along a discharge tube 9 4. Copper cathode-feed mechanism 10 5. Diagram of experimental set-up 11 6. Pattern of Stark s p l i t t i n g s of He 3614A 18 7. Energy l e v e l diagram of 2 S - 5 Q f o r He 3614A 18 8. o -type doubling of 0-0 band of HC1 + iii V state .......... 20 9. Diagram of energy levels and tran s i t i o n s of Z - T\X and £ - TT. 22 10. A - t y p e doubling of 0-0 band of HC1 + i n ^IV state 24 2 LIST OF TABLES Page 1. Experimental conditions 14 2. Calculation of e l e c t r i c f i e l d strength 16 3. Combinations relations 20 4. Rotation terms of 0-0 band of HC1 + i n % + s t a t e 21 PRINTS 1 & 2. Spectra of HC1+; and the 36141 at high e l e c t r i c f i e l d s ... 19 1 INTRODUCTION The determination of dipole moments of OH, NH and CH by means of Stark s p l i t t i n g s has been investigated by using an o p t i c a l method; 1 and to obtain the same quantity of a charged molecule by the same method was the object of the experiment. The spectra of HC1+ had been investigated by Norling and Kulp, 2 and t h e i r analysis was used to i d e n t i f y the spectral l i n e s of interest i n t h i s experiment. 1. D. Phelps and Dalby, Canadian Journal of Physics (January, 1965); T. Irwin and Dalby, Canadian Journal of Physics (October. 1965). 2. Polke Norling. 2. Physlk 104. 638 (1935); M. Kulp, Z. Physik 62, 7 (1931). 2 THEORY One of the properties Of a diatomic molecule which characterises i t s behaviour i n an e l e c t r i c f i e l d i s i t s e l e c t r i c dipole moment (which i s c a l l e d the permanent e l e c t r i c dipole moment of the molecule, a quantity which arises because the e l e c t r i c charge within the nucleus of the molecule i s not symmetrically distributed). The perturbation produced by the action of the e l e c t r i c f i e l d with t h i s e l e c t r i c dipole moment produces a s h i f t i n energy of each of the perturbation-free state Of the molecule ( i f A-doubling be neglected; see A-doubling on page f ) by a quantity w s - y u . i (aee page k) In practice, the s h i f t i n energy i s obtained o p t i c a l l y on plates taken from the grating spectrograph. The estimation of the magnitude of the e l e c t r i c f i e l d strength imposed on the molecule i s f a c i l i t a t e d by finding the atomic Stark s p l i t -tings of He, which i s acted upon by the same e l e c t r i c f i e l d at the same 3 time. 3. For the estimation of e l e c t r i c f i e l d strength from the Stark s p l i t t i n g s of helium, see the a r t i c l e by J. S. Poster, Royal Society London Proceedings A 147. 117 (1927/28). PERTURBATION AND MATHEMATICAL REPRESENTATION OP STARK SPLITTING To the first order approximation the perturbation brought about by an electric field is obtained by solving the secular equation of the perturbation matrix which gives i.e. but W, W. 21 I = i (Z, + £ 2) ± t J .4 |w;J*+ o-2- where = £ 3 J(J+1) (see page 4) and S = A where A i s the l a m b d a - d o u b l i n g . Hence, i f _. 6 is measured from Stark splitting, and A calculated from combination relations for electronic bands, the electric dipole moment JLL 4 will be obtained. 4. Actually, for any Stark splitting the quantity to be measured on the plate is S = 2_8 (see fig. 1 below). | 4 THE CHANGE IN ENERGY DUE TO STARK EFFECT ASSUMING HUND'S COUPLING CASE a. Fig.2 Vector diagram f o r Hund's Coupling Case (a). In Hund's coupling case (a), i t i s assumed that the interaction of nuclear rotation with electronic spin S as well as electronic o r b i t a l angu-l a r momentum L i s very low, whereas the electronic spin.and o r b i t a l angular momentum i s coupled very strongly together to the l i n e j o i n i n g the nu c l e i . The component of the electronic o r b i t a l angular momentum along the i n t e r -nuclear axis i s represented by A ; whilst the electronic spin along the' internuclear axis i s represented by 2 . When these two couple together they give«n_the t o t a l electronic angular momentum about the internuclear axis. -A. then couples with the nuclear angular momentum N to give J the t o t a l angular momentum of the molecule. Here j& is the mean component of the electric dipole moment in direction of the internuclear axis, /LT I S its value along the J-axis. And, /W-j.E is the change in energy due to the electric field strength E on this electric dipole. In the presence of the electric field J, the total angular momentum, is quantized along the field direction and this quantization is denoted by M. Thus by trigonometry that relates a l l the above quantities as shown in fig. 2, the above result follows. 6 LAMBDA-DOUBLING ( A-DOUBLING) AND ITS THEORETICAL REPRESENTATION A molecule which i s i n an electronic state other than the 2. state ( i . e . A other than 0), has doubly degenerate ro t a t i o n a l l e v e l s , i f the off-diagonal elements of the rota t i o n a l and spin-orbit interaction 5 energies are neglected. But once t h i s interaction i s taken into account there w i l l be a s p l i t t i n g of each rotat i o n a l l e v e l (each of which i s being denoted by a value J") into two components, (This i s ca l l e d the removal of degeneracy). The change i n energy f o r z n i levels i s given by^ ( j ) = K( j ) where K i s a constant, (see page 24.) The above i s obtained i f the perturbation i s taken to the f i r s t order approximation, and i f the multiplet state i s assumed to be i n Hund's case (a), i . e . large multiplet s p l i t t i n g — A » where A designates the spin-coupling constant f o r fine structure interaction and B v " designates the r o t a t i o n a l constant (see page 15 f o r the calculation of the constant A). I f the Z dire c t i o n i s along the internuclear a x i s , L and S are the electron o r b i t a l and spin angular momenta respectively, J the t o t a l angular momentum exclusive of nuclear spin, and A i s the quantum number associated with L z, then the off-diagonal elements of the molecular Hamil-tonian w i l l consist of the terms (2B + A) (L_S- + LySy) and -2B(,J_L„ + JyLy) which give r i s e to A°type doubling. The molecular Hamiltonian H due to r o t a t i o n a l and spin-orbit; I interaction H = B[(J- - S 2 - L_)2• + ( J y _ S y - Ly) 2] + AL ZS Z + A(L_S_ + L-S-) = B ( j ( j +l) « A 2 J + BS(S + l ) + AL ZS Z - 2BJ.S + B d ^ 2 +Ly 2) + (2B + A)(L-S-' + LyS-) - 2B(J-L_ + J yLy) The l a s t two terms i n the expression f o r H are the off-diagonal elements i n A. 5. G. C, Dousmanis, T. H. Sanders and C. H. Townes, Physical Review 100, 1735 (1955). 7 SPECTRA OP HC1+ Prom the *2+ state to both 2TJ. and 2TT, states there were f i v e 2 t bands observed,7 which were found on the plates taken from a prism spectro-graph of low dispersion. The 0-0 band of 2 S + --*TT.L was chosen because i t could be photo-graphed i n the t h i r d order i n a region which was near the re g i a i of maximum r e f l e c t i o n of the grating mounting {maximum r e f l e c t i o n was b u i l t i n the spectrograph i n the v i c i n i t y of 10,000A). Another reason f o r choosing the 0-0 band was that the 0-0 v i b r a t i o n a l band was r e l a t i v e l y more intense than the other v i b r a t i o n a l bands of the same band system; and i n t e n s i t y was the deciding factor i n getting a clear optically-measurable spectrum on the photographic plates. 7. The f i v e bands observed were: 3-0, 2-0, 1-0, 0-0, and 0-1 band. 8 EXPERIMENTAL SET-UP AND TECHNIQUES The techniques involved were to get the HC1 + spectrum by ex c i t i n g the neutral HC1 gas molecules at low pressure i n a high e l e c t r i c f i e l d . fJ?his high. f i e l d produced the Stark s p l i t t i n g . HC1 gas was passed into the discharge tube together with some helium gas which acted as the c a r r i e r gas and at the same time gave r i s e to the atomic Stark s p l i t t i n g s f o r the estimation of the e l e c t r i c f i e l d . To the two ends of the discharge tube electrodes were attached, and an e l e c t r i c f i e l d was set up along the discharge tube using a high voltage d.c. power supply. The power supply gave a maximum output voltage of 20 Kv. The reason f o r not getting higher f i e l d s than those used i n the retolts was not l i m i t e d by the power supply, but by the rapid evaporation of the cathode wire under the experimental conditions (see below). Close to the end of the cathode was a projecting side-tube which pointed to the s l i t of the d i f f r a c t i o n grating spectrograph. Through t h i s s l i t the spectrum of a v e r t i c a l section of l i g h t from the discharge of the excited molecules was photographed (see page 3 o ). Therefore, the cathode had to be o p t i c a l ^ aligned with the lens, the s l i t and the grating (this was best done by using a neon l a s e r ) . The region of interest i n the discharge was the cathode dark space which was about 1-1 l/2mm. above the cathode. I t was here that the potential drop was greatest, (see f i g . 3 taken from Cobine's book on "Gaseous Conductors"). Therefore, the height of the cathode with respect to the s l i t of the spectrograph had to be adjusted, too. (This could be done by shining some l i g h t behind the cathode to cast the image of the cathode wire onto the s l i t , and by moving the wire up or down to get the right height). 9 The cathode was made of molybdenum and i t was in the form of a 1mm, diameter wire. It entered through a hole inside a copper cathode-feed mech-anism (see fig. 4 ). The upper portion of the wire was inside a quartz tubing whioh was fitted to a rubber stopper to go into the discharge tube. The copper mechanism served also as an outlet for the heat dissipated by the wire when the experiment was going. This heat generated was dissipated by an elec-tric blower. The incoming mixture of gases (HC1 + He) was pumped through the dis-charge tube by a mechanical pump. The total pressure was adjusted to 2-6 mm. of Hg. (read from a manometer). The incoming rate of each of the two gases was controlled independently by means of two controlling, adjustable needle valves. The gas mixture streamed through the discharge tube where i t was excited by the applied electric field to give the emission spectra. The gases were trapped by a cold trap in liquid air; residual gases which were not trapped had to be exhausted through a ventilation channel, because the hydro-chloric acid gas was extremely corrosive. (The whole experimental set-up is shown diagramatically in fig. 5). Pig. 3. Potential gradient along the discharge tube showing the different regions of a glow discharge. 10 Quartz tubing to shield the side of Mo wire leaving the t i p of i t as cathode Rubber stopper to f i t the whole mech-anism onto the dis-charge tube DeKhotinsky wax to hold the quartz tubing i n place and to seal the inside of copper support Adjustable copper barrel for changing the height of the cathode wire Air-tight space evacuated during the experiment Copper flap Screw connecting cathode wire through barrel Copper support Cathode-wire adjuster, a round piece of copper with insulating plastic handle Screw to hold cathode wire i n place Mo wire cathode 1 m m . i n diameter Pig. 4. Copper Cathode-feed Mechanism. (Not to scale) Fig. 5. Diagram of Experimental Set-up. 12 EXPERIMENTAL DETAILS AND DIFFICULTIES Good optical alignment could be obtained by using a laser beam taking advantage of the narrow structure of the beam. The height of the cathode dark space, the region of the steepest drop i n potential i n the dis-charge tube, was adjusted by shifting the whole system of glass-work upwards and downwards so that the image (magnified image) of the cathode would form right on top of a piece of white paper put on top of the s l i t . The main d i f f i c u l t y i n obtaining the Stark s p l i t t i n g expected came about because of the highly reactive nature of the HC1 gas. It reacted with the cathode wires so readily that i t made long photographic exposures d i f f i -cult- The cathode wires would have burned down and changed the configuration of the cathode dark space long before the exposure time was over. Long ex-posure was essential because the intensity of the spectrum of HC1+ was weak even on the most sensitive photographic plates available (Kodak 103a-0 plates). The choice of cathode material had been Al, W, Cu, Fe, C and Mo. Mo was the only material which could stand the 2-3 hours' exposure i n the presence of the amount of HC1 gas used i n the experiment; after the experiment the Mo wire changed i t s height relatively l i t t l e (approximately by lmm,)* This change was much less than changes for other wire material i f they were used under the same experimental conditions. This change i n height of the cathode wire automatically produced a shift i n the location of the cathode dark space. But for Mo this shift was tolerable because from most of the spectrographic plates obtained the spectra did not show any noticeable over-lapping. The proportions of HC1 to He passed into the discharge tube had to be such (see table l ) that the HC1+ spectrum,as well as the He atomic lines, could be obtained under the experimental conditions prescribed by the supply of e l e c t r i c a l power and the geometry of the cathode wire. Typical values of 13 HC1 gas i n the mixture was 0.2-J0.6mm. of Hg. i n pressure and He was 1.5 - 5.0mm. of Hg. It was found that i f the pumping rate of HC1 gas was in excess of the above amount the cathode wire would burn away significantly before two hours* exposure time was over; and i f the rate was smaller than the above, the HC1+ spectrum was too weak and could not be seen. When He was not used as a carrier gas the HC1+ spectrum was weak; when the amount of He used was be-low 2mm. i n pressure, the cathode dark space was relatively bigger than at a higher pressure and not much electric power was needed to maintain the dis-charge; but then the potential drop at.the dark space and the intensity of the resulting spectrum were low; i t was found out that some 2-5mm. pressure of He would give better re s u l t s . 8 Yet with this higher pressure inside the discharge tube, a higher voltage and consequently a higher current, was needed from the power supply; and the cathode wire would burn away faster. Also the cooling of the cathode wire became a problem; i f the cathode wire was not cooled s u f f i c i e n t l y fast, i t would soon become red-hot and turn into an arc discharge (rather than maintain a glow discharge which was required i n the experiment).9 It not only had changed the configuration of the discharge but also produced so much heat that the cathode wire burned down very fast and undesirably. In order to t e l l whether the discharge would give good spectra for HC1+ and He, the intensities of the coloured discharge were estimated by eye. HC.1+ gave a greenish colour around the cathode, and He gave a purple posi-tive column. After a few plates had been obtained i t was possible to t e l l roughly how intense each of these spectra would be before taking an exposure by looking at the colours of the discharge and by making necessary adjustments for the intensities. 8. American Journal of Physics. _3JL No. 8, p. 634, (August, 1963). Note that Cathode dark space i s also called Crookes dark space. TABLE 1 Experimental Conditions Voltage Current Pressure (HCl+He) HClsHe (Kv) (Ha) (mm.Hg) (mm.Hgsmm.Hg) 7.1 2.0 3.3 0.3s3.0 (printed p 6.0 3.3 3.5 0.3s3.2 6.8 3.2 3.8 0.3°.3.5 6.8 4.4 4.2 0.6§3.6 7.4 2.6 2.9 0.5s2.4 (printed p 6.8 4.5 2.2 0.5*1.7 15 TO SHOW THAT THE lTij, STATE BELONGS TO HUND'S COUPLING CASE (a) z i.e. LARGE MULTIPLET SPLITTING—A » (see energy level diagram on page *3 1 0 F^ CT) - F,"(T) = P, (T) - P,2(T) = Q3p) - Q2(T) =. R, (Jj - R^jJ With 7 - = 't | i v e ^ C.- e. 7 " = \ ) ' ° - F.VO = P, (0 " » 0*0) - 0 , ( 0 = *«0) - R 1 X 0 ) ' - 2 8 400.qs- 27737.il or 28444.07-2778°-8O ° r 28445.55 -2y]B2.2S^) - 64332 C W . ' 1 o r 4^ 5.27 o r 64i.30 Tke average = 443 . 3 0 ' i , " ' B u t , F/CD- F,'(J) = B;/^TTTF+WM) u/^,e -4- = Y ^ B;=B; T a k i n g B0' = ^ 7 8 7 / , i t jives 4 6s .30= 9.787 { 4 x 4 + r(r-4)} •67.7s-1 = + r a-4r Y - +4 ± .1)4 + 4 x 4S85,fefe - 1 (4 ± I35.5J 2 = o r -65.7 •A = ^ . 7 or -4s. 7 T/i/'s vesu/t s k e w s that A » S/nce A » ' 3 J -He. A - doutlm^ is d i r e c t l y proportional to f ^ e t o t a l mo lecw la r a . i g w U r m o w e n t u m , " 10. Folke Norling, 2. Physik 104. 638 (1935). 11. G. C. Dousmanis, T. M. Sanders and C. H. Townes, Physical Review 100. 1735 (1955). 16 DETERMINATION OF ELECTRIC FIELD STRENGTH FROM He 3614A BY A COMPARATOR The position of a line was determined by superposition of line profiles on a screen of a comparator. This process had an error of - 0.005 mm. e The dispersion around He 3614A was 27665.027 cm"1 (He) - 27660.340 enT^Mo) 138.484 mm.(He) - 137.500 mm.(Mo) = 4.687 cm"1 = 4.77 cm"1 0.984 mm. 1.0 mm. TABLE 2 Calculation of Electric Field Strength. Stark com-ponents of He 3614A Measure-ments taken from print Readings i n mm. D* D Undisplaced F' line d 29.489 Separation from normal line i n mm. 9»0 Separat ion 42.9 from normal ^ line i n cm." Electric f i e l d i n Kv. per cm. Measure-ments taken from print Readings i n mm. 31.888 32.052 Separation from normal line i n mm, 6.60 Separation 31.5 from normal . line i n em." Electr i c f i e l d i n Kv. per cm. 6.43 30.2 0 0 0 0 0-0 45 C, C G' G 38.484 40.276 45.020 2.24 6.54 -10.7 -31.2 38.484 39.515 39.759 1.03 -4.85 1.28 -6.12 P« 47.114 8.63 -41.2 35 17 Note. Prints 1 & 2 are shown on page f<j; also see f i g . 6 & f i g . 7. For Stark splittings unprimed letters denote parallel components and primed letters denote perpendicular components. 12. J. S. Poster, Royal Society London Proceedings A 117. p. 147, (1927/28). Fig. 6. Pattern of Stark splittings of He 3614A. D' D Pig. 7. Energy level diagram of 2 S — 5 Q for Helium 3614A. Hi$H fie Id rn IS.. P. • 4 • z o • / 3 Z o I 3 2 o I - 0 Note. This shows the electronic transitions due to Stark s p l i t t i n g solid lines give parallel components (Am = 0), these are denoted by un-primed letters; and dotted lines give perpendicular components (dm = i l ) these are denoted by primed letters. 20 THE EVALUATION OP p-TYPE DOUBLING USING COMBINATION RELATIONS ( R ^ ^ - Q ^ K ) ) (see energy level diagram on page 2 2 ) . 13 Prom the energy level diagram on page 2 2, i t i s obvious that R^dO - gives the energy difference between the z 2 + state, this s p l i t t i n g i s referred to as r, -type doubling. TABLE 3 Pig. 8. The values of the ^-type doubling essential for the calculation of A-doub l i n g , (see page 23 ) 13. Polke Norling, Z. Physik 104, 638 (1935). 21 THE CALCULATION OF ROTATIONAL TERMS OF THE 0-0 BAND OF HCl + IN STATE (This calculation i s also needed i n the calculation of A-doubling as seen on page 23 ). This i s the calculation for finding the differences between term values of two neighbouring levels i n the 2_T+ state, each of these (except the lowest one) i s doubly-degenerate and i s speoified by the quantum number K where K = A + N. K - total quantum number apart from spin, 7\ = the component of electronic orbital angular momentum along the internuclear axis, and N = the angular momentum of nuclear rotation. From Norling's article on HC1+, B and D the rotational constants for the vibrational state v* = 0 are: B = 7.34; D = 6.26x10."*^ TABLE 4 K K(K+l) K 2 ( K+l) 2 BK(K+l) DK 2(K+l) 2 BK(K+l) - DK2(K+1)2 0 0 0 0 0 0 1 2 4 14.68 0 14.68 2 6 36 44.04 0.02 44.02 3 12 144 88.08 0.09 87.99 4 20 400 146.80 0.25 146.55 5 30 900 220.20 0.56 219.64 6 42 1764 308.28 1.10 307.18 7 56 3136 411.03 1.96 409.07 8 72 5184 528.47 3.24 525.23 9 90 8100 660.59 5.07 655.52 10 110 12100 807.39 7.57 799.82 14. Folke Norling, Z Physik 104, 638 (1935). 15. X(K) gives the term value when each level of 2 i s doubly-degenerate . 22 Fig, 9. Diagram of Energy Levels and Transitions of 2 ^ + - Vj. an* Vr3 2 4 5 5 4 5-5£" 3 t -3 f -X — z etaaJu a " « o f a of d'aaOC <3 o? &=• + F, -+ F t -- 1 • - IV + F'-+ - F,. - Fz • + F,-+ F1 - F, ~ F.-+ F, •TT, r"->-5" 5 K* 5 I 3 c 0 4 4t-4 * 4t-Mr -z ' i -"+F» —- - F» -rr r-t 3 • - f , - -Fl - « -F . 23 THE EVALUATION OP A-DOUBLING PROM COMBINATION RELATIONS (For A = /\(j**-l/2) with B = 7.34; refer to energy level diagram on page 22 ). In the following calculations X(K) « BK(K + l ) - DK2(K + l ) 2 whose values are obtained from page 21 . A(O) = 1/2 (Q 2(0) + R 1 2(0)) - X(l) - Q 1 2(0) = l/2(781v24:+;782.25) - 14.68 - 766.54 = 0.52 Alternatively, A(0) . 1/2 (Q 2(0) + R 1 2(0)) - R 2(0) + X(2) - X(l) 1 6 = 1/2 (781.24 + 782.25) - 809.74 + 44.02 - 14T'6S - tl.47)(0.6.) =?.0;46 A(l) = 1/2 ( R 1 2 ( l ) + Q 2 ( l ) ) - 1/2 ( Q i 2 ( l ) + P 2 ( l ) ) - X(2) + X(l) '» 1/2 (782.25 + 780.80) - l/2 (751.39 + 750.58) - 44.02 + 14.68 = 1.21 A(2) = 1/2 (R12(2) + Q 2(2)) - l/2 (Q 1 2(2) + P 2(2)) - X(3) + X(2) = 1/2 (777.16 + 775.12) - l/2 (731.15 + 729.75) - 87.99 + 44.02 = 1.72 A(3) = 1/2 (R 1 2(3) +Q2(3)) - 1/2 (Q 1 2(3) + P 2(3)) - x(4) + x(3) = 1/2 (766.96 + 764.29) - l/2 (705.74 + 703.62) - 146.55 + 87.99 = 2.38 A(4) = 1/2 (R 1 2(4) + Q 2(4)) - 1/2 (0^,(4) + P 2(4)) - X(5) + X(4) = 1/2 (751.39 + 748.14) - l/2 (675.11 + 672.46) - 219.64 + 146.55 = 2.89 A(5) = 1/2 (R ± 2(5) + Q 2(5))- 1/2 (Q 1 2(5) + P 2(5)) - X(6) + X(5) = 1/2 (730.60 + 726.76) - l/2 (639.38 - 636.01) - 307.18 + 219.64 = 3.44 A(6) = 1/2 (R 1 2(6) + Q 2(6)) - 1/2 (Q 1 2(6) + P 2(6)) - X(7) + X(6) = 1/2 (704.59 + 700.14) - l/2 (598.41 + 594.59) - 409.07 + 307.18 = 3.97 16. In 2 ^ states the rotaional terms values of the doublet are given by F X(K) = B rK(K+l) + 1/2 YK and F 2(K) - B K(K+l) - l/2 ar(K+l) , where IT is a constant. In this calculation, X(2) i s taken from the degenerated 2f level with K = 2, but R^O) i s measured from the lower of the two non-degenerate level, therefore a value of g£^£pjy where K = 2 has to be subtracted as shown above. 24 Pig. 10. This plot shows that the A-type doubling of the components vary linearly with J (see page ID ). 25 Using the least square f i t to find the slope and intercept of the graph for A-doubling. Let y = a + bx where y i s the ordinate and x the abscissa, then a is the intercept on the y axis and b the slope of the graph y = y(x). From the mathematical analysis to find the least square f i t , b = jpf and a = y - bx where ~ means average value. Using the data on page 2 3 , X y xy x2 1 2 0.48 0.48 2 1 4 1 2 1.21 3.63 2 4 1. 2 1.72 8.60 2 2£ 4 1 2 2.38 16*66 2 42 4 1 2 2.89 26.pl 2 81 4 11 2 3.44 ?7»84 2 121 4 22. 2 3.97 51 f6l 2 169 4 2 ^ y = 16.09 144.83 ~ 2 ^ x2 " 4 X = 2 2 y = 2.299 xy 20f69 2 x2 _ 65^0 " 4 b xy-xy = ° - 5 7 4 6 ; a 0.2889 For 1 X - 2 y = a = bx = = 0.2889 + 0.5746 x 1 2 0.5762 This agrees with the value obtained on the graph (see page 24 ). 26 CONCLUSION DEDUCED PROM THE BEST PLATES OBTAINED PROM THE EXPERIMENT If S (S = 2 A 6 ), the change in energy due to Stark sp l i t t i n g , had been discernible, then i t would be at least (0.35 - 0.05) cm."1 (S = 2At - 0.14 mm. giving A£= 0.07 x 5 cm."1 = 0.35 cm."1), which was the separation between two lines obtained at this grating setting that could be definitely resolved on the comparator. (AZY- I J ( J + I ) J + T where for J = l/2, _n.= l/2, M = l/2, A= A(0) = 0.58 cm."1; and taking E = 45^° cm. For /U. equal to one debye (a unit of the electric dipole moment), / c E i s equal to 0.168 cm."1 i n a f i e l d of 10 Kv. per cm. Therefore, i f such s p l i t t i n g had been observed for any of the low J lines as mentioned above, i t would give; (0.55)2 - £ ^ E M - n - 12 J ( J + D „ + O-EM-n-T yuEM -a. = j(j+l) ^126 = /c4.5 x | x | .1225 = fy^ EM-n. J + .0841 .196 191 .168 2 2 • yu ^ 0.78 debyes 1 x 1 2 2* Since no such s p l i t t i n g (not even broadening of any of the lines of low j ) had been observed on the plates taken with electric fields up to 45 Kv, per cm., the electric dipole moment of the charged HC1+ molecule 2Vx state could not be greater than 0.8 debye was the conclusion. 27 IN THE ANALYSIS OF THE H C 1 + SPECTRUM Since the cathode used i n the experiment was Mo, the strong atomic lines of the metal due to the spark discharge of cathode material appeared together with the H G 1 + spectrum and i t made the analysis more complicated. Also, there was the rotational isotope effect; for every Q2 line and R 1 2 line of the 0 - 0 band of 2 £ f - 'lTT± there was a weaker line close to i t 3L 1 at lower wavelength due to the presence of the Isotope HCI57, which was less abundant than HCI35. There was one peculiar point about the spectrum of H C 1 + obtained; at the high f i e l d region (see prints produced on page 19 ) there was a sharp reduction i n intensity of the H C 1 + spectral lines. This phenomenon was not observed for spectra of OH, NH, and CH which were obtained by the same method. The only explanation for this large reduction i n . intensity of of the H C 1 + spectrum was that i n the high f i e l d region a l l the positively charged H C 1 + ions were accelerated towards the cathode. This process increased the number of collisions of these charged particles with other particles and a lot of these H C 1 + ions lost their energy i n c o l l i s i o n with He to give Stark s p l i t t i n g of the latt e r (N.B. In the stream of gaseous mixture there was a lot more He than HCl); consequently,, there was not as much de-excitation of H C 1 + molecules i n the form of electronic transitions ( i2;+-2TT j i n the cathode dark space as i n the region of the positive column where the HCl molecules, on the whole, did not lose as much of their energy to excite the He molecules by c o l l i s i o n as i n the high f i e l d region. (see print on page i<J ). 28 AN IMPROVEMENT FOR THE EXPERIMENT If the cathode can be cooled s u f f i c i e n t l y f a s t , i t w i l l keep the sputtering, a continual disintegration of cathode surface, much lowers and at the same time the discharge can be run at higher power and thus acquire a l bigger drop i n potential at the cathode dark space, which i s needed i n order to f i n d such a small dipole moment as that of the charged H C 1 + molecule. One way of doing i t i s to have the cathode wire connected to a good e l e c t r i c and heat conductor which i s to be cooled by c i r c u l a t i n g water around i t con-stantly. (The e l e c t r i c and heat conductor can be of the same form as the cathode-feed mechanism used i n the experiment.) < 29 BIBLIOGRAPHY 1. American Journal of Physics. J j l , No. 8, 634 (August, 1963). 2. Cobine, J. D., Gaseous Conductors. McGraw-Hill Book Co., 1941. 3. Dousmanis, G. C , Sanders, T„ M., and Townes, C. H., Physical Review. 100. 1735 (1955). 4. Poster, J. S., Royal Society London Proceedings A. 147. 117 (1927/28). 5. Herzberg, G,, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules. D. Van Nostrand Co., 1953. 6. Irwin, T., and Dalby, P. ¥„, Canadian Journal of Physics. January, 1965. 7. Kulp, M., Z. Physik. 62, 7 (l93l). 8. Norling, P., Z,__Physik„ j ^ , 638 (1935). 9. Phelps, D. and Dalby, P. W., Canadian Journal of Physios. January, 1965. 30 APPENDIX There was one possibility which would make the conclusion vulnerable. In the analysis of the photographic plates taken i t was assumed that the spec-trum of HC1 represents transitions of molecules of HC1 i n the region of the cathode dark space where the atomic He atoms were simultaneously excited. But a ve r t i c a l section of the discharge was photographed (see page 8), with the high f i e l d region at the focus; there was the possibility, which was assumed to be slight throughout this piece of work, that there were not as many HC1+ molecules in the high f i e l d region as there were in the outer portion of the cone of light photographed where the HC1+ molecules were acted upOn by a lower electric f i e l d . Therefore the spectral lines of HC1+ might have come from transitions i n a region of relatively much lower electric f i e l d strength. If this was the case, then the conclusion found above (on page 2j) would not 17 be accurate and needs to be modified. 17. Dr. F.W. Dalby has investigated into this point more thoroughly in his ifork on Stark effect of CO. 

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