The Hydrogen Atom Citation Langer, Rudolph Meyer (1927) The Hydrogen Atom. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/J73T-8Q43. https://resolver.caltech.edu/CaltechETD:etd-03262004-134242 Abstract [See scanned thesis for Abstract] Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Physics Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Millikan, Robert Andrews Thesis Committee: Unknown, Unknown Defense Date: 1 January 1927 Record Number: CaltechETD:etd-03262004-134242 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-03262004-134242 DOI: 10.7907/J73T-8Q43 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1131 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 26 Mar 2004 Last Modified: 03 Oct 2019 23:05 Thesis Files Preview PDF (Langer_rm_1927.pdf) - Final Version See Usage Policy. 5MB Repository Staff Only: item control page

THE HYTROGEN ATOM Thesis by R. M. Langer In partial fulfillment of the requirements for the degree of Doetor of Philcsophy. California Institute of Technology Pasadena, California 1927 THE HYDROGEN aAtToMW Re Me Langer Dissertation Submitted to the Board of Examiners of the California Institute of Technology according to the requirements far the degree Doctor of Philosophy in Phy sicse 1927. = THE HYDROGEN ATOM by Re Me lengere ABSTRACT. A critical examination of dispersion theory indicates that a@ measurement of the refractive index of atomic hydrogen is important for the theory of mattere Such an experiment is fully described and discussede The 2 o.ac)xro7? result is that fern = [.38 # 0-A6)X/o e Incidentally, it is found that a partial pressure of half a millimeter of atomic hydrogen can be had in a discharge tube while the discharge is one ‘Thermal conditions in such tubes are discussed and investigatede The experimental result is at first sigmt not in support of the new . 4 quantum mechanics which requires py! = 23X10 e However, by assuming that ye is connected with volume in the kinetic theory sense it tums out , 2, + that the expectation from the theary is effectively hal ue hF X/6 This leads support to the physical reality of the quantity YY y and leads to a prediction. of an increase in refractivity at very low pressures for almost any gaSe Pictures are given of the normal hydrogen atom and also its _ excited states and of the configuration under the action of a light wavee ~]— One of the most impressive features of classical electrodynamics is the ease and directness with which the phenomena of dispersion can be explainede The laws of dependence of the refractive index on frequency, density and tempera- ture can be described very successfully and the relation derived connecting refractive index with dielectric constant is indeed a triumph for the theorye In fact so sound are the foundationsof the theory that it has become a test of hypotheses of the structure of matter. the notions of atomic structure developed according to the quantum theory a5 it stood up to about a year ago have failed in. this test and for that reason as much as for any other they are being discarded. ‘the failure consisted chiefly in the fast that the frequencies UW; calculated from the formmla ; WV f —/ = oe ‘ a 2 P rm VA Yo- Vv ‘as derived by Sommerfeld, Epstein, Debye ami others on the basis of the older quantum theory were not in agreement with the observed frequencies of anomalous dispersion. =2- ‘This difficulty was so keenly felt that guided largely by a formula proposed by Ladenburg and improved by Kramers a new quantum theory was formu~ lated to adjust the matter. I mean to say that the matrix theory of Heisenberg, Born, and Jordan, is almost equivalent to assuming at the start that the atom is somposed of harmonic oscillators which are known to give anomalous dispersion at the frequencies which they absorb or emite The quantum conditiong PY-9P ~ ar? is merely a matrix statement of the rule which Kramers showed led to a satis- factory dispersion formula. The method of Schrodinger is not so brutally direct in achieving the Bale resulte On that account alone it is to be preferred. It has also the advantage that instead of considering just the energy relations involved in the problem, it gives description of the whole process. In other words it states the distribution of electric charge as a fonction of time and space under the action of the electric field of a light wave and permits the calcula- . tion of the resulting electric moment and connects this with the refract ive index as in the classical theorye It is in fact the first serious attempt at a cpmplete detailed account of the matter. Our formulae have heretofore -3 “phenomenological laws with qualitative justification on the basis of models -which no one believede The theories proposed in the past contained always more or less arbitrary quantities which were determined only by experinmnte The Schrodinger mechanics however, makes bold to predict quantitatively, all observable facts of dispersion (perhaps anomalous dispersion is not to be insisted on too strongly). ‘Where as the explicit expressions involving density temperature, frequency, field strength, etce, have not been published as yet, the principles according to which they can be derived, are imowns It mast be emphasized that we are now for the first time in position to use all qumtita- tive experiments as a test of tie theorye However, in attempting to take advantage of this possibility, one finds that so far only one case has been sufficiently treated theoretically. This case is the hydrogen atom in the normal state. This state of affairs makes the experimental determination of the refrastive index of atomic hydrogen & matter of considerable importance. What follows ia an account of such an experiment together with a dis- cussion of its relation to the theory. First, the principle of the measurement will be given and then mention will be made of several schemes to carry it —hn cate ihe wethod chosen will next be described and the result stated and analyzed especially from the point of view of precision and reliability in the face of the many spurious effects which play a parte ‘The observational evi- dence will be compared with the predictions of the theory of Schrodinger and cond1usions will be drawn as to the structure of the hydrogen atom and as well as to the interpretation to be plaed on the quantity which is called charge density in the new mechanicse de PRINCIPLE OF THE MEASUREMENT. In the determination of the refractive index of a gas there is no apparatus comparable with the interferomtere Which form is most convenient depends on the particular problem involved but the principle of the measurement is the same for all, namely - the optical path of a beam of light traversing a geometrical distance L in a medium of refractive index ph is ple A change in optical path ig indicated in an interferometer by a shift of fringes. If one path is kept constant and another changed by A ( B L) then the fringes du to the superposition of a@ monochromatic beam of wave length A which has tra~ versed one of these paths on « chherent beam which has traversed the other, =H = “will shift according to the equations y= 4 pL) A a (1) . where 4 N is measured in fringese As AN, A and L are easily observable quantities A is readily computede If we have a value of jo for comparison ‘then any other KK is knowne The reference is furnished by taking for a “vacuum equal to unitye In the experiment under consideration only the roughest sort of numeri- eal value can be hoped fare We may at first disregard the minor departures from the standard laws and making the approximations that are allowed because ia is close to one we may write, if P is density and T temperature f* —~ Crclard (2) and Oh - oO me aT (3) If then, the fringe system is determined by a certain length of path containing molecular hydrogen at pressure p, on changing a known fraction of the molecules into atoms, a shift will be produced according to an equation which can be deduced from (1) and (2); namely, ~y i _ WL ae sp) — [py rt AN = “= == £4) i? where L is measured in coms if } is measured in cms, p is the initial pressure (#) ~6- "ye molecul ar hydrogen in MIDS » f the tempe ra ture at which it has the pressure p | (the volume being assumed invariable) and where } is the fraction of hydrogen which *s dissociatede The quantities “4 and “14 are the refractive indices of molecular and atomic hydrogen respectively under standard conditions, hee 760 mn, 0°Ce The gamin “bd the Michel son interferometer are both suitable for the determination of the quantities in (4), especially because they permit large values of L and therefore give high sensitivity. Possible Methods. The main difficulty in the experimental technique is to prodwe the sufficient atomic hydrogen and keep it long enough to make the as aeuremntne Perhaps the most attractive means i& to use high temperatures to produce the dissociatione We can calculate the dissociation as a funa ion of the temperature from the equation of van t'Hoff =m where k is the equilibrium constant of the reaction H, = 2H, 1ee- BR yy” Using the syecific heats and entropies of atomic and molecular hydrogen given by lewis and Randall, we can integrate the equation ami gets - RT log k = Q, - 305 T log T + 200045 “” + 117? where Qo, the heat of dissociation of molecular hydrogen is now known definitely to be very close to 105,000 calories per molee This equation shows that for a pressure of 1 om, dissociation begins to become appreciable at 2000°% and at 2500° most of the molecules are broken upe Duffendack has designed a furnace which attains such temperatures and with it he has produced dissociation in hydrogen and other gasese Wich such a technique in mind, preliminary experi- ments were carried out to find whether interferometric ne ieatenents could be | made under conditions where violent convection was taking placee Whereas a great deal could be done by judicious arrangement of the apparatus, still it was found that the fringss were too unsteady for accurate reading in tubes subject to temperatures of only a few hundred degrees over room temperature, and results were so discouraging that this method was given upe If the convec- tion of gas were tos only difficulty involved, it might have been worth while . -g= to catime, but it was found that the construction of even small furnaces was a matter of considerable difficulty, and calculation showed that with short | paths and intense extraneous éllumination and temperature gredients in the optically flat windows which were necessary, the sensitivity that could be expected was hopelessly lowe | Methods which involved the production of atomic hydrogen in one vessel and measuring it in a connected vessel through which it was made to stream were regarded as unreliable because of the difficulty of measuring pressure, density and concentration of atomic hydrcgene the yield which can be obtsined from collisions of the second kind with excited atoms such as mercury, proves, in cases which have so far been reported, to be so small that the effect on optical path length would be negligible. The only other methods known for the production of atomic hydrogen in cmsiderable concentrations are through the agency of electric discharge. o“ The inform’ as to the action of the disclarge on the hydrogen gas has heretofore been of a qualitative characters Yet comcelusions can be drawn So 5 SOURCE aq R. OBSERVING —=\_ |» APPARATUS | | \ Pee hea ee Fa FI GES THE INTERFEROMETER ~g~ mat are reliable. It is known with certainty that the Balmer spectrum is due to the atom ani the many lined spectrum to the moleculee the conditions under | which the atomic spectrum is strong are just those which from chemical reasoning are favorable for the existence of the atomic forme in the sense of Born end Frak energy sinks (catalysts and reduciable substances) must be absent in order to prevent the escape of the peat of dissociation when two atoms come together. _ The experiments of Wood, Bonhoeffer, Mohler, Urey ami Smallwood, have shown conélusively that atomic hydrogen is present in large concentrations in dis— charge tubes showing the pure Balmer spectrum at pressures of the order of one Mele It was decided therefore, to use the electric discharge as dissociating agent devising conditions and apparatus to avoid as far as possible the disturb- ing factors involved. NTAL A. THE INTERFEROMETER used finally was a modification of the Michelson type. the optical arrangement is shown diagrammatically in figure Ie ‘The ~10~ ‘paths are somewhat over a meter longe 4n important feature is ths fact that the | two beams produced by the splitting device M are maie parallel by the mirror Rye i and HK, were rigidly fastened to a heavy steel base while Ry, and Hy were supported by two plates which were each held by springs against three adjusting sorewBe and Distances were calculated so that small adjustments of the screws behind Hy io were sufficient to equalize the two paths so that white light fringes could be foumde she mirrors wore about 10 cm above a thick reinforced concrete slab in some of the work, and a ribbed cast iron surface plate in the reste the se rigid bases which were approximately 10 x 70 x 150 cm rested on three rubber or felt pads (1 inch sheet rubber was better than felt and the iron base was better than the concrete). In trying various ideas for the elimination of convection, for the application of cooling agents, etce, other arrangements of the optical paths were used. sometimes they were at right angles to each other, and sometimes one was made vertical by mounting one mirror on a four inch pipee But the disposition in Figare I is vastly superior to all the others both in ease of adjustment (which is not an easy matter in an instrument of such size) and in steadyhess of fringes. . 9119 . a this latter property this scheme is like the Jamin interferomter for the paths are everywhere close together and are almost equally affected by disturbing " Gnfluences such as vibrations, air currents, differential thermal expansion, otCe Be THE DEVICE M , used instead of compensating plane mwrallels, is a novelty which is strongly recommended especially when specially made instruments are used - for which adjusting appliances are not availablee It consi sts of two. matched prisms cemented together on their largest faces with Canada Bal same Befo re Sementing, one of these faces is coated with a half reflecting filme The prisms must be matched to the extent that their refractive indices mst be equal for all wave lengths and the angles marked a in figure 2Imst be closely equale This is accomplisped best by working with one stick of double height and sawing it in two after polishinge About a dozen such cubes have been made up of glass and quartz and the following process was found to be easy after a little practises A uniform semi- transparent film is coated on one prism and after making sure that there are no particles on the diagonal faces a drop of thick Canada Balsam is put on one and ILLUMINATION nae FIG (12) the two prisms pressed together with as much force as ones arms can supply. ‘The — is warmed gently on a hot plate to about 50°C turning it over and over to “equalize temperatures as much as possiblee In this stage the solvent of the Canada Zalsam is driven off while the film is kept liquide When the faces are all about as hot as the fingers care to handle the face OA is made perpendicular to OBe The codition that one wishes to fulfill is that any incident ray such as PQ is equally divided by the fase OC and after the separated rays have travelled over exactly equivalent paths they are joined again at som point R into a single ray RS. When this condition is obtained, the eye will see white lig::t fringes when the illumination is placed as in the figuree To bring this about, a weak monochromatic source with a somewhat weaker white light background is used» Fo- cussing the eye on the face OB and getting the edges at 0 superposed the prisms are pushed around until monochromatic fringes are seene The block is permitted to cool sanewhat so that one must exert appreciable force to move the fringes. If the filter becoms too stiff the block must be warmed slightly on the hot plate from time to time. Pressure is applied to make the fringes move until the white light fringes appeare ‘The search should not take fifteen mimtese ‘When they are in view the block is allowed to become cold adjusting their position and direction =135= “gt froquont interfalse When cold the fringes hold their position (if ty have : ‘peen ad justed properly} while cooling) for months without moh creeping. The device has the following wusual advantages: (2) All rays are Compe nsa ted in a single piece so that repeated adjusting after each change in apparatus is unnecessary. (») It is the most economical in light losses since there is the minimam number of air-glass transitions and all are at approximately normal inci- dences am since it is umecessary to make a heavy coat to get rid of false reflectionse (c) ‘The semi-reflecting film is protected from deterioration by chemical or mechanical agents and the troublseoms process of getting a good coat is done once for alle ; (a) There are no false imagese The reflections from 0@ ani OB are easily disposed of by making @ different fran 45° or simply by using a telescope or other observing apparatus which is focussed on the eroper fr ingese It is a relief to get rid of this amoyancee (e) No holder or adjusting screws are requirede A bit of soft wax or @ light spring keeps it in place since it is a geometrically stable figures ~14— (f) It constitutes without any auxilliary parts a remarkably simple and rugged Michelson interferomtere It can be held in the hand and passed around e There may be some applications of the Michelson interferometer which it will not serve, in other respects it may be more versatile. It should be mentioned ‘that orystalline prisms can produce double sets of fringes which may become mixed up under some conditions of usee In these cases it has been found useful to separate the fringe systems with a Wollaston Prism or to eliminate one set with a “Nicole C. THE DISCHARGE TUBESe In the final state of the apparatus, the two arms of the interferometer of figure I cantained identical tubese In the process of development a great variety of shapes, lengths and other toatures was tried with special ends in viewe Thick and thin tubes were tried coiled im all sorts of wayse Large and small aluminum platinum ani copper, electrodes were triede Out— side sheet metal and mercury electrodes were also usede Several tubes were Orn shaped to fit completely into cooling baths and in order to try liquid air, was made to go inside a specially made Dewar flask with a hole thru the bottom for observation. This was a masterpiece of Mr.Clancéy’s art and I regret very much =-15= that the only thing it accomplished was to produce spurious effects which wasted “9. great deal of time before their true mture was diecoverede The shape designed at the las is shown in figure 3. It is a cylinder of specially selected straight pyrex tubing, varying from 60 to 90 cm in length and from 0.6 to 2e5 cm in internal diameters The side arms are short capillary tubes which can be closed by stopcocks.a few centimeters from the main tube. The electrodes E are large aluminium discs or cylinders through which a hole,bored equal in size to the internal diameter of the glass tubee The elec~ trodes are waxed to the discharge tube and beyond their outside face a short length L of glass tubing continues the discharge tube a few centimeterse On the ends of these pieces are waxed the matched optically plane parallel plates Pe B represents a binding poste Two such tubes were mounted in the interferometer arms by means of wax or V-blockse They were accurately aligmd so that all the field was visible out to very nearly the walls of the tubese Connections were provided from one tube to another, to the source of hydrogen, to the pump, pressure gauge, etc. Various auxiliary devices were attached directly to the center of the discharge tube on different occasions with the object of determining the pressures and temperatures CONF INANCAD= & FILO TA WIALdAO= Jd iy yay FIGNL FIVCHIS/G L804 DNIONIG=G SIIOALIAFTI= F & OA eee ] = ie -16= . in the dischargee The most successful will be described la ter. This particular structure of tube was devised for the following benefitse (a) The parasitical volume was negligibly small so that when the stop= cocks were closed the average densi tyfrema ined constant regardless of temperature changes e (b) By putting the electrodes around the tube instead of off in side arms, one could look through all of the gas so that the special temperature conditions which are found to prevail at the electrodes play a part in the optical pathe In this way density gradients along the tube are prevented from having any in~ fluence on the fringeBe (c) It is essential to be able to view all parts of the cross section of the tube in order to be able to take into account tne temperature and density gradients at right angles to the line of sight. (ad) The pieces L had to be added because of the effect produced by the Canal rays which streamed for some distance through the hole in the electrodese (e) Connecting tubes of eq@Al length were necessary in order to equalize dispersion in the two arms and thereby permit the use of white light fringes with & central black fringee For the same reason the end plates of the two tubes at na to be optically equivalent. (£2) ‘whe small area of metallic surface presented by the electrodes to the gas greatly reduced the catalytic recombination of the hydrogen atoms. ‘the “ asnereased heating effect was taken care of by the large bulk and surface with consequently high heat capacity and heat dissipative power of the AB cylinders or discs. ‘The fact that most of the Al surface was exposed to the air outside helped in heat dissipation and yw rmitted cooling with moist cloths. By this means it was found that Wood's suggestion to have very long tubes so that the electrodes would not affect the center of the system was unnecessary and whereas two me te tubes with large metal lic surface were found to be blue for a considerable distance from the electrodes, these tubes gave pure Balmer spectra right up to and through the hole in the electrode | a These points will be considered again laters De THE ELECTRICAL SYSTEM. ‘he binding posts B in figure I were connected to & large ood@enser with an adjustable spark gap in series. ‘The capacities used went up to about eO01 mfde ‘the camdenser was charged by high voltage transformers, S0me of them fiving as high as 25,000 voltse Most of the results, however, were obtained with a 10 KVA transformer giving 16,000 volts at 50 cycles. vhoke ~18= “oils and series resistances in the primary regulated the power and the voltage. Condensed discharge was most frequently used, but the spark gap could be closed “and unc ondensed discharge was thoroughly investigatede Attention should be called to the fact that contrary to camon opinion a eamdenser in series with a discharge tube freqvently improves tne performance of the transformer by raising the power factor in the second ary It. is surprising to observe the imreased intensity that one may derive from a small transformer by putting in the proper capacitye Moreover since the discharge is not condensed there’ is no perceptible proadening of the linese Ammeters and voltmeters were used on the high side and in addition to these a wattmeter was used on the low side, so that some idea of energy and field intensity could be obtainede Be . EB OBSERVING APPARATUS was sometimes visual, sometimes photographice The illumination was provided by a high current density carbon are (20. - 35 amps. in 1/4 to 1/ 2 inch carbons) or else by incandescent lamps using as much as two thousand wattse Mercury light was also used but could not be had in the intensity of the arce The matter of intensity was extremely important; first, because of the many extra glass-air transitions (probably 30 or more) in addition to the ~19— “apual losses in the imperfect reflectors and the unavoidable waste in the half - gilvered film.of the interferometer. The second reason for high intensity is the unfortuate brilliance of the light refl ected from the walls of the tubee this, ‘This nuisance could be reduced by having parallel lighte To achi eve/ the source (which was extended and therefore required no lens) was placed at great dist are | (up to 10 metres} from the apparatus and the beam diaphragmed down in several places to just the size of the tubese A third cause requiring high intensity was the unavoidable presence of the light from the di scharge tubes This source had every advantage over the proper source except intrinsic brilliancy. Because of this extraneous light it was impossible to observe reliably without color filters except with a most brilliant arce It was mainly on this account that observations were made with spectroscope and spectrograph. For then one could attem toa part of the spectrum which was not illuminated by the hydrogen dis- ‘chargee <A further advantage was the possibility of observing the fitness of the tube by the purity of its spectrum. However, one had to sacrifice the view of the whole field at one glance and therefore all methods of observation had to be tried in turme The lavish use of diaphragm is to be highly urged for such worke Two or three were used between the source and the dividing arrangement M and one -20— . wes placed near each mirror and others distributed wherever possible in the : beam beyond the interferometer. Their importance in improving the visibility of the fringes can hardly be overestimated. For direct visual observation a home made telescope was usede Since the Wack band of a white light fringe system was being observed one could focus on the mirrors R, or Hp ani use spots or etched lines on these mirrors as fiducial marks from which to judge the shift of fringes. This scheme rendered immaterial any relative motion between the interferometer and the telescope or eyee Color screens were aleo used to eliminate the hydrogen dineharge ani to clarify the fringese If one had a very sharp filter that did not coincide with the hydrogen lines the improvement was astonishing amd the precision of a reading was tripled at least. In using a spectroscope or svectrograph the fringes are focussed on the narrow slit at a distance determined by the size of the image desirede One can use the cross hairs of the spectroscope or a fine wire across the slit as fiducial marks as well as the etched line memtioned before. The fringes are made horizatal ami one sces through the instrument the spectra of the source traversed by a horizontal black line and by almost horizontal fringese ‘The -25- deviation of the fringes from the hori zontal is a measure of the difference of “aispersion of the gas in the two pathse ‘hen the discharge is turned on, the | line spectrum appears superposed on the continuous background. But in a good tube, there is very little light due to the discharge between the Balmer lines, and one is hardly disturbed by the extraeous light, and it serves to indicate when the discharge is passing through tne tubee The photographic plates used were mainly, Ilford high speed panchromatic or Wratten and Wainwright panchromatic - the Mirst mentioned being best of all in speed, smallness of grain, and flatness of sensitivity over the visual regione Fe AUXILIARY MEASURING APPARATUSe Besides electrical instruments alr eady mentioned, several indicators had to be usede There was, of course, a McLeod gauge for pressure measurement, designed especially for accurate readings, in the range from .01 mm to several cms. This was accomplished by having a mo- . t derately small bulb, a couple of small auxiliary bulbs in place of a very long capillary and a moderate length of large capillary tube. But it was unnecessary to rely on the Mcleod gave for the pressures The interferometer is a perfectly good instrument for this purpose and was “22 used almost exclusively for the determination of pressures used in calculationse By the same means and using atmospheric pressure, all volumes between stopcocks | could be determined with extreme accuracy and these calibrated volumes used to expand gas from atmospherid pressure dow to ary lower pressure the final pres- sure being as accurately known as the ratio. of the volumes. ‘There was no diffi- culty then in ordinary pressure measurements or in adding known increments to the pressure, but the determination of pressure while .the discharge was on (which was N&@Sssary to find the percentage dissociation) was quite another matter. Attempts were made to accomplish this with the McLeod gauge, with drops in closed end capillary tubes attached to the discharge and with rubber diaphragms connected to a minute mirror mounted so that a motion of the diaphragm pro~ duced a rotation of the mirrore None of these were pushed hard enough to warrmt judgement on their virtues. instead the interferometer itself was used for this purpose and also 4 dark space gauge shown in Figure 40 The ground joint am right angle bend enabled one to vary the tilt of the gauge until the face of the cathode was exactly at right angles to the sighting tube with which the distance from the cathode to the edge of the dark space was measurede The sighting tube was simply a tube of bakelite closed at the end towards t:e eye STOP -COCH “ “i Teli § DISCHARGE TUBE 7O GROUND GLASS SOlIVT CA rHone a iat ott | w 9 ke a Tw wy3 CROSS w J D = DARK SPACE S : C =CATHODE GLOW & fa os } W = WAX eee | B =BINOING POST ite | 9 = GROUND END < | S | PINHOLE ea EYE L1G. 4 DPAKA SFACE GAUGE ~PB as except for a tiny pinhole about 0.2 mm in diameters At the other end two fine hairs were stuck on with shellac to make cross hairse This tube was mowted on a Comparator so that a motion parallel to the motion of the edge of the negative glow could be followed and read on a scale graduated to #1 mm. The voltage across the gauge varied from about 350 to 425 volts, it was supplied ty @ storage battery and was measured on a voltmeter in parallel with the gauge. 4 galvanometer in series gave the current flowinge The procedure in making pressure measurements with this gauge and with the interferometer, and the formulae involved will be taken up under another headings The use of a dark space gauge was suggested to me by Sinclair Smith. No accurate temperature measurement of the inside of the tube were madee The calculations of temperature eiven later are considered more reliable and more significant than direct measurements at particular pointse Ge PROCEEDURE IN MEASUREMENT: For the determination of the fringe shift, due to the passage of the discharge, all stopcocks were closed so that no change in density could take place, the fringes were watched or photographed under =P : quiet conditions with no discharge. The discharge was now flashed on ani a sudden jump of fringes was looked for. In order not to heat the tube unduly, the discharge was kept on only for an instante A jump in fringes was looked for again when the discharge was snapped off, this procedure was repeated over “ant over again at all pressures from the lowest that the diffusion pump would give up to several centimeterse The power was varied from the smallest that would pass through the tube to several kilowatts. Frequencies of 25, 50, 60 250 and 500 cycles were employed. All available light sources were used in turne Moist hydrogen, collected over water from a tank, or generated by elec- trolysis of NaOH, nitrogen, air and helium were placed in the tube. Wavelengths from about 4300 to 7900 2 were used in illuminatione Attendant: conditions of the discharge tube, vibfations in the neighborhood, preneinos of mercury vapor or its absence were taken into account »{ current voltage and powere were all observed). The sensitivity of the visual observation was estimated by using mechanically produced and calibrated fringeshiftse On the photographic plate, the shift of the fringes with respect to the fiducial mark, was measured wi th comparator for several wavelengths in different parts of the spectrum. Any peculiar behavior of the fringes was verified and observations repeated until -25- “the cause had been tracked downe So large a number of observations were taken (many thousands and so great a variety of cmditions were imposed and so care- . fully were these conditions analyzed, that tinere is no qwstion but that the full behaviour of the fringes was completely understood and that the results which will be stated later are reliable statements of facts, no matter what conclusions are derived from these factse The pressure measurement 6 with the interferometer were made by opening _ the stopcock between the two tubes (all others being closed) ant passing the discharge through one. Gas flowed from this one into the other because of disecciation and temperature increases The shift in fringes accompanying this Change in density was measurede At the same tims the power in the electrical cirouit was measured, In the case of the dark space gauge, the edge of the dark space was sighted without the discharge, all stopcocks being closed, ex= septing the one between the discharge tube and tre gauge. The ai scharge was now passed and the pover noted. The change in dark space determined the pressuree Temperature conditions were observed by the motion of the fringes in difrerent portions of the circular field. From this motion the density distri- =_26— vation could be deduced, and from it the temperature distrihtion. Another “means of making a temperature estimte was to measure the pressure change ‘with the dark space gauge using helium in the tube, in this case no dissocia— tion could take place ad the change in pressure was determined only by the average change in temperatures Along with these temperature measurements, the regular fringe-shift measurements (all stopcocks closed) were made for the determination of index of refraction of atomic hydrogen, and all discharge conditions etce, were observed and correlatede RESUITS. When all accidental shifts are avoided as far as possible, and when accomt is taken of those which remained in certain wnimportant limiting cases, the fringe-shift due to the change from molecular to atomic hy drogen is zerde In other words, according to equation 4, the refractive index of atomic hydro- gen under standard conditions is one-half that of molecular hydrogene Numer~ foally at about 6000 & | = =1 = 1038 x 10 by =27 = Another way of putting this is to say that the effect of two hydrogen atoms on a light wave which does not coincide in frequency with an absorption line is the same whether the atoms are united to form a molecule or are free to move any distance from each others This result is quite in accord with the ideas of some chemists who feel they haveevidence shar ing that the hydrogen molecule is just a pair of loosely associated hydrogen atomse It is also in . accord with the spectroscopic evidence of the similarity between the radiation from molecules and the line spectra of the atoms of whim they are composede | This similarity has led to the assumption that there is a permanence of quantization of electrons when their atoms combine to form molecules. Al- through 5 ince there are energy chm ges involved in the warping of the charge distributions, one cannot expect the refractive index to remain quite unchanged still since the heat of the association is small compared with the electron energy, the change in refractive iniex should be fairly small. The exact equality between 1, -1 am au, 4 cannot of caurse be concluded from these measurementse It will be obvious that the possible difference is determined by the accidental effects which have persisted in our observations, by the precision of the observations, and by the quantity of -28~ “atomic hydrogen which was present in the tube while the observations were being madee ‘the numer ical value of thié difference will be estimated bber one ‘The final result will be that we may wri te A) -1 = [1638 + 26 ]x 107+, The second result of the experiment is that in a properly arranged tube, free from reduct ble substances and using moist hydrogen at pressures in the neigh- borhood of 1 mm. so that pure Balmer spectrum is obtained, concentretions of 20 percent or more may exist over periods of tim of 2.01 of a second. ihis has, of course, been observed before and it is not surprieing that under condi- tions suitable for the excitation both of molecular and atomic hydrogen that when only the atomic spectrum is shown, there should be a considereble frac= tion of atoms. In fact, I think it is perfectly sound to conclude that wider these conditions, the absence of the molecular spectrum while the discharge is passing, shows an absence of molecules during this timee Since the resonance potentials of the two systems are so close to each other, and since as far as we know, there are no“metastable states, the probability of excitation mst be comparable, and there is no means of explaining the quenching of the molecular spectrum other than the absence of tls molecular forme How long the atoms persist after the dissociating agency of the discharge has been removed is another =29~ “matter. cut from the chemical kinetics of vorn and rranck, and from numerous experiments of Wood, sonhoeffer, Urey and Smallwood, amd others, we believe that the homogeneous recombination of hydrogen atoms is & slow process compared with the intervals of .01 or a second or less between dischargese Some data on the rate of this reaction is had in the measurements with vary ing frequency, ‘put it is rather too sparse to provide definite conclusionse However, the work is being carried on and a good value for the rate of reaction is looked for by such measurenent Se The third result worth mentioning is the fact that the pressures which exist in discharge tubes are of the order which could be calculated from the increase in temperature, due to the energy supplied to the rabess Quantitative results are not very precise, but they are sufficient to answer @ doubt which is very common as to whether one may define temperature in a discharge tube or whether the oxistence of numerous high velocity particles, mov ing under the action of electric field, destroys the usefulness of this comeption.e The answer is, that if one uses the gaslaw PV = NRT to determine temperature from the pressure, then the temperature is a perfectly definite t ning -30— ANALYSIS OF THE OBSERVATIONS. Be SPURIOUS EFFECTS It is considered essential to discuss before anything else, the possible undesirable effects and to show how they were taken into account « of the many people with whom the results have been discussed no one has brought up a possibility which has not been considered. Moreover, the fact that in the final design no measurable shift was obtained over 4 wide range and variety of conditions ‘gives one cmsiderable confidence in the belief that nothing of importance was neglectede Follows a list of difficulties which may perhaps are peculdar to this particular application of the inter~ ferometere Ie Motion of gas into side armse The volume not included in the light path was only about five percent of the totale If the main tube was 100°C above room temperature and the side arms at room temperature (this is an extreme case), the relative density would be 4 to 3 If the subscript refers to the large volume and 2 to the small and O to the initial state, we may wri te foe fh. O. 95 f+ 0.0sf> fF and whe nse ~3]=— showing that one hundred degrees difference makes only a one percent change in density and therefore by (2) in «1-1. This is for smaller than the precision of the experiment and can be entirely disregarded. The parasitic volumes will then be considered zero in the case where all stopcocks are closed. Il Change in length of the tube due to thermal expansion when the discharge is tumed one In effect this reduced the optical path by substituting for air at atmospheric pressure, 2 gas at very low pressures AN = (1 ~ Hale) CL at (5) Zz where “C air at atmospheric pressure and 15°C is = 1.00027 0 » ™ wave length or 6000 A coefficient of expansion of pyrex = 366 x 107° per °C a u At = average change in temperature of the tube ™ } index of refraction of the gas in the tube wa i length of tube = 90 om This gives a shift of 14x 107% fringes per degree change in temperatures This is very small, even for extreme temperaturese Moreover the rise in tem- perature is gradual and would not at all interfere with visual observation even ~32— ie it were large since it was a sudden change that was to be looked fore In the photographs the exposure was only about one second in which time the change in Length must have been small, especi ally considering that the tube heated only to a certain temperature and fluctuated only slowly and slightly from it when the discharge was turned on and off. Finally the change in Leng th was measured by attaching the mirror x to the tube which was fastened only at the other ends In this way the effective shift was maltiplated over a thousand fold since the formula now is ANF Oe FS A A The shift before the tube reached equilibrium was a few fringes showing that the change in length was negligible in the case when only la- 1) was effec tive in prodwing a shift. III Temperature changes along the length of the tubee Equation 1 is more properly written AN= HA [ASE : (6) x singe we have shown . | we can write DN x \u ani from equation (2) if only temperature changes Ans Seatac a [ed L (7) A P is here the average density over the anss sectione Now the integral represents the amount of matter in the tube (since practically all of the tube is in the optical path) and is imiependant of temperature so that AN |pou =O and /\ N = 0 for this cases IV Electrostatic effectse Several phenomena come under this head. It is conceivable that if the electric parts have large distributed capacity rigidly 2 attached to the interferometer, the mechanical forces due to the attractions f on induced charges, especially with such high voltages, may warp one of the arms more than the othere Such an effect was apparently observed under some fonditions especially when external electrodes of large area were used. In swh the high capacities were visible and could be removed or reduced. The characteristic features of the effect are its starting suddemmess and ite in- 3 Ae dependance of the strergth of discharge or pressure in the tube. This last point definitely showed that it had no cmmnection with the properties of hydrogen and indeed it was found that He or air did just as well. At any rate it was noticed and disposed of. . Another possible effect is the change in 4 with field intensitye This would not be expected to be importante It should be proportional to field intensity which was low. At most it was a few hundred volts per cm . ‘ when the voltage was on the electrodes and no current passing. ‘vhen the discharge was on or between discharges it was of course, much lowre It should be proportional to pressure snd therefore should be more nbticeable at high pressures. It was looked for under these favorable conditions and found not to be appreciable. V Heating of the plane parallel ends of the discharge tubee For a time the flat ends were waxed directly to the outside of the electrodes without the extension pieces L shown in figure 3. It was noti oad that at low pressures @ slow shift took place, in the direction of increasing refractione The change was greater in the center than at the edgese On simtting off the dis- charge the return was slower than the original changee The magnitude of the -B5— effect increased for a time as the pressure increased ani grew rapidly immediately after the discharge was tumed on and more slowly later on, reaching a steady value in about fifteen seconds. All these properties are characteri stics of temperature effectse It was concluded that the heating was due to the bombard- ment of the ends by camal rays rushing toward the electrodes ani passing on thr ough the hole in them this was plausible because the temperatures coeffi- client refractive index of glass is sometimes of the order of a couple of wits in tne fifth decimal place, and a heating of the inside face ‘could produce the effect observede Yor example with a heavy flint glass an average change of temperature through the plate of 1°C might produce with plates 2 mm thick (since there were two of them and the light passed through tori ce) a disp ce- ment of a taith of a fringée The effect might have been removed by using at opposite ends, plates with temperature coefficients that ha different signs. ovut the method chosen was easier and cheapere ‘ith extension tubes L of two or three centi eters lenet h the effect disappeared. One could see the red beam of canal rays streaming to-~ wards the end of the tube but stopping before getting there. nowever the siall positive effect which was found at the lowest pressure may be attributed to this -36— causes ‘the mean path of canal rays at this pressure (about 1 mm) is usually much smaller than 2 cms but it imst be remembered that in this case the rays were protons and of very small diameter. VI Ions, Excited atoms ani Electronse It might be expected that these constituents could contribute to the refraction. In the usual case where condensed discharge was used they can be disvosed of izmediately because the excitation existed for such a short time: probably less than .0001 sec. It could not be blurred out perceptibly by a moving mirror with a time resolving power of that order of magnitude. After the excitation ceased the excited atoms and electrons would disappear in 107” sec. and the ions in 107 seo. It may therefore, be comsidered that they last only while the discharge is actually pascinge Since this is only for a small fraction of the total time between successive discharges, ayy effect which they produce will be unnoticed by the eye or the photographic plate. When ordinary discharge is used the current flows during most of the cycle but on the other hand the current density is less in the same proportion as the time is greatere Now the excited atoms in hydrogen under heavy discharge =~4 according to Ladenburg, Kopfermann and Carst are only about 10 of the total ' nuniber and since their value of (4-1) awey from absorption lines is not many times that of the normal atom, their contribution is nile It remains to estimate the number of ions and electronse A great deal of experiment d work has been done in this direction, some of which are probably ‘less accurate than the following calculatione In n is the number per em” of charged particles carrying the current and >-their average velocity then i the current densi ty J 2snew | (8) For the high current density of 1 ampere/ om” this gives q 18 4.77% 10. Now s nce the carriers under these conditions are probably all. electrons or protons their velocity can hardly be under 10° om/ sec. and camot be more than the velocity of lighte Therefore 12 _S a bxlo~ > 9 2X 10 (9) The limits could be narrowed easily and interesting conclusions could be drawn. Suffice it to point out that 6x10 perocm is a fraction of a per cent of the atoms in the gas at a pressure of 1 mm and since the refractive index of protons or electrons is low they are without influence on the Me asurenente ~38— VIIe Variation in density over the cross section of the tubee This is perhaps the most important disturbance. It occurs because of the temperature gradients which exist becuase the heat generated by the discharge escapes thru ‘the glass walls. If one starts with straight fringes then the discharge causes them to bow in the center of the fielde The motion is in the direotion of diminishing refraction in the center which is therefore of lowest densitye A better method of observation is to start with tne fringes curved just enough so that the discharge straigitens with power and pressures It never attains mangitudes of more than one fringe and can be reduced by means indicated by consideration of the theory of the effecte Let us make the most unfavorable assumptions and say that the heat is developed uniformly through out the volume and that it is dissipated only by conductione The first of these is not nearly true and is rather too conservative, for we know that the greatest voltage gradients are near the electrodes which have by far the greatest heat dissipating capacity. As a matter of fact any lack of uniformity of heating would prdvide faster cooling and would be advantageow for our conclusionse fAn important example of such non-uniform heating is the ion and atomic recombination on the walls)e The asswaption that only conduction TQ ne is effective is of course only approximate. That it plays the most important part at moderate power is shown by the bowing of the fringes at very high power the temperature gradients are more efrective in starting convectione Hadiation ‘accounts for only a few percent of the energy but even this much is important when it comes to calculating percent of dissociatione Using the assumptions nevertheless, we can find the temperature gradients from the definition of thermal conductivity which says that if Q@ is the heat passing per second through wit surface and n the normal to it, then —-kIAT La In this equation k is independent of pressure at least down to 1 mm. In the steady state, which is soon reached, the heat passing every second through a unit surface on a cylinder concentric with the axis of the tube (dis- regarding the end convection) is the heat gencrated in unit length divided by the area per unit length Qe Wwe 2 we qa) wry] -2a0Yr Qarv b where Wis the energy furnished to the tube, L the length,2r,; the internal diameter and r the distance from the axise This gives fran (10) ATL Ww 4 ~~ hime 27% aL. whence - Te = VW ydvr- _ +2 - 2MFCRL Ur Ek L (12) where T, is the temperature at distance re It is seen from this that with a given energy density the difference in temperature between walls and ceater is proportional to the square of the diameter of the tube. Withthis in mind, sone tubes were used with diameters of 6 mme These tubes showed no temperature bowing until fairly high pressurese From the gas law one can write fr = Ban _ (as) 2 where M is the molecular weig t of the Bas, P is the density at distance Yr and p the pressure which is the same all overe The reciprocal of the density is quadratic in r which explains the bowing of the fringes ana further the factor p shows why the effect increases with the pressurée Calculation from (12) and (13) leads to the expression for Pp . . Nem Inno ee (1 7 3 -_ vw = . (ew Ve Sree Yaris ™ “Al where is the average density which equals the initial uniform density and is given by r =z -—~_2 P ~ +d + ¥. ¥ b o ' (14) can be also written p Tote | OP | in which Tj is the temperature at the wall where r = ri, ieee _ WwW 4m RL There must, of course, be a value of r such that RQ > fe Since neither (12) nor (15) contains the p, this value of r is independent of the pressures Moreover figure 5 where Rle is plotted as a function of t/t; shows that for all values of W the density is very little changed from the original density at from seven to eight tenths of the distance to the wallse Here the fringe shift is very smell and since it is easy to block out some portion of the field for radii larger than 08 of the total radius (indeed it is very diffi- cult not to do so) by fixing attention on this portion the observation is free from disturbance due to density gradientse As a matter of fact the whole shift at a pressure of 2 mm and energy of &00 watts in the tube the shift is only two ~42— teaths of a fringe and cmvection mkes it still less. As the data given further on show, the photogra mic observations using thin tubes were not much affected by this cause up to pressures of about @& , centimeter, and knowing the csuse it is possible and safe to correct for it, if desired, at the lower pressures which alone are important and in which the effect is very small indeede It must be felt from these facts that density gradients are not seriouse Still a direct experiment was brought to beer which was free from the possibility of error in this reppecte Unfortunately it was not started soon enough to be thoroughly developed else it would have been a sufficient means of clearing up practically all of the difficulties encountered in the measuremente It was found that NaOH is one of the best catalysts tor the recombination of atomic hydrogen to molecular. Accordingly in one of the tubes of the inter- ferometer NaOH was distributed by allowing a dilute solution to enter and pumping off the watere The tubes were connected in series ani the di scharge passed through them with the stopcocks between closed, but the hydrogen gas at the same pressure in bothe Now since they were thermally, electrically and optically the same in all particulars, the temperature changes, density gradients etce, 45 oe were the same in homologous portions and in the interferometer used the changes in one would neutralize the changes in the other as far as fringesshift was concernede ut between discharges the recombination in the NaOH tube would be - $0 fast that the concentration of atomic hydrogen in it would be zero: amd so any whift of fringes would be a measure of the refractivity of the atomic hydrogen in the othere No shift was obtainede Moreover on opening the stopcock between the tubes the passage of gas from the pure one to the other as indicated by the fringe-shift showed that cosiderable atomic hydrogen was presente The “observat ions were not repeated often enough nor were the conditions varied enough to entitle this experiment to all the weight it might have deserved had it been properly performede It will be continuede Be THE ZERO SHIFT. Most reliance is to be placed on the photographic runs with the thin tubee Table 1 cives the average of twelve series of runs with pressure varying fron 1 mm to over 2 cme Figure 6 is a grathical representation of Table 1. The procedure used in getting this data was to photograph the fringes in a very fast spectrograph (£ 207 lens) first, without the discharge at the lowest pressure then with, them aan see ir area Cj ine whhe TABLE 1 Pressure in Millimeters of HG Average Fringe Shift MMe Fringes 0095 +0040 129 ~0.015 308 ~.006 5e7 0.001 726 0.009, 905 0.004 11.4 0.005 13503 0.022 1502 0.047 19 ~0.066 then without, then withe ‘These five exposures taken one after the other indicated any accidental drifts due to temperature changes, turbulence in the air vibra- _ tion due to traffic nearby, leaks in the apparatus, etce, etce Only such plates were used as were free from such disturbancese After the five exposures were made at the lowest pressure, gas was added and five more taken on a single plate which would have over fifty exposuresBe The next plate would be under different conditions of exposure, energy, type of discharge etce, in all the variety that could be ivaginede Since there were from two to five fringes in the field each exposure provided from four to ten measures of the position (maximum and minimum darkness) of the fringese ‘The ina ividual readings were just like the average in being close to zero, or at the high pressures slightly negative. It is not a matter of -~45— finding a small effect hidden by larger accidental errorse Once in a while an apparent shift would be observed, but it would have all the earmarks of an accident. It would coms where it shouldn't, it would not be repeatable and would “have no connection with the discharge cmditions. At low and high pressures this was not 50, but the systematic errors in those cases have been explained. The plates were measured with great patience and is believed that the averages given are good to better than a hundredth of a fringe. In calculating the e-ror of the experiment such precision will not be claimed in order to err on the safe sides The visual svservations being so much easier and quicker and subject to closer corrdation with contemporary c oditions were performed in greater aumbers ani varietye Here the reliability of a single observations is not so large because of the distracting influence of the electric sparks and the light in the tube and because of the fact that attention is divided between watching the fringes and closing the switch (this was sometimes done by a second person). The direct visitm spectroscope most often used was a beautiful instrument (made by Schmidt and Haensch) giving high man@nification and high dispersion so that tne field of vision could be made almost free from light from the dis~ charge and small shifts detectede The telescope too was always available so that after seeing the spectral condi ti ¥ 2, ition of the tube in 4 n the spectrograph ~46~ one could mmmediately shift and observe the thermal conditions with the telescopes As one watches the fringes over long periods many motions are visible unless things are very quiet. Nevertneless a sudden shift correlated with the discharge is easily detected and distinguished from meaningless drifts. The practised eye notices a sudden change of a tnirtieth of a fringe under favorable conditions. But a twentieth is hard to miss and a tenth can be very well estimatede In saying that no shift was observed it is meant that taking all observa- tions into account, inclading the photographic, the shift mst have been less than 0.03 fringese In order to estimate the possible error we shall assume that the shift was 0.03 fringes and see what effect that might have on the My ~l1) in equation (3). Ce CONCENT?ATION OF ATOMIC HYDROGENe Before being able to give a numerical value to the error, one mst find the cocentration of atoms at the moment the Bhift was being observed. This question has been investigated experimentally using the anparsatus already described, but it is considered worth while to make @ calculation on the basis of other experiments and it is believed that the results obtained are as reliable as those given by the experiments first mentioned. ~47— Bonhoeffer has measured the rate of recombination of atomic hydrogen and his measures at 0.5 mm fit exactly the law _ kt (17) ¥ ~ Bo © ‘where Y is the fract ion of EH, molecules dissociated and k the so-called specific rate of recombination at 0.5 mm the value 2 The quantity k must be a function of the pressure which is zero when p=0. Let us say for the tim being k = Kop and then we can write for (17) Y = % & r : (18) where p is the initial pressure of molecular hydrogen in millimeters, In sone of our experiments the voltage was supplied from a 16,000 ve 10 kw. transformer with a large condenser in parallel and a variable spark gap in series with the tube. In a few cases the gap was closed giving a 50-cycle sine wave, at other times the gap broke down at least twice a cycle giving condensed dis~ charges certainly less than a thousandth of a secend in duratione The interval between discharges was, ther-fore, never more than one hundredth of a second and usually the time during which the discharge was on, was a negligible part of the cycle. The apparent position of the fringes will correspond to the average value of the dissociation which we proceed to calculate using the most unfavorable ~A8— assumptions, namely, that the intefval between discharges is 0.01 seconds “Je ‘have then ‘ Lote) anthony ~100%8 e. t y ° A (19) o yt nm 100 Xe ai 2 |. artim fe . (19") The next difficulty is to decide on the pressure dependence of the initial dissociation YX, e Conéidering that in the beginning of the region of pressures used, the current through the tube for a given voltage increased with the pressure and considering the facts that at pressures up to about 1 ome, there were often several discharges per cycle and that the power andvoltage inputs were increased with the pressure up to about 12 mm, it would be an underestimate . at low pressures and an overestimate at high pressures to say that the initial dissociation did not decrease with increase of pressuree Since both of these are unfavorable to the conclusions we are to draw we shall make the assumption with a clear consciencee For the constant of initial dissociation we again refer to Bonhoeffer, who finds 207% for the fraction %, at some unmentioned pressure, probably about 005 mne When the 10 kw. transformer and the short duration condensed discharges at 8000 to 16,000 ve giving current densities of: SSaud_ amt . brit 5 - ae , : : i af A , ‘ J a ry n ” - rr . nek vs 2 —— b+ a ur rt pce a = - | . se ws a a - aa a eas i ba u y Mw See ae ae mee ; ; Yr as i ow ts : chun . t ann agp s i as eER 4 - sa tJ a fdr : ~ r q . " an . : as +h ' ++ nae ES : t ane pretty ee 3 ti : mae x eoanen a a es Ht an ” “4 e . : ann ar Hi ae TTL nae & 1 ‘ " rn ToT " on " - v “fe r ia 7 iB 4 r y aan . tT “ re p e a Lt te 1 Li ! ~ : oases B ann 3 " C aus = a aa = a8 mas - 7 Ty tl Hs - tif | +4 - - SO SG nea mh pon nee a 4 4 mow | 44 = mR Be Ch Benes ee s } Ah dadeded of esto Be H r = ae ; . . | +] : = | opal i! : : Hee i +. t “ S Ses SeRe eRe obeted 3 } > "T - Stobbbtetd oe 4444 7 GEOR eet nae a 4 pa ad oe - u oe ie eo 2 ae ee tte} 4 aan SREn Be . 19 5 = + 5 Fs 4 4 ~$ u et ] 0 os te = =e +t tt ppt ee ee AQ a . nundreds of amperes per square centimeter = while the discharge passed - (average Low frequency currents over the whole cycle went up to several amperes per square ' gentimeter) are compared with the milliamps used by Bonhoeffer, it seems conser~ vative to write y= 02 giving from (19°) iin _ 10 ete Cc Poy "Pee j-e ” so that for the partial pressure of atomic hydrogen we have, approximately, Pa = gaa | re | (20) As ton, the power of the pressure according to which the rate of re- combination increases it might be said that fot this type of reaction n=2 is plausible, but from the point of view of the chemical kinetics of -Borm and Franck, it is well to consider the case n = 3. Figure 7 shows the partial pressures of atomic hydrogen as calculated from (2) for each of these values of ne The maximum partial pressure of H is 0.90 mm. and 0.46 mm for n = 2 and n= 3, respectively. The assumptions made lead, therefore, to no extravagant values of the dissociatione -5O~ The experiments in connection with this apparatus twepend in the first place on the fact that to an approximation the refractions of two hydrogen atoms is the same as that of a hydrogen molecule. In using the interferom ter as @ pressure gauge, one need not distinguish between the atoms and molecules “put can say that the position of the fringes depends only on the density as in equation (2). The procedure is to watch the fringes when the two tubes are open to each other and the discharge passes through one of them. The gas leaving one decreases one ovtical path and since the connecting tube is small, it increases the othere Thus we get a value of the density change from which we could calcu- late the pressure change and therefore the dissociation if one knew the tempera- turee Now since the temperature of the outside,of the tube was known and since the dievet button of temperature could be estimated by the bowing of the fringes the dissociation could be founds However, it is really necessary to go more deeply into the calculation of the temperature. A complete analysis can be carried out but is by no means a simple mattere Part of the complication is due to the fact that there is mm ‘a solid bounded on one side by a fairly conductive low pressure gas which is & =-51- perinanent variable source of heat and on the other by a cold gase The expres- sions resulting from the geometrical shapes are unwieldy for the juggling around of the curious and unusual boundary conditions which obtains The whole calcu~ lation is of prime importance for a part of the experiment (anomalous dispersion “absorption, etee) which has not yet been carried out and will be reserved until the data is ready. Here only an outline will be drawn to give an idea of the conditions existings Since glass is thin walled and is about four times as good a conductor as hydrogen gas, while the air outside is a comparatively poor conductor we may neglect the thickness of the glass and imagine that the hydrogen extended out to r, the external radius of the glass tube and is there separated from the air by a polished surface. Again neglecting end effects, @ the excess temperature over the outside air due to an instantaneous source of heat at time t = 0, and of strength wat’ is given by the cmduction equation 3) 21>°6 ae 3 os \2 , + 28 ] bay a oY” Yr OF subject to the conditions W Ah? 8 = = GQ when t= 0 and r{ ry (22) i lm (23) _ where W is the power GT is a element of time, C.. is the heat capacity of the hydrogen and h is a constant determined from the steady state (kh is sometimes called emissivity). fhe solution of (2) 2 ort 7 — py & (24) where Tol r) is Bessel's function of order zero where 2h eC. . _ y +f 2 ,* ay ae oe Ye Lp hf J, (; wre) y (25) thOe | re (pi rh TS Qasr) and where the }'8 are the roots of the transcendental equation Bol te) —h Je(ne) oo (26) These roots can be found graphically very easily by noticing that vo (X) . Xk ——— J, re h 5 +4 ea 2 THA 7 t i 4 i SOR RRaaE Hae ee Ruues woes 5 - fs : rH ; ; an em ee e rt i we wo . ae n a : tt cee esse. F $4 + . NR + . : + SSaueenenan a 5 a 9 0 ana 5 oh a ee "1 z if Y-e22 ae an : Q " ® t 3 cS hte r am 4 d ~ ~* . i 1, : - a oa u +4 ped of Ley : ft ; Bean am ; ; ces eoReaheage . + oh ht dade tate 4-444 Fi E $ es un 4 E i = was. 4-4 . ++ : +i ‘ r 1 y a a | +. wis “ i - aoue b " . 1 : 5 2 + oy +44 TT : " rat LC LS wits TT : + ~ a w aan Ht 2S S: o an HE yd . - 5 rT Plant byt - ' ; ue a . = 2 ip OS oe s F rr SCC eae senes ene bs ane KORBGGE s - a is a fh 5 ' The Fie 5 t 2 a. By mks ane an 5 ab e its HH i Al Sern - ane Usaeneu ~ : eaaee sscte 4 Wy NEEL Stee Tr ane . i Sens i & nee Bonne Re ima mt 4 PTT TT gene rT 5 7 sense TH a au rh 2 i " 5 cehne a a a tt Toy ; ‘ ; L144 aS aS see 2 eo neh 2 aw als bo aaah tse) os 2 as Heese oan ote - t 4 ‘4 A pi-¢ <p 4eh) S$ | +4 at eee zm a ei ae a i bb Sangean 6 mw : +144 aaneRey : 4 BaMnBe 4 teh ad Gate be be - 4 er } is oso Oat he eh ] ret we ~ ap ich metoot och Bod of = be - AEE Et ah beled - 3 med Ba * ane ot tebetebd ttf fof epee debe tte 4+ Rueda bonus p 1 Ru ia aan Oe Woe owe y oe 1 - } ams ae ee a wats ae 4] ra an os! = agne fede fete 4 { Oa maa t : Sao ae! 4nbn eRe ; 4-4 ; 4-4 e A ttf + . i ue htt ‘ a0 wee a = wees s f ae a oh se peeueneeess eeeee peoeas on annee + t eo wt Ht gam i +t Teas t gat: toh Het et CASE ee i St A ; Cen ses eh : pases te Be cae Re i: can ee rae +r Prt t = Lite CHICAGG " i -53= where x =H tr Plotti and Jo@) th ph otting y; = =, Yo = on the same gra 1 Te h z ay (x) the intersection satigfies 266 This is done in figure 8. Only first root need be considered because py, is about four and the final expression for —— temperature having ; in the denominator of the \ th term is so rapidly PF} yO convergent that only the first term need be considered. Since the source is gbermenant one (and in the experiments the frequemy was 500 cycles so that it may be considered constants) the actual temperature . at time t after the discharge has been started is __ t ah W Jo luz) be aG CH) = [. (t- T)AT = te Cy, Gh DIG; mye 7 i 7) (27) hw Je aso) Apert (Gt)= = 27, 2 |/-e d ; t,o . Ay Cu} +h Jolie) ; | a pela 5 RV | now the diffusivity QO = C, ~ C, (28) and we have ahw \ “My ot | Do = BSS GeGhObigges [ee or by a previous remark _ 2hw Solr) _ eet (H) (0%) = ERY he iio U < | (29) It turns out that the diffusivity has the enormous value v 1325 ~ -P so that the exponential term is negligible and the steady state is reached Ou immediately and as far as the gas is concerned equation (12) appliese The glass tube has tremendous heat capacity in comparison with the gas and therefore its diffusivity is much lower and the time taken to reach its steady state where the temperature drop across it xés small is longere Because its walls are thin in i with its diameter it can be considered as a flat slab and because the gas immediately reaches the steady state the boundary condition inside is that the heat supplied is constant. A servicable solution for r, CF Cr, can be finally obtained from . ard W. avt ~ 7 _” (H) (vt) = ~ 8try; are Le > ar ps e fe ~ {1 +2le “de | (30) o Tr - ro VE we can use the uniformly convergent For small values of ~55< expans ion x . 3 Ss ~----) 2 oth 4 2 73 Tze which gives : <, JI{r~ e= lan dott Feb Gy 12(aq tein)? r | (au) Por larger values far example r=r,; + 1m, t = 25 sec for which ae « 1.47 we can use the asymtotic expansion A> 1A [3 365 ~ ir - 7 (\- oe; +p ne)” ) and get re om 3 ay. Waite et | ott _ (ot) +15 (<) oe OO a eLar |r Vy 7 TO (82) The outcome of these calculations is to indicate that at tile very start equation (12) may perhaps not be conservative, but after the tube is slightly warm it is alri ght to use tnis form in the process of finding the dissoc iat ions This is so because after measuring the expansion one finds the dissociation by first subtracting the part due to temperature chargee fhis part is certainly exaggerated if in the expression about to be derived we use for the lowest temperature of the gas, the value found by measuring the outside temperature of the glass adding the steady state drop through the wallse it will be ugeful in these calculattons to introduce T the average temperature th the gas ¥ T - Ty, aa kL WE ready | No or, 4 eT) ~ 8 “ugqkb 2 : or _ Ww Tee eb OM) = oie (33) It is ® which is the effective temperature of the tube in prodwing the pressure change aside from dissociationg and we see fron (33) that it can be calcmlated directly from We To derive the necessary formula we define the dissociation by Naw Y Pony AO Woe, (34) where n is the number of atoms in the discharge tube and On, the tumber of moleculese The total number of molecules n, in the system is constant and if Ono is tie number of molecules in the cold tube which is at room temerature T and -~57~ which contains no atoms, we can write ie = Many + Mom FAM = Rom ti MMat Mm) (86) if Vy and V, are the volumes of the dischmrge tube ani the cold tube respectively, and if PR, is the initial pressure and p the final pressure which is constant thr oughout the system, we can write the gas law PV, © (Om, +ng) RT PV = tng R® . . (36) Pol¥, + Ve) =n, R . Substituting from (35) and solving for ¥ = | R Ort. y. tL (ee > >) PV T. or a Vy AP Re v = 2 +(e & =) | * (37) By an elementary calculation using (Nis the fringe- shift if one tube N _ 2AC AN = ==4 aud also equation (4) with all numerical were pumped out) N e values in ite y=2 )- (4252 _AN\T 7 /.029p + AN/T (38) =~58— It might as well be pointed out here that when the dark space gauge was used (37) served to calculate YX but since the volume of the gage was entirely negligible this becomes ; — : ~ _ 2 ] p- | RL 39 Y pp (39) or more c nvémiently y= 2 [AE IE 7” The pressure changes in the gauge were calculated from the well known law in which the dark space d is given by d= 12& + we for hydrogen (41) P c and a .- 13G + AT for helium " (42) P VE with the voltage kept constante In these expressions the second term depending on current dens ity can be neglected for our purposese The data calculated fran equations (38) on, show that the dissociation depends on the condition of the tube and slightly on the frequency and the powere -9— Te values at the pressures used ranging from 065 to 2 mm (usually above 1 mm) reached twenty to thirty percent using the gauge data ani somewhat more when the interferometer method or the helium check method was usede These values are in good agreement with the estimates from Bonhoeffer's datas The measures are unfortunate in involving big corrections for small effectse ‘oret of all is the unoortainty of the value of ¥ the powere This apparently simple quantity is hard to get ate ‘The wattmeter readings which were actually used do not represent the energy dissipated in the tube. Energy escapes at the electrodes in no in- considerable amounte More important are the losses th the transformer and the condensers as well as the high voltage voltmeter and other parte of the circuite The first two may account for 2070 of the power and the voltmeter might sometimes | have required 150 to 250 wattse Such losses if they could be corrected for might show double the values of the dissociatione For high powers the error might be very largee For example take equation (40) for small and high power such that AP. AT ra might be e4¢ Suppose that — calculated from VY to which it was closely proportional was also e4 so that .) = O6« If not the trivial correction of 5Y for radiation is made of W, the value of Y becoms 490, if 20% is allowed for de = . caadenser lose y 20%- Ie 259o is attributed to Voltmeter loss Q = 40% 6 ~60= ‘It is seen that this work mst be carried further. De ESTIMATE OF ERROR. Iet us not insist on the possible high values of na Nw , and be satisfied to say that gt = ve was & least 0.25 at original pressure. : om 2mm, that the shift was no more than 0.03 fringes and that accidental errors were absente Substituting all valves into equation (4) we have partial pressure of atomic hydrogen is 0625(1 + 0.25)p +t 0.03 = O.25 GO 27% Lash > (pn) i? | ~e 160 ~ & X10 . 243 or 0.25+-90-273 p28) mz ) + A an [138 26 ave | tas) This is the figure that is to be compared with the the ary Apparently there is a bad di sorepancy. The theowtical Gayo 1) calculs tea for example from the second order Stark effect term as derived by Epstein and others gives (Hi _/ ) > 2.3 xo The order of the discrepancy can be judged by using the theoretical value to calculate the expected fiinge shift at 2 mm using masured atomic ~61~ hydrogen concentratione Substituting in equation (4) - -4 —4 590-273-1252 [4,3 x10 7-1 38x10 ) 6x10” .293 +760 we get | AN = «11 fringes A shift which would have been plainly visible in every observation, even under bad conditions. Another point of view is to say that if the shift was less than 0.03 fringes, there must have been less than 84o atomic hydrogen in the best cases This is out of the questione The estimates of 25Jo are conservative, for the tube in which the fringe shift ‘was measured was in the dest of condition and equalled tates in which other observers claim 100p dissociatione In such a state of affairs it behoves us to examine closely the theory underlying the predictions which are tested by the experimen te 62 THECRY OF THE NORMAL HYDROGEN ATOM. Schrodinger's wave equation for this case gw? ' 2 A We + SOME +2") wre (44) yy has been well investigated, and the solutions satisfying the necess:ry condi- tions are known to have the form Fon.” [. (>) y ¢) © a (45) ™ ed) The y are spherical harmonics ani since we are dealing with nomal ‘nH hydrogen we may disregard them because of the restriction that A n=+1 and because tec electric moment induced by a light wave is parallel to it, so that “\m=0. Since n is zero for the normal state the only functions oO oO that appear are y and y which are constant and we may confine our atten~ tion to the functions 0 {r}. Explicit formulae are available for this m function but as is so often the caze, we find it most convenient for actual numerical calculation to derive the value of a directly from the fundamental integrals which arise in the method of Laplace, namely —63— where C is a camtow which has to satisfy a condition, a sufficient but not necessary form of which is Lone n- Kes Ter7> -# ne") ” (+8 tn ‘me =) z-20 4 » iy, : For negative values of E in (44) 8 must be an integer and (47) is satisfied b choosing a closed path around the only pole Z = = typ For positive B, (need not be an integer and.to get the whole transcendental a more conpli cated path is required ani one mst be satisfied with an apvroximate solution. ‘the mmin difficulty is to get the normalizing function and this can be found from the work of Oppenheimere | Knowing all about Swe can go on and inguire about the distribution in space and time of electric charge density. This is given accarding to Schrodinger by (- = va Va (48) If we denote by 4 the properly normalized part of (44) vinich does not depend ‘on the time, the charge density in an isolated hydrq@en atom in thet nomial state f= 1, m= n= 0, stb jected to the action of a light wave F ocow Law 2/t (EF, E a, (ra (+) ype u(y) - ZF em 2nrve Seno a (49) (E,- EY - ba of mer . | . [[- ev OO)? aw 6 -Ul)4,(b 0 Ly eo A (6) | fever palrdalEx)dedy (82) From this point the Schrodinger method is to follow accurately the where am classical theory in which the electric moment is — Ms: |evay and the index of refraction is given by 2), tax MG) J Fay 29 ve | (52) Where M(t) is the variable part of the electric mom and N the number of particles per ome ) 65 Applying these to (49) there results finally Pf © (EE) oi : hi )e 20M PB EL) A Egy Tis equation is identical in form withthe classical expression for a set of oscillators with natural frequencies (EB, - By ) md also a set with continuously vary ing frequencies cf ~ B)e The numerical values for the first three terms of the summation and for the contribtion of the continuous spec- | trum are given in order for the case of the hydrogen atom in the nomal state | undisturbed by outside farcese (2 a= 152400 “4 O28 rio 0.06410 aa 100 The sum which is still low, is already greatly in excess of our experi- mental values out we have imagined that the atom is slow, vate as a matter of fact it is in a gas at pressure, let us say, around 2 mms Now if we say that (49) MM@BMily described the distribution of charge in space, we see that under the action of the light the normal hydrogen atoms which originally (figure ) was a spherically symmetrical distribution of charge decreasing in density exponentially with r is greatly expanded end the hydrogen electron is spread partly in large shells as shown in figure ° —~66=— ‘hese shells correspond to excited states of hydrogen. ihay are importmt in the dispersion because of their large moments. on the other hand the chenpe that another atan will approach to a given radius depends on the square of that radius so that these higher states will suffer many more collisions than the lowest statée foote has shownthat whenever a collision may affect a quantum state it doese in other words collisions of the second kind have 100% efficiency. Calculating the number of ccllisions on the basis of Kinetic theory it turns out that all the higher states are comletely destroyed in the time taken for the passage of one wave train and their , ee to coherent scattering lost and so should not be added in to the electric moment. This MKS [+ , ~f( equal to 1508 or less since there is som loss from the lowest term. In any case the resultmwis now equal to the experimental value within the estimated errore 67 = CONCLUSIONS « The experiment is therefore not in disaccord with the theory but actually offers evidence that the theory is literally true. The excited hydrogen atom is apparently really a shell of electricity and in general the quantity Ze ib describes the space occupied by an atom in the kinetic theory sense, and once ‘more we have a concrete model of the structure of matter. Moreover it is to be expected that the vos of excited states takes place in all atoms and that therefore the refractivity will depend on pressure ani deviate from equation (2). Pressure effects have been looked for, but always at high pressures, while thds one is probably over above pressures of one nme It is hoped that an opportunity will be had to search for this chanze at very low pressurese It may give important evidence on the excited states of atoms and moleculese The author realizes that any virtue in thés work is Largely due to his privilege of starting, planning and almost completing it at the Norman Bridge Laboratory in Pasadena, Califomias The problem was first brought to his notice | by Profs Ste Loria and engaged his interest because of some theortical c msidera~ tions by Profe PeSeEpsteine The deep inituitive insight of Prof. Re A. Millikan played a guiding role throughout the work and furnished besides strict crit icism in particular placese The author is prow to attribute his knowledge of exrerimental tecmigque to association with his colleagues at the California Institute of Technology, expecially IeSeBowen, WeReSmythe, AsLeKlein, Re Kennedy, Sinclair Smith, C.BeMillixan, WeVeHouston, OeOldenberg, CeEckart, E.C.thite, and others who were always willing to discuss difficalties and always able to offer valuable suggestions for surmounting theme Thanks is due to the Naval Research Laboratory, ani especially to Dre Ee O« Hulturt for permission to continue the wrk there ani for providing many usual facilities for its prosecutione