The Scattering of Electrons in Gases Citation Arnquist, Warren Nelson (1930) The Scattering of Electrons in Gases. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TSJM-GE32. https://resolver.caltech.edu/CaltechETD:etd-03172009-151505 Abstract It is found (1) That the angular distribution function of electrons scattered in mercury is not a monotonic function of the angle, but has a minimum whose angular position is an inverse cotangent function of the energy of the electrons. (2) That the angular distribution function of electrons scattered in air is a monotonic function of the angle within the range investigated. (3) That measurements of small angle scattering in mercury are in qualitative agreement with the work of other observers. 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 1930 Record Number: CaltechETD:etd-03172009-151505 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-03172009-151505 DOI: 10.7907/TSJM-GE32 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 989 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 17 Mar 2009 Last Modified: 03 Oct 2019 23:04 Thesis Files Preview PDF - Final Version See Usage Policy. 8MB Repository Staff Only: item control page

THE SCATTK.qIN G OF ELEC T~ON S I N G.b.dE3 THE.:jIS BY WARR:Ell NELSON .A.::tNQUIST UT PA~TIAI FULF ILLLI:EliT OF THJ.: ~J:QUIRJ.:1,1:'11T TS FOR THE DEG~EJ; OF DOCTOR Ob-"\ PHilOSOPBY CALIFO.'..iNIA INJTITUTE OF TEC.:UWLCGY PASADENA , CALIFC1N IA 1 9 3 0 SUl1iliARY OF R~'JLT.3 It is found ( 1) ·:rhat the angular distribution function of electrons scattered in mercury is not a monotonic function of the angle, but has a minimum whose angulo.r pos ition is an inverse cotangent function of the energy of the electro ns. (2) That the angular distribution function of electrons scattered in air is a monotonic function of the angle within the runge investigated. {3) 'J:hat measurements of small angl e s ca ttering in mercury are i n qualitative agreement with the work of other observers. E I B 1 I 0 G R A P HY 1. K. •.r . Oorn:pton and F. J.. i.'lohler, Bul. Nat . Research Council, Vol. 9. 2. K. '.!.1 . Co mpto n and Irving Langmuir, 'ieviews of l1Iod. P:13sics, vol. 2. 3. C. qamsauer, Ann. d. P '.1ys ik, 64!_, 513. 4. E. Brrtche, Ann. d. £hysik, 4, 387; C • .~amsauGr u. ~. Kbllath, Ann. d. Physik, i, 91; T. J. Jones, Phys. Rev. , 32, 459; R. B. Brode, Pro. '3..oy. ::)o c. , !§.~_, 134. 5. E. G. Dymond, Phys. J. ·J . :. :ra::c: i.rT 8ll, I::.:·c, . l .at . Acad. of ;.;:.ciences, 14, 564. 7. G. 2. ]arr1well, Phy s . ::lev., 34, 661; Dymond and "Iatson, ~ev., <;:>0 ~' ,1 '7, r:z. :tv""'• Pro. Roy. So c., 122, 571. 8. J. k. :Pearson, Journ. Optical Soc ., ];2, 371. 9. 1i\ Thiddington, Nature, 124, 758. 10. P. L. Cor) eland, Phss. 11. JI'. 1. Arnot, Pro. Ro;y. Soc., 125, 660. 12. I. Langr:rni1· ancl H. A. Jones, :Phys. ~ev., 35, .982. ~ev., 31, 357. I ·:rflE l?ROBLEM In the studies of the atom, as a struc ture made up of r:ucle i and electrons, a great deal of inforrns tion l1ae been obtained from experiments a_ealing vv i th energy r oJ.ations . Iv1odern s~~: ectroscopy has revealed an enonnou.s complexity of 'lexci ted states 11 to which the atom may r)e r8i:::ed, and the quan tum theory has given a ver'j satisfacto::cy description of the phenomena. servin~ the The problem hae also b e en attacked by ob- ener~y losses suffer ed by electrons in their ir.teraction v.r i th a tome and molecules. .A complete account of ( l) the experiments in this field is given by Compton and Mohler, ( 2) and by Compton a.'Yld Langmuir. Another method of a ttack ias been to observe the effective cre ss -sectional area presente c to a moving electron by an atom. This was done moPt accurately by a method due to ( 3) ~amsauer which a.as since been refined and f;:pecia.lized by ( 4) others.. The re sults are e:x:presP.ed by a qua.nti ty O(' w'.1ich is the area in sg. cm. presented to a moving el e ctron by one c.c. of the gas under conPide :t>· tion at a pressure of one mm. of mercury. The reciprocal of' ()(. ie thuP the mean free path of the electron in the gas. If a homogeneous beam of electrons passes through a gas we may say tl1a t an e lectron hap, collided with an a tom if it s uf fere an apprecieble <.; 11c::.11 6 e in energy or momentwn. 2. '!'.Te shall c al l t ~-iost: ' coJ.li ~; ions in wb.ic [1 t!1 e e n ·.;rg~' dot::f· not chant; e appreciably nelas tic 1' coll.is ions and a l 1 others chang e whic~ is compa rabl e t o the lowest resona nce potential of ti~1e a tom, and. a corres :poncii ng change in momen tum ·will be defined b.>1 the g eom e try of the apparatus in an~,r particular care. In an,y theory prof esP ing to g ive a complete picture of the atom as an electrical structure i t will be necef:Fa ry to know t'ie fie la. o f force in its neighborhood. to do t n.i f' only d eta il. b~/ 'nl e can hope inv eP tigati ng t he se mom entum tru.nsfers in Because o:f' th e enormous diBpari ty i .r~ masses , it is obvious tha t th e electron a lon e need be f ollowed . This problem of det e.cmininb' t he angul a r dif·. tribut ion of e lectron s Ecc:.ttered by atomf' has only rece n tls cla imed att en tion. ( 5) The early experi- ( 0) ments of Dymond a.nd Harnwell were i n di sag:ceemen t, but so me of the di ff ic u ltie s of t a e pr ob lem were made c lea r. Both obser- vers ha v e s ince report ed results wh ich seem to be in qua li( 7) tative agreement with the present theories. A series of experirnen tf' waP. begun a t t r1is I ns titute by Mr. John I>ear;::.on and th e author in an attempt t o improve t :1e tec b.n ique and to mea,pure the s catterins a t l a r ge ang les. An account of the first result ::c obtained was g iv en by Mr • .Pearson in his Doctor's Thesis at thi s Institute (1930). It if with th e f urth e r development of the expe rim ent and th e re Fu lt s obt a in ed th a t this thesis will deal. 3. II THE .APl?A.:tA rru s A detailed account of t'.le desi gn and construction of t he apparatus has been given by Mr. Pearson, but for complet eness t ern essential points o i' construction and further modifications are given here. F I~~T: The scattering chamber should be free from electric and magnetic fields. The early experimentf' already (5),(6) referred to showed t~at thi s was imperative. It was decided to construct the whole apparatus of brass and two pairs of square Helmholtz coils, 150 cm. on a side, were made to neutralize the ea rth's magnetic field. Storage batteries furnished the current for these and a potentiometer mersured v e ry accurately the curren t wh ich neutralized the vertical component. The chamber was a cylinder 5 inches in diameter and 4t inc hes deep. A v e rtical cross-sectiona l :plan through the s lits 31 and S;z , which were in optic a l ali gnment, is shown in Figure 1. The pumps and pressure c auge were con:nec- ted to the chamb er by pyrex glas f' tubes at two diametrically opposite openings not shown in the figure. SECOND: The source of electrons wr.s an 8 mil tungsten wire b ent in the fo rm of a narrow hairpin about as long as the slits and heated with A.O. throu£: h an insulating traneformer. The filament was spot-we1a.ed t o leads which led through the glass stopper, Q, as shown. were firmly fa~tened Later filaments to these leads by twisting tightly and 4. , T I .. S, . I I I I I . 1'1~ -- :~ 1 F i g. 1. G, C<? li)1 L N 0&V\ I ~~ ! l- L B 89 + I A t. 't' - -L £ B.,, + ~ Fi g . 2 . + I 5. seemed to work just as well . The emission waP controlled by manual operation of resistances in the fil E.ment heating circuit. The loop in the filament was supported by a n ickel wire which served a s the cathode lead. The inhomogeneity bec aus e of the "I Rn drop in the fil rment was thu:::: cut down and in most cases the spreed because of this effect Was less than 3 v0lts. An acc elerating grid, A, of fine mei=h nickel gauze bent i n the form of a semi-circle with it s axis parallel t o the sl its and convex toward the filament was part of the electron 11 gun 1• and served to focus a large part of t he emis s ion on th e slits and thence to t he chamber as a narrow beam. The stoppe r, Q, fitted into t he glaPs tube, T, which in turn fastened to t'.'le chamber as shown. The variou s ground glass joints were made vacuum tig ht with picf~ wax and those near t i e hot f il ament wer e water cooled. The dimen sions in t he electron gun were made small so that arc discharges would not occur. Sputtere d tungsten on the glas s near the ele c- /~eu/s trode/\sometime s caused insulat ion troubles but it was f ound possible to burn thi s out by applying high voltages. THIRD: In order to int erpret the results as single scattering it i s necessary that the mean f ree path of the el ectron shall be larger than t he dim ens ions of t he chamber • .According t o the kinetic theory t his is given by 4 f f times t ne mean free path of the g8s atoms. Direct mea s uremen ts of electronic mean free paths hav e given values in most cases ( 2) larger t han this, so it can safely be talcen to calculate an 6. u pper limit t o t he pre s sures which cs n be used. is appr oxi mat ely 10-l mm . for the gas es used. ~ Thi s limit In all the s c atteri ng experiments und erk' ken , thiF c ondition was amply sati sf ied. F OU~Tq : I n the result s of t hi s experiment f ir s t r ep- or ted, an anomalo us loss of energy of the el ectronP in the main be2m w ~ s described. In ord er t o i ~ ve st ig a.te t hi s point more clo s ely, an auxiliary grid of nickel wire was mounted betwe en t he f i xe d Faraday cag e and the la s t slit. Thi s grid, which could be maintained at any de s ired potential, i e shown i n F i g . 2, but t hr ough an error was left out o f Fi g . 1. Results showed that this formed a fairly g ood equipotential surface. E'I F T]: A schematic diagram of the electrical connections i s shown in 1t'ig. 2 . The filament , F , was maintained at a negative pot en tial, E, with res pect t o g r ound and the accel erating grid at a positive potent ial, A, wit h r espect t o , F . All the other pot en tials were with respect to ground. V"' milliam ~ t e r, The M, measured the current t o t he slits and chamb er . Gz, i s the retarding grid and its pot ential will be called, Bg. The potentials, E , A, a n d B9 , were obtained f r om poten tiomete rE'. fed by a D.C. mo t or g ene rat or set a nd batteries supplied, Bp• and Be· -9 The galvanometer, G, had a sensitivity of 8xl0 amp. per cm. and was prov ided with shunt s in order to read l arger curren ts. A Dol azalek el ectromet er s hunted wit h a large r e - s i s t ~ n ce, R, measured t he current to the rotat i ng collector C.3. It was regularly 0 1)(::1·8. tcJ Bt a sensitivity of 2000 mm. 7. per volt. An analysi s of the theory of the ins trument and a ( 8) met hod of obtaining grea t e r sen s itiv eness i s giv en by Pearson . The re s i s t anc~ , R , wa s a narrow lin e of i ndia ink drawn on draw ing pap0r, boil ed in par ~ f f i n , and sealed i n a g la ss tub e . After many trial s one wa s made wh ich had a c on s tan t r es i stan ce of 2xl0 If ohms. Ano ther resistance ( 2xl 0 9 ohms ) was us ed t o read larg er curr en t s . Thus it was possible t o meas ure curr en t s as small as 10 It i s int e re s tin g t ha t these hi gh re- _,,,. amp . sistan ces should be as c onstant as t i1ey were fo und to be. Even at high voltages (2000 volt s ) the re s i s tanc e decreased less t han ! of its value at 1 vo lt. The resistance of the insulation about t he lead to c ollect or , C..!, was measur ed and 1 found to be of t he order of 10 G ohms a t 200 volts and so a correction to t he el ectrometer readin gs becau s e of thi s was not larg e enough to be cons idered. All t he s lits were 13 mm. lo ng and 1 mm . wide except S"° 3 , 1 The slits , ;:) I ' were. 14 " The rotat in~ co l lect or was wh ic i1 were .8 mm . wide. apart, S2. were Z<.- n ' and S 3 l". . 0 mounted in a ground me t 1 joint in the cov e r, which was sea led to t he c hamber with picien wa x. The i n dex , P, attaci1ed t o the rotat or gave th e angular position on the en g r av ed scale <9. A two s tage mercury pmnp bac k ed by an oil pump was us ed to evacuate the appar r tus . Liquid air traps i s olated the pumps and Mc l eod gauge from th e ci1amber . Wit h th e pumps in opera ti on , t he pressure was lower than could be rea d on -6 the gaug e; i.e., less t hon 10 cm. of H9. Under fa vorabl e running conditionR, the s ystem wouJd ho ld ~ vacuum of 8. -S" 5xl0 cm. for a couple of days wi thout pumping , shovving th a t it was quite ti ght for 2 meta l a pparatus. Because the chamb er was cons truct ed of brass , it was impos s ibl e to bake out, but it wa s found that after se veral days of pumping and int ermittent bomb ardmen t with an int en se e lectr on beam, the vacuum conditions were very good. III PROCEDURE The value of the current necessary to neutralize the horizontal component of the ea rth' s magne tic f ield had been det e r mined with a magnetic pendulum before t he apparatus was mounted in position. It was found tha t comparatively l arg e va riation s in thi e curren t had no effect on I!/, the current to t he galvanometer, s0 t his adjustment was never critical. The current in these coil s wa s set at t hi s valu e and then, with the el ec tron gun furnishing a s teady current to t he s lits, the current in t he oth er pair of coils was varied until the galvanometer deflection was a maximum. Experiments showed that thi s cur r ent was s lightly di ffer ent when Bg and Bp were zero, t hr,n when the po t en t i El s were adjus ted so that only full speed electrons could re Pc h the collector. This difference is due to t he formation of s low speed s econda rie s at or ne s r t he slits. The voltage, A, was then varied in ord er to ge t a s int ens e a beam as possible and the reading of, M, was kept constant during a run. With (I, 1 for full speed electrons f ound in thi s 11rt11. 9. way, runs we re tak en obs 8rVing , I 9 , as a function of Bp, or Bg, as will be described later. Also, 1 9 , as a function of the ve r tic a l magnetic field w1s i nvesti ga ted. nshapen of t he main beam. This gave the , In g enera l this was n ot symmetri- cal about th e value (r 9 Ji wh en a n ew f il ament wa s being tried "'4lC, out, :-:- nd so it was necessary to a gain line u p t he fil ament with the sl its. This wns a slow process, but when it was done carefully, the rea dings at positive and nega tive angles checked very well. Fortunately for t he experiment a good filament would last some time. Mercury vapor wa s the most convenient gas to investigate and so mo s t of the work was done with it. A mixture of ice and water was placed about the "liquid air trapn nea r t he chrunber which contained a small quantity of liquid mercury. The temper Fture of this b ~) th dete rmined the pressure of mercury vapor in the chamber when equilibrium was rea ch ed, as long a s the bath was below room tempera ture. The other liquid r ir trap next to the McLeod gauge was con nected to the chamber by a long narrow glass tube and consequently had little to do with the pressure in the chamb er. Liquid air was u sually left on thi s trap a s it didn't seem to make a difference whether it was cold or not. The ice- water·mixture was vigorously agitated by a stream of air bubbling through it and the t empera ture was checked with a thermometer. The Inte rna tional Critical Tables gives the value l.8xl0-~ mm. for the pre s sure of mercury vapor at 0 0 C. 10. wh ich was used i n the ca lculations. Experiments were att empted with hydrogen but it was found impos s ible to keep th e pressure const an t lo ng enough to take a run because of some kind of a "gette:.cn action removing the gas . Electrolytic hydrogen was introcluced i n to the vacuum ti g ht appa r a tus throug h a liquid air trap and allow'ea to come t o equilibrium. on and observationsstarted. I1hen the filament was turned It was noticed that the pressure stea dily dimini s hed as long PS t he .::l ::: ctron g m1 was ope·rating . -3 In one ins tan c e the pres ~ u:ce fell f r om 2. 7x10 -':1 1. 2x10 cm. to cm. in half an hour and then remained constan t for over thr ee hours after t~e filame n t wa s turned off . This phenomenon was observed several times and so wo r ~ with this gas was given up. With air i n t he apparatus at simil a r pressures the ph enomenon wrs not noticed. I n mak i ng s catt ering mea 2urement s the current t o the r otat i ng c o llector, r.,was obs ·3rvecJ. as a function of the angular position fJ • ExperimentF s howed t irnt no curr ent re ~' ched the c ollector c3 in vacuurn when9was greater than 15° . Thie ab~ence of s cat teri n8,' a t l a rge:c angle s was used as a criterion for go od vacuum condi t i ons . Because of the inhomo- g0neity in t he ma in beam it was cons idered :practical to mear:m re ela s tic s c a tte:cing only, an d so the va lue .o f Be was always adjusted t o collect the f ull sp eed electrons. an gle~ ~~ At greater t han 30° s i rnultane . : ,u s read i n.gs of Ie and were made. At times the main beam wouli va r y cons iderably mer. due to variable s lit ecattering or f il ament va riati ons , but 11. the ratio I~ for a g iven angle and pre Psure wa s remarkably constant . ' In gen c: :.c ~"- 1 two readings at each setting were made and if these checked to within 516 they were accepted. At large angles it was also necessary to cor~ect for the positive ions which di ff used i n to the collector. This wa s conveniently done by raising the bias Be about 10 volts above E, and observing the current to the c ollector. :B1 or very large angles the positive ion current was often greater than the electron current. Fluctuations in the line vol~ a ge were particularly bothersome during the day, sometimes making it impossible to operate. However, experiments were conducted in tae early morning when conditions were usually very constant so that one man could operate the apparatus. More weight was attached to curves taken under the conditions in interpreting the results. IV RES.ULTS l. ENK.'i1GY OF ELECTRONS; Typical curve s show ing r9 as a functi on of Bp before the introduction of the ret 1:1 rd.ing grid are shown. The initial drop a t sma ll v::lue s of the retarding field w0e due to the exclusion of slow speed secondaries. When the mercury was present this group aleo included positive ions which were attracteG. to t~e collector ~y the negative field. The subsequent rise in the curve in the case of gas was due, probably, t o a decrea se in ionization as t he electrons 12. I 0 0 0 P < 10-s;,.m, l!g, 2 E • ISO V./ts. F i g. 3. 0 4 p =2.s xto- 111m 119 Vqrcr. £ =I SO Ve Ifs. :&'ig . 4. 13. were slowed up. This part of the curve ws s very unsteady when gas was present, while in vacuum the curve was quite flat. The most interesting feature is the ea rly drop in the curves which was repeatedly found regardless of the value of E. According to these curves the electrons have lost some 25 volts of their original energy which is much too large to be due to contact e.m.f.'s , etc. A similar effect has been ( 9) observed by Whiddington in gases but the present phenomenon seems to be more complicated in that it is present even with good vacuum conditions. ffowever, when the grid G2 was used to retard the electrons and Bp = 0, curves similar to the upper curve in Fig. 5 were obtained. When gas was present , the middle of the curves was always lmver thfl n either side as in Fig. 4. Two grids of different mesh wire screen were tried but the curves rema.ined essentially the same. 'l'hese facts make it difficult to explain the phenomenon on the basis •• 30 i!.O P <. 10·5",,,,,,.115. ID £ •200 Volts. 40 120 Fig. 5. 14. of electrostatic interpenetration of fields and as the effect seemed independent of current densities, ordinary space ch£·r 3e doe s not help. Further, it was foun d that Bp could be any value between zero and about 30 vol ts po Pi ti ve with re!:'.'pec t to B9 and the reta rdation curves would not dro p off below the bias E. But wh en Bp was made less positive with respect to B9 the drop off occured below E and when Bp = Bg curves eimilar to the lower curve in Fig. 5 were obtained. It should be no tice6 that in this case there is supposedly no f ield between collector and grid but, nevertheless, a curve similar to Fig. 3 was found. ( 10) Some direct experiments by Copeland on "Secondary Electrons from Contaminated Surface s 11 ha ve shown the effect of coating the collector, in this cas e a tungsten wire, wita an oil f ilm. This produced an insulating layer wh ich very efficiently reflected the incident electrons wh en there was no field at the surface of the collector tending to prevent the charges from leaving. If such a film were present on the surface of the collector used in our experi men ts , which is quite possible as br8.sP contamin E.tes very easily, it is easy to see ~ow reflect 150 volt electrons. the c ollector at 140 volts can The incident electrons will collect on the surface of th e film until the potential due to space charge becomes sufficiently nega tive with respect to t he plate so electrons can pasP to the pl ate. But, as the plate i s made more and more negative, a point is finally reached where ~he surface cf t hB fi lm i s at a potential E 15. and the current starts to drop o±'f. Jowever, t :ie collector is not yet at t :1e potential E and so curves like Yigures 3 and 4 were obt f" ined. Further experiments with other co2.- lect ors are being conducted to test this point more carefully. It seems at least i n view of this evidence that the speed of the electrons in the main beam may s.afely be taken &s given by E. 2. FOCUSING EI!':E' ECT: When r9 w s obs erve d as a function of the vertical magnetic field , an interesting focusing effect was observed. l!' igure 6 shmivs a typical curve. 'l1 ~~ e low broad peak represents the observations in vacuum and the sharp peak the corresponding measurements in mercury. wid th" iP indicated in both cases. The "half To obtain the resultant magn e tic field in gauss, multiply the difference in ab scissa of any point with the abscissa for (r,Ji by 1.10. 'r his effect lr14X. has been observed in cat hode r ay oscillograph tubes and has been qualitatively explained as due to pos itive ions of low mobility, compared to electron speeds in the electron beam. The effect varied with current density, pressure, and velocity of elect rons but wa s not s tudied in detail. It is important in the present scattering experiments as giving a measure of the number of positive ions present in the scattering volume. 16. 40 Shape of /11/ain Beam £ "/SO//olt"s. 30 2. o. 0 10 c~,..r~1tt i11 lle/,,,.;,.,/tz:. Coils - J F ig. 6 . 17. 3. SCATTZRING CURVE3: - _L ff 'J:he equation : f (e} = Ie sin & I9 (1) P Ie i s the was us 0d in interpreting the results ( appendix I) . s cattered current reaching t he collector c , r9 the main 3 beam , e the angle of setting and P the pressure. f(fJ) is the probability per unit so lid angle of an electron being sc~ttered through an angle e in going· 1 cm. t nrou,:;·;;_ th e gas considered, ~ f (B} at a pr essure of l mm. of mercury. 'i1he curves- show plotted in arbitrary units against e in degre es . 3ecause of the very small currents scattered at larg e anglee , the values of Mand A were usually adjui?ted to give a maximum current. However , it was po8si ble t o work with lovver current den s iti es . Results in a typical case are shown in Figure 7. The smooth curve is drawn through the crosses, which were ts.ken when The value of (r1 \ the focusing effect was very pronounced.. flntlX, with gas was 5 tim e2 the corresponding value in vacuum. Several months later, using a new filament, the curve marked with circles was taken when conditions were adjusted so that this focusing effect was much smaller. (r,}, wa s i n ,_, . LdllS case "'4X. but 10% grea ter in gas than in vacuum. I n plotting this curve the "K 11 in the ab0ve equation hud to be ad juF:ted by a small fact o r to bring th8 curves together. 'i1his ''K" which includes the s lit scattering and some of the geometry of the chamber VJas D l way s found t o vary fr om day to day an d someti mes during the progress of a run. ]:owever, qua li tr ti ve results were all tha t were hoped for En d it c an be seen that 18. /0 Scattering /17 fi'!ercttr'j 8 _.,. P=l.Bx/o mm.I-lg. £ =IS-O Volts. 6 0 ; f(B) ' 4 2 0 so 70 F ig. 7. 19. the two curves ar e almo s t id ent ic a l. cu rves taken i n mercury at l ll of the s ca ttering app eared as if t hey l ar~e ang le ~ would be qu.Lte mono to n ic except fo r a definite min i mum, as if the sca tter ed c urren t a t a particul ar ang le we.s en ti r ely mi rs i ng . Bec au se ~f the sp re ~ d of el ect ron valocitieR a~d the f i n ite re so lvinc power of t ~ e s lits this appears a s a r a ther broad mi n i mum whose l ocation is a definite f unction of the speed of the el ec trons . E = 100 to E = 200 vo l t f' g iven i n Fi g . 8 . a ~1d t ':e Curve s were t aken fo r of th e resul t P i P surnm s1~y It was impo ss ibl e t o work wit h s l ower el ec - trons b ·e cause t .fiG s lit s ca tt er i ng i ncrec' Peli ve ry f a st for these and practically no curren t reached t ha c ollectors. ;;l1o ve 20C vol t P. t he minimum 'a pp ea r s i n t he s t dep pa rt of the curv es ~n d s o i s smoo t hed out . ~n i ntereP ti ng correla ti on E. l:il.·•..4~4f' /, 1,0 Cat8,.;~ .8 /(JO 6$'. !2S S7 IS'O so 17S 44 ,6 200 04 /()() ,,,.0 J ClfrYt!S 3 7 3 I . . " " 00 12S £ Fi g . 8 . l't'.r 20 . the electro ns i n vo 1 t s . 'f i1L_-; i P som eti1ing li l::--; •H'.1a t would be ex pected if t:1e s catt er ing followed a n inverse s quare law .:.1he ag:ceem ent s hould not b0 empha:=:iz ·cl too much , of fo rce. ho~3v er , a2 it may b ' only fortuitoue. Jcattering meas urements e t lG.:cge ane le f' were taken with air a2 th e s catter ing g a s an d Fig. S give2 t~e re s ult s It wa s ne cess ary to use sli g htly b.i c:· her fo r E = 150 v o lt s . enoug~ prePsures to obt a i n large s c a ttered currents to measure but the condition for s ing l e s c attering was st ill s &ti Pfiedo contra~t In to th e curves for me rcp.ry , t hiP one s i m:y le mono to n ic d ecreas e as e i n creases . F~1 01.1.1 s a ~: '.:.i!=' curve can be e.'1own t o agree very closely wit h an inver se squa·re lmv of :forc e but no t 0no ugh curveP were t alcen with oir t o rna~>::e thj_ s ver:.; certain, r::: it wa F thout; ht that the P- catte.ring iin •3 to a mixture of gas e s wou ld be ha rd t o i n t e rpr et. focusing effec t Tuns ~ow ar d resi s t ~n ce fcunc~ .ni th 1 Ve r y little ~:: ir. the c ompletion of the work t he l a rge R ( F ig. 2 ) developed an e . m. f . and a~ it u2uully tool:: 2 evert1J. monthc fer a new resi sb_rn c e to beco me it vvas dec ided t o fo~ It l a~ ~ e WO.'' tr~1 to meef'n:re the s c a ttering a t :::r'.lal l 1::..~1gl ·es &ngle e ex ce pt that low fi l ament founa. thc. t the v 2 lue of (r ) und e r the~' c ondi. tions. 9 "1tt K. ~ni sr i cDs were u s ed. did not vary a:pprec i ubly :' '.ie rJa in b earn war. m ec:. Pur ed at t be be- s inn ing of the run ~ma_ c~e cked at t :1e end. wap c ons t ;:;,~1 t , c omput ed a ~ before and the reeu lts are 'I'l~e value of s~ own k ff&) by the circles 21. S catferin3 lnAir / / P =1.3 X/O- ~mm. rr 3. £,..ISO Jl" lt".s-. -tt(e} ·- _,, _ 90° ~ i g. 9. 60 Scattering inhft!rc /./r.:;. -4 /J P =I. 8 x ltJ mm. 11.9. £=ISO I/oil's. 0 /iJ ... 0 /() F ig • . 10 . 23 . ( 2) i r.. F i g . 10. qecent l y La ;.gmuir hus s :iown t(iot :r:.:cactic a ll y a ll the mecsuremJn t s o f th e s catt ering fm1cti on fo r el e c t r ons emI' ir/c"I &t sr::ic:::. 11 a n:;·1 2E' can be express e ,l b;y the equati on : 11 f (fl} = f - e2. (e~:o e s;i '2) wh ere ~ i ~' t ~1 e "rnean e quare angl e of a.ef l e ction ". Using the dat a obt a in ed i n thi f ex perimen t , t he cons tan ts in t his equat i on c an b e obtained graphically b,y plot tins log f (fJ} ags i ns t e2 • Wh en thi s if~ don e and f(e) plott ed ' th e Sm(lOth curve t' ;1own i n t' ig. 10 i s ob t a ined. Th e exp erimen tal :points ( 11) f i t thiE: equation qui te 1.v ell. Arnot has r ecent l y r eported d.ir ect mea purem;;nts of the an gu l a :c· scattering of 82 volt el ectrone in me r cury. 1a n5muir h.as P i1own are c onsist en t wit h equat i on ( 2 ) wh ere that t hen: re sult s e. =/.' · 30 . A value of 0 ~ 0 80 =Ii:, 7 was f cund i n the ·oresent ex·oe rim en t s f or 150 v olt ~ ( 12) el ectro n2 . ~ langmuir a n d J ones ho.v e me o surGd t'.le small ang le sc a tt e ring i n mercµry Oi,' an i nd irect metr:o d r.nd they fin d J.:'.)D ~ -- 100 , approx i mate ly , f0r 150 volt e l a c tronA . mathod does not di s ti ngu i s h sharpl y b e t we en l o sr of lo ss of fo r ;rrn rd r:iomen t um , lat e t ~1e value of f(B) of the unc er t a in t y in 11 1{" Ci0ir.1 e v e r. It i ~- 'l 'h e ir ene r g~ an d i mpo ss ibl e t c c c<. lcu- from th e present ex1Jerimen t s b e c ause '. 'K" {e quation 1) . Ar.; was men tioned , vvo uld v a.ry from d ay t o day as muc h as a f a ctor 5. All that c an be said i s the.t t b.e va. l u e of the t otal :probab i lity of s catt ~ ri ng ~ as c omputed from thi s da ta i s i n ag reaman t 1P it'.1 th e value found by othe r . observers i ri ord er of me.gn i tude. The c al cul a t i on i s shovm in .Append i x II. 24. I t has been object ed that since the ~ c attering volume increap ·a s rapidly at small ang l 8E , tl1e:ce is 8Jl llll c ertainty i n th e int erpr e tati on of the results a s the main beam doe P not remai n const 4'nt t'.1.rouc; hout the s catter i ng volume. Jo •v ever , a t t be 2.ov.r :press ures used in t L1is ex1) cri - ment , t l:.i f' i s not a ser i ou;:-· obj ecti on bec n 1ee i t i € eas ily computed that th. e c hange i n t he ma i n b eam w'.len less t i1 an 11s i n cros s in3 the s ca t t ering vcilmne . e= s" is A muc h more seri 0us ob j ect i on present s its elf becau se of the length of the sl its. j t the s e angles , an e l ectron may ent e r the c oll ector havi Dci b 8G11 defl e ct ed aE lit t l e as as ILT e Or a s much. e 1Jiq,zd3+-A z. 'lh" i s the l engt h of Iv cos r = cos - wh ere 3 t he sl it and "d " it s di et an c e from t he s catt er ing volume. 'lfa en e == S" di ffe rence . J Cfr = I 8 ° Wni c h i s qu i 'c: e an a ppr eci able ? ur t .her wo rk may jus t i fy a c orrecti on for th is effect. v CONClU:... I ONS I t i s f ound (1) el~ctronf' That th e angular distribution function of s cattere :l in m'2 rcury i f not a mon oton ic Juncti on o f t he ang l e , but h ~; e a rni n i mum wi10 ee an0ul a :c po s iti on i E an inv er s e c ot 2ngen t fun ction of th e (2} ene ~gy of th e el ectrons . That th0 angular di s tributio n fun ction of el ectrons e c a tt e r ed i n a ir i s a mo noton ic fun ction of the an g l e wit hi n t he rs.nge i nve st iga t ed . 25 . Th.at measu r 3nHnt2 of small a rigl s 2catt e ring ( 2) in mercury a r e in qualit a t iv e a greement wi th t~e work o f oth er ob se rver ::~ . Dur ing th e courPe of t he experiment th·3 f ollowing ,phenomena were obse rv ed : 1. The apparent loss of ene r gy of t he electrons in the main be ~ m as measured by retarding :pot enti als. 2. Fo cus ing effect. 3. The "getter" ac t ion which prevented work with hydrogen. In con clus ion the author would like to express his appreciation and ind.ebtedness to Professor R• .A. · Millikan f or his ;inter es t, advice and encouragem0nt in the wo rk, t o Mr. S.e lby Skinner for his patient assistan ce in taking rea dings and to Mr. Juli us Pears on and J.,1r. William Clancy for the technical a ss istance which they so kindly contributed . APP .HlJ DIX I Let a curr en t I 0 pass through the fir st sl it s into th e chamb 0r and. denote by Ig t ile curr ent colle cted_ by the f i xe C: Far aday cage and by I e t ha t c ollected by the rotat ing cage s et aJl:l an angle e • Le t the cur1·ent i n t he main beam a t t he s c a tt ering volume be I and t he total curr ent s cattered in th.i s volume I s • The currents are dimini s hed by s catter i ng in pass i ng thr ough th e gae a cc ording t o t he well-known relation I ""/ =- -L 0 e -C(1)f 11 II where -r i s the curr ent in the beam after tra v er s ing a distan ce " 1 " in a gas at pressure "'p "when the absorpt io n co effici ent i s II II 0( • Le t (l-k 2 ) be t he fr a c t i on of th e c urr ent s ca tt 0red by s lits s 2 th e fraction s cattered by s 3 • and (1-k ~ ) Wit h these no t at i ons the follo1J1.r ing rel a tions hold: -r e_ o( JO x, .I =_Lo I <f]( =- q,? I o e -~p-x., ~ = - clcl.I J(f ( 1} a I(, ( 2) I -o.pd.J - L e Is ffa}tfl /f3 e I o e -olf' r~, r-dc.J hz. =I, i (3} ( 4) f ~) ie. th e fract i on of th e total s c at t ered c urrent t hat i e. s c a tt e red in the dir e ction e per unit s olid ang le and cfJl i s the solid angle sub t ended at t he scattering V O lume by the collect or. By u s ing equat i ons ( 2 ), ( 3) , and (4) we c an for This equation co n tains correcting factors for finite sol id ~.fl.), s catt e ring volume {o "X,) , density of gas ( p), and for di ffe rence i n pat h l eng th {c/z. - ~} . S.ubsti tu ting angle 6'x,:: ~$ s /J? ,, " where W is the widt h of slits s3 we have : wher-e: o( It i E o bvious from th e d efinition Of f(e} that: ff(&) c/SL "' "( Il.. o( ( 7) E..,,. ,, ,, This can be solved for 0( provided the constant C i s known. ii A.P.P.ENDIX II If the scattering of electrons through 8mall angles ( 2) i e properly d es crib ed by the equat i on , (9. f (&J = f(e~=O e - ea o where ( 1) eo is the mean square angle of deflection and f {e) is the probability that an electron will be deflected through an angle e per unit f' Ol i d angle in go ing a unit distance in the gas at 1 mm . of me rcury pre ss ure, we may calculate the total eca.tt e ring produced by the gas . ( 2) Comb ining (1) and ( 2 ) and notici ng that most of the contribution to the integral comee from s mall angles because of the exponential t erm we may write: rr 6., _,/ =i .'-"- 2 17 f (81 f 'l!J a() 1k s e-e;t cl& = 2Trf(S~= () But : f{S} was measured. denoted by c;z J -s;a e!tJ 4 Let this quant i ty at ?.A. . Then: Fr om the g rap h ( Fi g . 10 ) iii t:J :: 0 be If we a ss ume K b 0comes Rz.: /:t~ in equation ( 6) .Appendix I the value of -o<f' ( 61. 3 el2 -tf5) _e_ _ _ _ __ o( The ex pon ential t e r m i s practically unity s o we have: I I o(::: I 23, 3 ( 4) Thi s r esult agr ees wi th t he v:c: lue obtained by Brod e -: :;, 7 t::... e·~ 2 c,,., z in order of magn itude at least. iv