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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 . S c , U n i v e r s i t y 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 t h e s i s as conforming t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1966  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements  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 that 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 reference and study.,  I f u r t h e r agree that permission, f o r extensive  copying of 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 granted by the Head of my Department or by h i s representatives.  I t i s understood that copying  or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  The U n i 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 i n which a high electric f i e l d was applied; optical plates were obtained from the spectrograph and analysed. Dipole moment of HC1 i n the V state was found to be smaller +  x  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.  iii  TABLE OF CONTENTS Page Introduction  1  Theory  2  P e r t u r b a t i o n and mathematical representation of Stark s p l i t t i n g  ..  3  The change i n energy due t o Stark e f f e c t assuming Hund's coupling case a  4  ..  Lambda doubling and i t s t h e o r e t i c a l representation  6  Spectra of HC1  7  +  .....  Experimental  set-up arid techniques  Experimental  d e t a i l s and d i f f i c u l t i e s  8 12  To show that  s t a t e belongs t o 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 e v a l u a t i o n of p-type doubling using combination r e l a t i o n s  ...  The c a l 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 £ +  state  .  z  20  +  21  The e v a l u a t i o n of A - d o u b l i n g from combination r e l a t i o n s  23  Conclusion  26  I n the a n a l y s i s 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  2.  Vector diagram f o r Hund's coupling'-case (a)  3.  P o t e n t i a l gradient along a discharge tube  4.  Copper cathode-feed mechanism  10  5.  Diagram of experimental set-up  11  6.  P a t t e r n 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 -  18  8. 9. 10.  3 .  4 9  5 Q f o r He 3614A  o -type doubling of 0-0 band of HC1  +  iii V  state  Diagram of energy l e v e l s and t r a n s i t i o n s of A - t y p e doubling of 0-0 band of HC1  +  ..........  Z - T\ and X  i n ^IV  £ - TT.  20 22 24  state  2  LIST OF TABLES  Page 1.  Experimental conditions  14  2.  C a l c u l a t i o n of e l e c t r i c f i e l d strength  16  3.  Combinations r e l a t i o n s  20  4.  Rotation terms of 0-0 band of HC1  +  in % state  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 d i p o l e moments of OH, NH and CH by means of Stark s p l i t t i n g s has been i n v e s t i g a t e d by u s i n g an o p t i c a l method; 1 and t o obtain the same quantity of a charged molecule by the same method was the object of the experiment. The spectra of HC1 had been i n v e s t i g a t e d by N o r l i n g and Kulp, 2 +  and t h e i r a n a l y s i s was used t o i d e n t i f y the s p e c t r a l l i n e s of i n t e r e s t i n t h i s experiment.  1. D. Phelps and Dalby, Canadian Journal of Physics (January, 1965); T. I r w i n and Dalby, Canadian J o u r n a l of Physics (October. 1965). 2. Polke N o r l i n g . 2. Physlk 104. 638 (1935); M. Kulp, Z. Physik 62, 7 (1931).  2  THEORY  One o f 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 a r i s e s because the e l e c t r i c charge w i t h i n the nucleus of the molecule i s not symmetrically d i s t r i b u t e d ) .  The perturbation produced by the a c t i o n  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; w  s  see A - d o u b l i n g on page f ) by a quantity (aee page k)  -yu.i  I n p r a c t i c e , 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 g r a t i n g  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 f i n d i n g the atomic Stark s p l i t t i n g s 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. F o r the estimation o f e l e c t r i c f i e l d strength from the S t a r k 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 f i r s t order approximation the perturbation brought about by an electric f i e l d i s obtained by solving the secular equation of the perturbation matrix W, W.  21  which gives I = i (Z, + £ 2 ) ± t  J .4 |w;J*+ o- 2  where  =  £  3  i.e.  but  and  J(J+1) S = A  (see page 4)  where A i s t h e l a m b d a - d o u b l i n g .  Hence, i f _. 6 i s measured from Stark splitting, and A calculated from combination relations for electronic bands, the electric dipole moment JLL w i l l be obtained.  4  4. Actually, for any Stark splitting the quantity to be measured on the plate i s S = 2 _ 8 (see f i g . 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 i n t e r a c t i o n of nuclear r o t a t i o n w i t h e l e c t r o n i c s p i n S as w e l l as e l e c t r o n i c o r b i t a l angul a r momentum L i s very low, whereas the e l e c t r o n i c spin.and o r b i t a l angular momentum i s coupled very strongly together t o the l i n e j o i n i n g the n u c l e i . The component of the e l e c t r o n i c o r b i t a l angular momentum along the i n t e r nuclear a x i s i s represented by A ; w h i l s t the e l e c t r o n i c spin along the' i n t e r n u c l e a r a x i s i s represented by 2 .  When these two couple together  they give«n_the t o t a l e l e c t r o n i c angular momentum about the i n t e r n u c l e a r a x i s . -A. then couples w i t h the nuclear angular momentum N t o give J the t o t a l angular momentum of the molecule.  Here j& i s the mean component of the electric dipole moment i n direction of the internuclear axis, /L  T  I S i t s value along the J-axis.  And, /W-j.E i s the change i n energy due to the electric f i e l d strength E on this electric dipole.  In the presence of the electric f i e l d J, the  total angular momentum, i s quantized along the f i e l d direction and this quantization i s denoted by M. Thus by trigonometry that relates a l l the above quantities as shown i n f i g . 2, the above result follows.  6  LAMBDA-DOUBLING ( A-DOUBLING) AND ITS THEORETICAL REPRESENTATION  A molecule which i s i n an e l e c t r o n i c state other than the state ( i . e . A other than 0), the off-diagonal  2.  has doubly degenerate r o t a t i o n a l l e v e l s , i f  elements of the r o t a t i o n a l and s p i n - o r b i t  interaction  5 energies are neglected.  But once t h i s i n t e r a c t i o n i s taken i n t o account  there w i l l be a s p l i t t i n g of each r o t a t i o n a l l e v e l (each of which i s being denoted by a value J") i n t o two components,  (This i s c a l l e d the removal  of degeneracy). The change i n energy f o r n i l e v e l s i s given by^ (j) = K(j) where K i s a constant, (see page 24.) z  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 m u l t i p l e t state i s assumed to be i n Hund's case ( a ) , i . e . large m u l t i p l e t s p l i t t i n g — A »  where A designates the s p i n -  coupling constant f o r f i n e structure i n t e r a c t i o n and B " v  designates the  r o t a t i o n a l constant (see page 15 f o r the c a l c u l a t i o n of the constant A). I f the Z d i r e c t i o n i s along the i n t e r n u c l e a r a x i s , L and S are the e l e c t r o n o r b i t a l and spin angular momenta r e s p e c t i v e l y , J the t o t a l angular momentum exclusive  of nuclear s p i n , and  associated w i t h L , then the off-diagonal  A i s the quantum number  elements of the molecular Hamil-  z  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 = B(j(j  2  - L_)2• + (  J y  _  - Ly) ] + AL S 2  S y  Z  +l) « A J + BS(S + l ) + A L S  + A(L_S_ +  - 2BJ.S + B d ^  2  Z  Z  Z  2  L-S-)  +Ly ) + 2  (2B + A)(L-S-' + LyS-) - 2B(J-L_ + J L y ) y  The l a s t two terms i n the expression f o r H are the off-diagonal  5. 100,  elements i n A.  G. C, Dousmanis, T. H. Sanders and C. H. Townes, P h y s i c a l Review 1735  (1955).  7  SPECTRA OP HC1+  Prom the *2+ s t a t e t o both TJ. and TT, states there were f i v e 2  2  t  2  bands observed,7 which were found on the plates taken from a prism spectrograph of low d i s p e r s i o n . The 0-0 band of S 2  +  --*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 r e g i a i of maximum r e f l e c t i o n of the g r a t i n g 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 f a c t o r i n g e t t i n g a c l e a r optically-measurable spectrum on the photographic p l a t e s .  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 i n v o l v e d were t o get the HC1 spectrum by e x c i t i n g +  the n e u t r a l HC1 gas molecules at low pressure i n a high e l e c t r i c f i e l d . J?his high. f i e l d produced the Stark s p l i t t i n g .  f  HC1 gas was passed i n t o the discharge tube together w i t h 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 g e t t i n g 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 r a p i d evaporation of the cathode wire under the experimental conditions (see below). Close t o the end of the cathode was a p r o j e c t i n g side-tube which pointed t o the s l i t of the d i f f r a c t i o n g r a t i n g spectrograph.  Through t h i s  s l i t the spectrum of a v e r t i c a l s e c t i o n of l i g h t from the discharge of the e x c i t e d molecules was photographed (see page 3 o ). Therefore, the cathode had t o be o p t i c a l ^ a l i g n e d with the l e n s , the s l i t and the g r a t i n g ( t h i s was best done by u s i n g a neon l a s e r ) . The region of i n t e r e s t i n the discharge was the cathode dark space which was about 1-1 l/2mm. above the cathode. p o t e n t i a l drop was greatest, "Gaseous Conductors").  I t was here that the  (see f i g . 3 taken from Cobine's book on  Therefore, the height of the cathode with respect t o  the s l i t of the spectrograph had to be adjusted, too. (This could be done by s h i n i n g some l i g h t behind the cathode t o cast the image of the cathode wire onto the s l i t , and by moving the wire up or down t o get the r i g h t h e i g h t ) .  9  The cathode was made of molybdenum and i t was i n the form of a 1mm, diameter wire.  It entered through a hole inside a copper cathode-feed mech-  anism (see f i g . 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 elect r i c blower. The incoming mixture of gases (HC1 + He) was pumped through the discharge tube by a mechanical pump. The total pressure was adjusted to 2-6 of Hg. (read from a manometer).  mm.  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 f i e l d to give the emission spectra.  The gases  were trapped by a cold trap i n liquid air; residual gases which were not trapped had to be exhausted through a ventilation channel, because the hydrochloric acid gas was extremely corrosive.  (The whole experimental set-up  i s shown diagramatically i n f i g . 5).  Pig. 3.  Potential gradient along the discharge tube showing the different regions of a glow discharge.  10  Quartz tubing to s h i e l d the side of Mo wire leaving the t i p of i t as cathode  Rubber stopper to f i t the whole mechanism onto the d i s charge tube  DeKhotinsky wax to hold the quartz tubing i n place and to seal the inside of copper support Adjustable copper b a r r e l f o r changing the height of the cathode wire A i r - t i g h t space evacuated during the experiment Copper f l a p Screw connecting cathode wire through barrel Copper support  Cathode-wire adjuster, a round piece of copper with i n s u l a t i n g p l a s t i c 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)  F i g . 5.  Diagram of Experimental Set-up.  12  EXPERIMENTAL DETAILS AND DIFFICULTIES  Good o p t i c a l alignment could be obtained by using a l a s e r 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 p o t e n t i a l i n the d i s charge tube, was adjusted by s h i f t i n g the whole system of glass-work upwards and downwards so that the image (magnified image) of the cathode would form r i g h t 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. the  I t reacted with  cathode wires so r e a d i l y 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 e s s e n t i a l because the i n t e n s i t y 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 A l , 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; a f t e r the experiment the  Mo wire changed i t s height r e l a t i v e l y l i t t l e  (approximately by lmm,)*  This change was much less than changes f o r 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 s h i f t i n the location of the cathode dark space.  But f o r Mo t h i s s h i f t was tolerable because from most of the  spectrographic plates obtained the spectra d i d not show any noticeable overlapping. 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 l i n e s ,  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.  T y p i c a l 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.  I t was found that i f the pumping rate of HC1 gas was i n excess of the  above amount the cathode wire would burn away s i g n i f i c a n t l y 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  c a r r i e r gas the HC1 spectrum was weak; when the amount of He used was be+  low 2mm. i n pressure, the cathode dark space was r e l a t i v e l y bigger than at a higher pressure and not much e l e c t r i c power was needed to maintain the d i s charge; but then the p o t e n t i a l drop at.the dark space and the i n t e n s i t y of the r e s u l t i n g spectrum were low; of He would give better r e s u l t s .  i t was found out that some 2-5mm. pressure 8  Yet with t h i s 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 f a s t , 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  I t not only had changed the configuration of  the discharge but also produced so much heat that the cathode wire burned down very f a s t and undesirably. In order to t e l l whether the discharge would give good spectra f o r HC1  +  HC.1  +  and He, the i n t e n s i t i e s of the coloured discharge were estimated by eye. gave a greenish colour around the cathode, and He gave a purple p o s i -  t i v e column.  A f t e r 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 f o r the i n t e n s i t i e s .  8. American Journal of Physics. _3JL No. 8, p. 634, (August, that Cathode dark space i s also c a l l e d Crookes dark space.  1963).  Note  TABLE 1 Experimental Conditions Voltage (Kv)  7.1 6.0 6.8 6.8 7.4 6.8  Current (Ha)  2.0 3.3 3.2 4.4 2.6 4.5  Pressure (HCl+He) (mm.Hg)  3.3 3.5 3.8 4.2 2.9 2.2  HClsHe (mm.Hgsmm.Hg)  0.3s3.0 (printed p 0.3s3.2 0.3°.3.5 0.6§3.6 0.5s2.4 (printed p 0.5*1.7  15  TO SHOW THAT THE Tij, STATE BELONGS TO HUND'S COUPLING CASE (a) l  z  i.e.  LARGE MULTIPLET SPLITTING—A »  F^CT) With  F,"(T) =  7 -  't | i v e ^ C.- e. "  »  - Q (T) 2  R^jJ  P, (0  -  2 8 400.qs- 27737.il or 28444.07- 778°-8O ° 28445.55 -2y]B2.2S^)  0*0)  -  0,(0  64332  CW.'  443.30  'i,"'  B ' = ^787/ ,  it  0  9.787  •67.7s- =  or  1  4^5.27  -  vesu/t  =  +4 1  A»'3J  total  mo lecw l a r  1 X  0)'  r  or  64i.30  u/^,e -4- = Y ^  B;=B;  jives  {4 x 4  r(r-4)}  +  ± .1)4 + 4 x 4S85,fefe 2  (4  ^ .  skews  S/nce  R  a  =  •A  -  + r -4r  1  Y  = *«0)  2  4 6s.30=  T/i/'s  10  7 " = \ ) ' °  F / C D - F,'(J) = B ; / ^ T T T F + W M )  Taking  =. R, (Jj -  *3  =  average =  But,  3  2  Tke  Q p)  P, (T) - P, (T) =  =  F.VO  (see energy l e v e l diagram on page  -He.  7  ±  I35.5J  or  -65.7  or  -4s.  that  7  A »  A - doutlm^  a.igwUr  is  directly  proportional  to  mowentum,"  10.  Folke Norling, 2. Physik 104. 638 (1935).  11.  G. C. Dousmanis, T. M. Sanders and C. H. Townes, Physical Review 100. 1735 (1955).  f^e  16  DETERMINATION OF ELECTRIC FIELD STRENGTH FROM He 3614A BY A COMPARATOR  The p o s i t i o n of a l i n e was determined by superposition of l i n e p r o f i l e s 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" (He) 138.484 mm.(He) 1  27660.340 enT^Mo) 137.500 m m . ( M o )  =  4.687 cm" 0.984 mm.  1  =  4.77 cm" 1.0 mm.  1  TABLE 2 Calculation of E l e c t r i c F i e l d Strength. Stark components of He 3614A  D*  D  Undisplaced line d  G' G  F'  P«  Measurements taken from p r i n t Readings i n mm.  38.484  29.489  Separation from normal l i n e i n mm. 9»0 Separat ion 42.9 from normal ^ l i n e i n cm."  0  0-  0  0  Electric field i n Kv. per cm.  40.276  45.020  2.24  6.54  -10.7  -31.2  45  Measurements taken from p r i n t Readings i n mm. Separation from normal l i n e i n mm,  31.888  32.052  6.60  6.43  Separation 31.5 from normal . l i n e i n em." Electric field i n Kv. per cm.  30.2  38.484  39.515  39.759  47.114  8.63  0  C,  1.03  1.28  0  C  -4.85  -6.12  35  -41.2  17  Note.  P r i n t s 1 & 2 are shown on page f<j; also see f i g . 6 & f i g . 7. For Stark s p l i t t i n g s unprimed l e t t e r s denote p a r a l l e l  and primed l e t t e r s denote perpendicular  components.  12. J . S. Poster, Royal Society London Proceedings A 117. p. 147, (1927/28).  components  Fig.  6.  Pattern of Stark s p l i t t i n g s of He  3614A.  D' D  Pig. 7.  Energy l e v e l diagram of 2 S —  5 Q f o r Helium 3614A.  Hi$H  rn  fie Id  • 4 • z o  • / 3 Z o I  3 2 o I  - 0  P. IS..  Note.  This shows the e l e c t r o n i c transitions  s o l i d l i n e s give p a r a l l e l components (Am = 0),  due to Stark s p l i t t i n g  these are denoted by un-  primed l e t t e r s ; and dotted l i n e s give perpendicular components (dm = i l ) these are denoted by primed l e t t e r s .  20  THE EVALUATION OP  p-TYPE DOUBLING USING COMBINATION RELATIONS  (R^^-Q^K))  (see energy l e v e l diagram on page 2 2 ) . 13 Prom the energy l e v e l diagram on page 2 2, i t i s obvious that R^dO  -  gives the energy difference between the 2 z  +  state, t h i s  s p l i t t i n g i s referred to as r, -type doubling.  TABLE  Pig. 8.  3  The values of the ^-type doubling e s s e n t i a l f o r the  c a l c u l a t i o n 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 H C l  +  IN STATE  (This c a l c u l a t i o n i s also needed i n the c a l c u l a t i o n of A-doubling as seen on page 23 ).  This i s the c a l c u l a t i o n f o r f i n d i n g the differences between term values of two neighbouring l e v e l s i n the _T state, each of these (except the 2  lowest one) i s doubly-degenerate  +  and i s speoified by the quantum number K  where K = A + N. K - t o t a l quantum number apart from spin, 7\ = the component of e l e c t r o n i c o r b i t a l angular momentum along the internuclear axis, and N = the angular momentum of nuclear rotation. From Norling's a r t i c l e on HC1 ,  B and D the r o t a t i o n a l constants  +  f o r the v i b r a t i o n a l state v* = 0 are:  TABLE K 0 1 2 3 4 5 6 7 8 9 10  K(K+l) 0 2 6 12 20 30 42 56 72 90 110  14.  K (K+l) 0 4 36 144 400 900 1764 3136 5184 8100 12100 2  2  BK(K+l) 0 14.68 44.04 88.08 146.80 220.20 308.28 411.03 528.47 660.59 807.39  B = 7.34;  D = 6.26x10."*^  4  DK (K+l) 0 0 0.02 0.09 0.25 0.56 1.10 1.96 3.24 5.07 7.57 2  2  BK(K+l) - DK (K+1) 0 14.68 44.02 87.99 146.55 219.64 307.18 409.07 2  2  525.23  655.52 799.82  Folke Norling, Z Physik 104, 638 (1935).  15. X(K) gives the term value when each l e v e l of 2 degenerate .  i s doubly-  22  F i g , 9.  Diagram of Energy Levels and Transitions of  2  ^ - Vj.  Vr  an*  +  3  2  5  5-  + F, -  5£"  + Ft-  5  - 1•  4  - IV +  3t-  +  3f-  -  4  F'-  F,.  - Fz • + F,-  + F  1  - F, ~ F.X —  + F,  z  etaaJu  a " « o f a of d'aaOC  <3  o?  &=•  •TT,  r"->-  K*  5" 5  5  4 4  4t* 4t-  "+F»  I  3  Mr — - - F»  -z  'ic  -rr  0  r-t  • -f,  3  - -Fl - «-F.  23  THE EVALUATION OP A-DOUBLING PROM COMBINATION RELATIONS (For A = /\(j**-l/2) with B = 7.34;  r e f e r to energy l e v e l diagram on page 22 ).  In the following calculations X(K) « BK(K + l ) - DK (K + l ) whose 2  2  values are obtained from page 21 .  A(O) = 1/2 (Q (0) + R ( 0 ) ) - X(l) - Q ( 0 ) 2  12  12  = l/2(781v24:+;782.25) - 14.68 - 766.54 = 0.52 Alternatively, A(0) . 1/2 (Q (0) + R ( 0 ) ) - R (0) + X(2) - X(l) 2  12  1  6  2  = 1/2 (781.24 + 782.25) - 809.74 + 44.02 - 14'6S - tl.47)(0.6.) T  =?.0;46 A ( l ) = 1/2 ( R ( l ) + Q ( l ) ) - 1/2 ( Q i ( l ) + P ( l ) ) - X(2) + X(l) 1 2  2  2  2  '» 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)) - l / 2 ( Q ( 2 ) + P ( 2 ) ) - X(3) + X(2) 2  12  2  = 1/2 (777.16 + 775.12) - l/2 (731.15 + 729.75) - 87.99 + 44.02 = 1.72 A(3) = 1/2 ( R ( 3 ) +Q (3)) - 1/2 ( Q ( 3 ) 12  2  12  + P ( 3 ) ) - x(4) + x(3) 2  = 1/2 (766.96 + 764.29) - l/2 (705.74 + 703.62) - 146.55 + 87.99 = 2.38 A(4) = 1/2 ( R ( 4 ) + Q (4)) - 1/2 (0^,(4) + P ( 4 ) ) - X(5) + X(4) 12  2  2  = 1/2 (751.39 + 748.14) - l/2 (675.11 + 672.46) - 219.64 + 146.55 = 2.89 A(5) = 1/2 ( R ( 5 ) ±2  + Q ( 5 ) ) - 1/2 ( Q ( 5 ) + P ( 5 ) ) - X(6) + X(5) 2  12  2  = 1/2 (730.60 + 726.76) - l / 2 (639.38 - 636.01) - 307.18 + 219.64 = 3.44 A(6) = 1/2 ( R ( 6 ) + Q (6)) - 1/2 ( Q ( 6 ) + P ( 6 ) ) - X(7) + X(6) 12  2  12  2  = 1/2 (704.59 + 700.14) - l/2 (598.41 + 594.59) - 409.07 + 307.18 = 3.97  16. I n ^ states the rotaional terms values of the doublet are given by F ( K ) = B K ( K + l ) + 1/2 Y K and 2  X  r  F (K) - B 2  K(K+l) - l/2 ar(K+l) , where IT i s a constant.  In t h i s c a l c u l a t i o n , X(2) i s taken from the degenerated 2f l e v e l with K = 2, but R^O) i s measured from the lower of the two non-degenerate l e v e l , therefore a value of g£^£pjy where K = 2 has to be subtracted as shown above.  24  P i g . 10. This plot shows that the A-type doubling of the components vary l i n e a r l y with J (see page ID ).  25  Using the l e a s t square f i t to f i n d the slope and intercept of the A-doubling.  graph f o r  Let y = a + bx  where y i s the ordinate and x the abscissa, then a  i s the intercept on the y axis and b the slope of the graph From the mathematical jpf  b =  and  y = y(x).  analysis to f i n d the least square  a = y - bx  fit,  where ~ means average value.  Using the data on page 2 3 , X  1  0.48 2  1 4  1 2  1.21  3.63 2  4  1. 2  1.72  8.60 2  2£ 4  2  2.38  16*66 2  42  1 2  2.89  26.pl 2  81 4  11 2  3.44  ?7»84 2  121 4  22. 2  3.97  51 6l  169 4  1  X =  b For  ^y  2  2  X  1 - 2  = °- 74 5  2  = 16.09  6  4  f  y = 2.299  xy-xy  2  0.48  2  2  x  xy  y  ;  y = a = bx  a  ~ xy  144.83 2  ^x  20 69 2  2  x  f  " 2  4  _ 65^0 " 4  0.2889  == 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  I f S (S = 2 A 6 ), the change i n energy due to Stark s p l i t t i n g , had been d i s c e r n i b l e , then i t would be at least (0.35 - 0.05) cm."  1  - 0.14 mm.  g i v i n g A£= 0.07 x 5 cm."  = 0.35  1  (S =  2At  cm." ), which was the separation 1  between two l i n e s obtained at t h i s grating s e t t i n g that could be d e f i n i t e l y resolved on the comparator.  (AZY-  I  J ( J + I )  J  + T  where f o r J = l / 2 , _n.= l / 2 , M = l / 2 , A= A(0)  = 0.58  cm." ; and 1  taking E = 4 5 ^ ° cm. For /U. equal to one debye (a unit of the e l e c t r i c dipole moment), / c E i s equal to 0.168  cm."  i n a f i e l d of 10 Kv. per cm.  1  Therefore, i f such  s p l i t t i n g had been observed f o r any of the low J l i n e s as mentioned above, i t would give; ^EM-n-1  (0.55)2 - £  J(J+D  2  .1225  O-EM-n-T = fy^EM-n. J  .196  =  ^126 191 .168  +  „  +  .0841  yuEM -a.  j(j+l)  = /c4.5  x |x| 2 2  • yu ^  0.78 debyes  1x1 2  2*  Since no such s p l i t t i n g (not even broadening of any of the l i n e s of low j ) had been observed on the plates taken with e l e c t r i c f i e l d s up to 45 Kv, per cm.,  the e l e c t r i c dipole moment of the charged HC1  be greater than 0.8 debye was the conclusion.  +  molecule  2  Vx  state could not  27  IN THE ANALYSIS OF THE H C 1 SPECTRUM +  Since the cathode used i n the experiment was Mo, the strong atomic l i n e s 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 r o t a t i o n a l isotope e f f e c t ; f o r every Q 2 l i n e and R 1 2 l i n e of the 0 - 0 band of £ 2  f  ' TT l  ±  there was a weaker l i n e close to i t 3L  1  at lower wavelength due to the presence of the Isotope HCI57, which was l e s s abundant than HCI35. There was one peculiar point about the spectrum of H C 1 19  at the high f i e l d region (see p r i n t s produced on page  +  obtained;  ) there was a  sharp reduction i n i n t e n s i t y of the H C 1 s p e c t r a l l i n e s .  This phenomenon  +  was not observed f o r spectra of OH, NH, and CH which were obtained by the same method.  The only explanation f o r t h i s large reduction i n . i n t e n s i t y of  of the H C 1 spectrum was that i n the high f i e l d region a l l the p o s i t i v e l y +  charged H C 1 ions were accelerated towards the cathode. This process increased +  the  number of c o l l i s i o n s of these charged p a r t i c l e s with other p a r t i c l e s and  a l o t of these H C 1 ions l o s t t h e i r 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 l a t t e r (N.B.  In the stream of gaseous mixture there was a  l o t more He than HCl); consequently,, there was not as much de-excitation of HC1  +  molecules i n the form of e l e c t r o n i c t r a n s i t i o n s ( 2; - TT j i n the cathode i  +  2  dark space as i n the region of the positive column where the HCl  molecules,  on the whole, d i d not lose as much of t h e i r 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 p r i n t 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 s p u t t e r i n g , a c o n t i n u a l d i s i n t e g r a t i o n of cathode surface, much lowers and at the same time the discharge can be run at h i g h e r power and thus acquire a l  bigger drop i n p o t e n t i a l at the cathode dark space, which i s needed i n order to f i n d such a s m a l l dipole moment as that of the charged H C 1 molecule. +  One way of doing i t i s t o have the cathode wire connected t o a good e l e c t r i c and heat conductor which i s t o be cooled by c i r c u l a t i n g water around i t constantly.  (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  J j l , No. 8, 634 (August, 1963).  1.  American Journal of Physics.  2.  Cobine, J . D.,  3.  Dousmanis, G. C , Sanders, T„ M., and Townes, C. H.,  Gaseous Conductors.  Review. 100.  McGraw-Hill Book Co., 1941. Physical  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. Irwin, T., and Dalby, P. ¥„, Canadian Journal of Physics.  6.  January, 1965. 7.  Kulp, M.,  Z. Physik. 62, 7 ( l 9 3 l ) .  8.  Norling, P.,  9.  Phelps, D. and Dalby, P. W., January, 1965.  Z,__Physik„ j ^ ,  638 (1935). Canadian Journal of Physios.  30 APPENDIX There was one p o s s i b i l i t y which would make the conclusion vulnerable. In the analysis of the photographic plates taken i t was assumed that the spectrum of HC1  represents t r a n s i t i o n s of molecules of HC1  i n the region of the  cathode dark space where the atomic He atoms were simultaneously excited.  But  a v e 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 p o s s i b i l i t y , which was assumed to be s l i g h t throughout  t h i s piece of work, that there were not as many HC1  +  molecules i n the high f i e l d region as there were i n the outer portion of the cone of l i g h t photographed where the HC1 lower e l e c t r i c f i e l d .  +  molecules were acted upOn by a  Therefore the spectral l i n e s of HC1  +  might have come  from t r a n s i t i o n s i n a region of r e l a t i v e l y much lower e l e c t r i c f i e l d strength. I f t h i s 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 t h i s point more thoroughly i n h i s ifork on Stark effect of CO.  

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