Space-Distribution of X-Ray Photoelectrons Ejected from the K and L Atomic Energy-Levels Citation Anderson, Carl David (1930) Space-Distribution of X-Ray Photoelectrons Ejected from the K and L Atomic Energy-Levels. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3YRX-MS96. https://resolver.caltech.edu/CaltechETD:etd-10142002-085252 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Physics Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Awards: The Nobel Prize in Physics, 1936. Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Group: Nobel Prize Thesis Committee: Unknown, Unknown Defense Date: 1 January 1930 Additional Information: The Nobel Prize in Physics 1936 was divided equally between Victor Franz Hess "for his discovery of cosmic radiation" and Carl David Anderson "for his discovery of the positron." Record Number: CaltechETD:etd-10142002-085252 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-10142002-085252 DOI: 10.7907/3YRX-MS96 Related URLs: URL URL Type Description https://www.nobelprize.org/prizes/physics/1936/summary/ Organization Nobel Prize announcement (Physics, 1936) Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 4075 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 15 Oct 2002 Last Modified: 06 Oct 2020 01:16 Thesis Files Preview PDF - Final Version See Usage Policy. 1MB Repository Staff Only: item control page

A THESIS SPACE-DISTRIBUTION OF X-RAY PHOTOELECT'RONS EJECTED FR01li: THE K AUD 1 ATOivIIC ENERGY-LETuiJS ******* ************************************* Presented by Carl D. Anderson ********************************************* In :fulfillment o:r the for the of Doctor of California Institute of Pasadena, California 1930. 1 A 13 S T R A C T Wilson ex:pans ion-chamber was used to A O. T. the from a. gas of ic :x-rays. Distribution curves were for electrons from both the K and the L atomic A more space-distribution was found for el evels than for those from the from the L K • The distribution of the electrons from the an increase in less isotropic 1 the of the incident radiation. the s. forward momentum of radiation, For a electrons from the K energy- level was found to decrease with an increase in the binding energy of the atom. Within experimental error, how- ever, for electrons from the K energy-level, even for different binding , the average forward momentum remained the same for a given veloc average or ejection or the electron. The momentum of electrons ejected from the 1 levels was than for electrons from the K level for a velocity of ejection. The average forward momentum of the electrons ejected from the K shell was in fair accord with recent results of values of from average L th.e theory. mechanics. The observed momentum of the were sl th.an those 2 of The e from a gas by x-rays has been extensively s means of C. T .. R. invest • The by several of the distribution curve for electrons ejected from the K on the and the of the incident radiation has and are in with the expressions. obtain.ed for the ihution of Results so far electrom~ are rather meager. from the 1 Aject.ed It has been shown, however, that a more isotropic space-distribution exists in this ease. In the present work, the distrib1..1.tion of electrons from the L energy-levels is found to become less isotropic as the frequency of the incident radiation is increased. The c. T. R. Wilson expansion-chamber employed in this investigation was essentially that described by Simon and Loughridgeo insure minor refinements were effected to accu..racy in data obtained. filtering of the ion from an x.-re.y tube wo.o found to produce ro.diat ion not suff ic monochromatic. electron s made of the of photo- filtered ion shmved the track-lengths to vary by a factor of ten, indicat a variation in the initial kinetic energy of the photoelectrons " of"-/; leoo I j,1 metal I/ cc~,C~ if t'Odia/°2 u , l1 I ~ 1 / I .i= I 1/ ~ pnmary .r-ray c\:/ / ' / ;;· /eod sh~dds i 1 I ftlter ~ uIr~\ · expoosioichamber 6etvn Fig. I. Fluorescence radiator as source of monochromatic x-raye. fluorescence x-rays :rJ. A. , in line-radiation of radiator. it obtained of 55-40 necessary to • 4 I Source tube Calcite .71 A tt tt Silver .56 A tt n " " Tin radiator The relat faint K f lfo VI A izer radiator .59 A A means of a ruthenium filter. filtered out consisted of a 3 mm. thiclmess of The presence of the K fl cardboard. The filter ized ruthenium of thin between two vertical nitrate were lines of lines in the other e. cases was not of increased accuracy in the In the of the tracks some in the stereo- comparator previously described were found of the The scale and vernier for the cross-hairs were replaced by a micrometer screw and scale calibrated to read to .001 cm. much finer cross-hairs and povler lenses were , and a frame and cross-hair were substituted for the s of the two employed. in the measurements was found to be an essential i.n the of raeasureme:nt. 5 the surf ace of the in the expans cover the ch.amber will due to the scatter various of ints on these surfaces. one rotate sl on It is one of so that the cross-hairs as seen to faces. of these s1rr- trivial If tllis is not made a very errors in measurement of one of the two 0 ions were taken these reduced five fold and track measurements could be within limits of 3°. A brief discussion of the errors in measurement may not be out of a at this point. may be clas- into three groups, random errors, errors and ::.statietical :flu.ctua.ti<ms. (l) ""'~"'""''··"'•"" errors variations which occur in a cross-hair upon a nuoloi a.nd , a.nd ( 2) the offco·t of' of the gas of as well as natural initial direction deflections the the effect o:f these random errors will cancel out to some ex.tent for a final effect will, in rrumber of meam.J.rements, their , be to broaden the curve decrease its so of fine structure, • ic errors error for cross-hair is directed . . . Y".. ~T...,.,.,.r, Hs forward i.f i.t occurs in one chamber, and of car:i.era, of ncreasi its forward it occurs in the chamber. of' the is to The final effect to the average f orv.~rd a forward of a number of tracks. This error may be corrected by tVlo meas\U"ements in the the on each comparator for the second measurement. an If, however, a.p- nurnber of tracks are directed as downward in the vu·-vJ.1.G4AJ,1V~i~f this error will a very small second order effect. balance a careful of x-ray beam about can a ment are Statistical may be reduced of a are made. but 7 ult is rather hard to estimate. It is to be noted the average later is sensitive to error in measurement. of of tracks occur, L.eo COS 6 = error of cos in cos where the 2° in the e • mean an , For this reason the value of e {cbs.) listed below The be in error by other data, however, should be considerably more accurate. A comparison of the ive merits of the method as to t11at in which two cameras are their f'ocal axes to one another, is hard to make since care and pre- cision used in the construct ion 01~ the is tb.e ""''"-=-..·m..................h factor. hol'lever, The latter fewer readings to be taken for each track and can be used re a di a number of tracks. EXPERIMENTAL RESULTS The curves, or emission per unit function of the of between the and the forward direction of the direction of Vlere in a number of cases to show the AIR 72 0 ,,,\ = .708A 0" 54 i 36 - 18 o· 30• ,,..:::'. .Pt:). J'ig. Il AIR 56 - A=.56zA 42 -- 213 ~- 14 0 0 o· 0 30° 60 ° .90° Fig. III !P0° !50° /80° 8 effect of the energy level from which the electron is and also the effect of a in the of "the incident radiation • In the results • II and III are obtained respectively from measurements on 272 tracks in air air by radiation of .56 A. Each small circle the mmi.ber of electrons ejected in a 15 plotted at an interval the to the center of the interval. 5 o· 0 corresponding Points are plotted every and therefore represent overlapping intervals. In order to study the distribution where the , C H Br was introduced into 2 5 The the expansion-chamber in an atmosphere of photoelectrons were produced by radiation of .59 A, most ejected from the K shell of the bromine atom. of them .About 64 per cent of the energy of incident radiation was required to remove the electron from the 36 per cent as kinetic energy. the The could be easily secondary and distinguished from one ejected length. than the K level of bromine or from by their path levels other atoms could be and omitted CzkBr -A-.586 A 64 48 oi o· _J ------'---'--------'--=~-' 30° 60° 90• Fig. IV 120· 150° 180" --- , ------- -----,---- CH.ii 48 1--~--+----+---~1 "1 =.706' A 24 12 0 1zo· 150· J'ig. T C /-!.] I .A::.48 7 A 36 24 12 0 60° goo Fig. VI 120° 150" 180. 9 in the Thus, • their the photoeiectrons in the K of bromine were included. IV represents the distribution curve for 233 tracks of electrons as before from the K level of bromine by radiation of .59 A. For the e :from of the distribution of electrons levels, C~I was introduced into L or the charnber in an and being' of .71 A and .49 A emiss from the L levels of iodine. The results of measurements on 200 tracks formed by radiation of .71 A are shown in v. In agreement with the work of the curve is broader than that found for the K electrons indicating a more isotropic distribution. represent the The small circles as before VI represents points. the a1stribut1on or Z64 photoelectrons ejected rrom the L levels of iodine radiation of .49 A. here ia narrower than in The curve V, indicating a decrease in the ieiotropy of the distribution with an increa5e in the frequency of the incident radiation. Watson and Van den Akker have shoVJn that photoelectrons ejected from the L and L energy levels have a 11 111 ibu- tion more isotropic than those from the K and 1 energy 1 levels and Robinson and Cassie have found the relative ratio electrons was of be 2.5. to photo- 10 number of L electrons to increase with an increase 1 in the of the incident radiation. The narrower distribution curve of VI may then be the of 1 is the presence of a 1 electrons v. case for the curve of expression derived A Wentzel on the basis of mechanics, the probab ion per unit by Of a electron from the K energy level as a function of the O, between the direction of direction of the x-ray of ejection. and the for ward the velocity where v V the of the incident and h, m and c are the • The solid-line curves of • II, III and IV P{fl) with the :proper of v ,;' inserted, on a scale to conform to the the curves • of the distribution about The observed a normal to the x-ray beam may be theory in all the ways. The value of cos (!J tracks, a of the with the over to may be 11 (see (z) first order terms if {" are retained. Ta"ble cos (J {c~lc.). the values of cos (J (obs.) II ~ Gas cos e (obs.) cos tJJ (calc.) "~'''~---- K Air .71 A .182 K Air .56 A 0210 K C2H5Br .59 A .133 L CH I 3 CH I 3 .n A .230 .49 A .255 L .210 .138 The e. verage forvi.rard momentum of the K electrons for a radiation decre~ses \vith an increase of the b .......~,..........~ of the at om. error, however, fli thin K electrons of the same initial veloc forward momentum. have the sar~e average It is to be noted, moreover, that in accord with the results of , and Watson and Van den of electrons have an average than difference in behavior of the for the lower for of the electrons. and 1 electrons is more • The bi-partition at the apex of a cone ch divides the into two groups of numbers, is lectrons ( :3) • v Calculation of cos 8D shows it to be to - to a c first (s) ~ (obs.} the values of cos Table III and cos ~ (calc.). TA~L.r.; III a.as ) cos t3(obs.} K Air .71 A .242 .262 K Air .56 A .292 .294 K c2R5Br .59 A .191 .173 L ~I .71 A .174 L CH I 5 .49 A .242 v c For electrons e value of - the from 1 cos ~(calc.) it ion for seems to occur nearer 90° th.an for those from the K , in the conclusions of The ratio of the number of electrons forward of the normal to the x-ray to ·the number 13 f {4): is 1 (4) values of f f (ca.le.} (obs.) and in Table IV. TAJ3LE Level ~ Gas K f_- _:1 (calc.) •71 A 2.17 2.30 K Air .56 A 2.59 2.58 K C2H5!3r .59 A 1.74 1.70 L CH I 3 .71 A 2.00 L CI\1 I 049 A 2.30 It is to be noted that no found in the behavior of 9 for the K and L electrons. Calculations made basis of G. Schur on the mechanics expression for the ibution of the 1 of an from om: . -'-/. ,sin' B + ~v- J/n 3tJ CPS B ( I - ~'r) fcoss I+ (I -t- ' c /I ..ll_ ;(r 14 mE~an , of of Hies remain other as before. Q( e) • V and VI curves of The the proper the curves be observed on a. scale to conform to the • Calculation of the average value of cos e for L electrons (Appendix B), in the manner carried out for K electrons, leads to the resul.ts, TABLE V' Level L L /\ Gas CHIZ! Ii) .23 017 0.49 A .25 .22 the observe.- average forward momentum tions a of the than the of Cos e (ca.le.} o.n A l1ere 1s not sat The the following results, Cos e (obs.} 9 , defined as above, leads to TABLE VI Level /\ Gas (ca.le.) o.n L CH I L A 3 to 2.0 r ' and are in accord. A decrease in the of the curve for L electrons, with an increase of the incident radiation, as was found in the above, is also to be of the number of 1 11 from the The ratio electrons to the L 1 and is (s for case, to TABLE VII Gas Level L L CH I 3 CH I 3 0.71 A 67 % 0.49 A 72 % % 28 % 33 16 For the harder radiat ion of 1 1 electrons e ion curve is to be due to the a narrov:er 17 APPElIDIX A SPACE DISTRIBUTION OF ELECTRONS of the incident radiation and the atom. For electrons of not too agree to f ir~t order terms in -v but may differ in the 0 order terms. We shall consider that relation derived by G. Wentzel, and communicated in a series of in January lectures at the Norman 1930. He finds for the ity of ion of a photoelectron from the K energy-level of an atom is the where measured between direction of of the incident radiation, of ion v the vel vector of the e the between the direct ion of the x-ray the ,J the of incident and h, m constants., c are the of the 18 If the 1• f' ... ized, and consider the of space ion per unit the , e is Jin..r& P(eJ [ / - ~ CPJ& OF cose The mean value of cos t1 over all the photoelectrons to the average momentum of the ion ion of the radiation, of the as follows: be calculated .,,-- P~J cos o de ; /) in the numerator: Consider first the I, where and c I, 19 ;_(1- 1/) 11. - d ti (a-} u)+ z .;:; a ----)u.. , sub st tl -f):, I ( j+j (P:..-4 2 -r tl-f,, ti 3-aJ sub st 2 + the limits of int - /,4 I /!Ja.J ' .;lj J (a -1f/ 2 /(}-bj, z and now the Cons of denominator in ): I= .2. u - du (i-"' (ii -)u.; 4 u -it< ~ substitut , tl 2 + q,,Z 4- I j, J .:t.. tl = J ~ ,/... + z.. .s 4 2 .. (a 21 Hence a 0~ +I ()ab I CvJ --1- b 4- I where and were spin and relat other (1), electron of Since in the and various cons ion above is made icant in terms of -v , c only to first order terms in .!.. c we find 3 -1- the third and COJ & order terms, ± s c (4) BI-PARTITION' 1UTCLE The it ion e, , the the apex of a cone which divides the groups of number is defined into two (5) 22 As saw a f & Hence J;J. Jr; :: z. ·- "'"' tJ/.J PJ I) ,b .!I ,h .1 (.. ti + .., tJf.) 0 ,,- and 2.. J& """" ~ c. ~ CJ :::;:" .3 ( L: (.d.'J<J ..J (3) then becomes: = .if;_j, J..- .J,r;j; UM&,, -+ Jb ~PJ ~ 2 .;!., ' a -6 z. (d- j, c;PJ ~,/ J 23 third and and order . v t erms in - : c 3a aj, + J Q .J Gt?J ~ where /-l- z,; t) and ..2mc .z.. c Hence RATIO OF lfil.MJ3ER OF EJECT:E.'D FORWARD OF THE PLAlrE UOI-h'UAL TO THE l'ITI'.£J.BER EJECTI~D BACKWARD. X-RAY BE.Mi! TO ~1he ratio of the number of electrons normal to the :x.-ray beam to the number for ward of the j , is r J ;?_ ( 7 J, by Ft~J Je () As shown in (7) section, ,.;! . a -'7 .J where <. + 24 Hence p .ii. b < ~ ..z.. -3.(),). -1- (a - .b/ 3 and ..,,/-~! d& 2. ii ~b .l .::;. ..7 i--1 (tl -1- j,/ .7 After ,za-3-1--Ja:z.£ - ) f ::::. Sub st ! - t:l J - 3t7J~ -,6 for a and b and ,2 + .J ect third £ c DIRECTION OF GREAT".tl;ST EMISSION The of the maximum of the 0 ( 25 3 =- 0 ()J &Y>t . = -.Ye1 26 APPE1IDIX B SPACE DISTRIBUTIOU L l~LECTR OMS a theoretical G. Schur has expression the evels of an from the L of for the He finds of a from the L I where 1L represents the mean value of the binding energy of the L electron-levels, and the other remained as previously defined. If the incident radiation is unpolarized, and if we consider the of the ion per unit is by, 27 Qto) oc - .J uln B + . - r}/J1 I Jtn ~8 ( lmAN VALUE The mean value of cos .l & -1- // (l I+ COS f) 8 , for L electrons, is by, (&) CtJJ 8 ()J - - & (BJ () J& I 28 c:. f c I- d:: 114 t:/r /+ Then, 71 J& c5/M t!J G (}J" B f d j t ;rr U!r,, 0 -,,- + g_ J 2 s1>? & cos & do -1- Cl (} J; = 4/S- qec 3 & C t7S 6l dtf) 29 7T + 7T -,,j/#1 tr t1 +- Jt;r'& c,cJ &- Je J 6' c,PJ t9 -/- CJ d Therefore, J, ::::. e are where a, b, c, d, by • ( 13). OF RATIO EJECTED X-RliY TO BAC1rnARD The ratio of the number of forward of the normal to • is x-ray beam to the number • ( 15) . 30 d& dB ! )zr ;2 For L electrons, as shown d& J/>7 d& - -1- ti J . 111 + (JtJJ & J B + Cle}lj,,J& CM&c/I} Therefore, :tr" 1. dt1 = a/J + c -1- cc/+ + cd + 4 4- -1- oec. 4- and 7T dB .-2. + -ac 4 QeC - Hence eel -f- y ·where a, b, c, d, and e are 4- • ( 13). 32 c Values of for 0.71 A lZ87 0.56 A 1621 0.59 A 1555 0.49 A 16'71 :tn Terms of Atom h-t O, N {Air) Br - K level 993 356 I ?158 L 111 'tt 393 ;;.;, 33 Velocities of ion of Electrons Atom Velocity 0.71 A O, N (Air) .262 c 0.56 A o, Radiation c 0.59 A Br K .173 c 0.71 A I L c 0 I L c A 34 c. • R .. Wilson l) Proco 2) u u n Vol. 3) tr tt tt Vol. Soc. Volo 85, • 285, 87, • 277, {1912) • 192, (1923) P• 1 ·g. Bothe 4) F. • Vol. ZelL::>. f'. 4, P• 300, {1921) Volo 12' P• 117' 5) tt H 6) n u " Vol. 13, :P• 368, (1923) 7) tt tf n Vol. 1 p. 319, 8) " rt n Vol. 20, • 237, 9) tt n 10) tr ff t1 Volo 26, P• 59, 11) ft tt tt Vol. 26, P• 74, 12) tt tt tt Vol. 37, P• 547, (1926) (192~1} Vol. 23, P• 214, :Bubb • Rev. Vol. 2~, p. 13) (1925) Vol. 49, P• 14) Phil. 15) Nature, Vol. 112, p. 363, (1923} Fritz Kirchner 16) • it. • 27, • 17) • Vol. 19) • 0 ' (1 , (1926) ' {1927) • 899' ( 1927) 35 20) o Bev. v-01. 26, • 697, (1 Vol. 30, P• 22) '!ft ~- • Soc. Jour. • 13, • 679, { c. Watson . Rev. Vol. 30' • 4:79, (l 23) ft 25) Vol. 31, :P. 728, (1928) " (1 Proc .. Mat .. A.cad .. Vol .. J 3.., Watson and J. A. Van den Akker 26) Soc. Vol. 126, p. 138, (1929) Proc .. M. P. Vol. 177, 27) 28) 29) 30) '' Vol. 178, :p. '' • et Rad. Vol. 8, P• 85, {1927} Jour. d. n n n n n • Rend. Vol. 186, 31) • 169, (1923) 32) " " Vol. 187, 33) '" ff Vol. Vol. 9, . • 225, ( ?58, (1928) • 1141, (1928) 447, ( 80, :D. ) 7 4.2, { 1 35) , { • et Jour. d. E. J. Williams 35} ' Vol. 121, p. 1 37) n Vol. 38) it Vol. 123, P• 565, {1929) !59) Proc. • Vol. 121, ' P• 758, (1928) , (1 c. D. Anderson 40) ... fi4'7, Vol. {1 , p. , (1930} Vol • • 549, ( A. IL. Compton 42) • H. Cassie 43) Proc. Soc. Vol. 113, G. Wentzel 44) Zeits. f. • Vol. 43, • 296, ( 37 J. l,ili) . 291, ( 192 7) Zeits .. 'f'. A. Vle 11 en.me chani s cher A. 1.llld G. Schur 47) Arm. d. 48) Ze:i.ts. f. • Vol • ' (1930) A. . Vol. 56, p• s. E. Szczeniowski 49) • Rev. • 35, P• G. Schu..r 50) Arm. d. • Vol. • 441, { (1929)