The Scattering of Electrons in Gases

THE.:jIS BY

WARR:Ell NELSON .A.::tNQUIST

UT PA~TIAI FULFILLLI:EliT OF THJ.: ~J:QUIRJ.:1,1:'1¹TTS

FOR THE DEG~EJ; OF DOCTOR Ob-"\ PHilOSOPBY

CALIFO.'..iNIA INJTITUTE OF TEC.:UWLCGY PASADENA, CALIFC1NIA

1 9 3 0

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 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 runge investigated.

{3) 'J:hat measurements of small angle scattering in mercury are in qualitative agreement with the work of other observers.

1. K.

•.r .

Oorn:pton and F. J.. i.'lohler, Bul. Nat. Research Council, Vol. 9.

2. K. '.!.1. Compton and Irving Langmuir, 'ieviews of l1Iod.

P:13sics, vol. 2.

3. C. qamsauer, Ann. d. P'.1ysik, 64!_, 513.

4. E. Brrtche, Ann. d. £hysik, 4, 387; C • . ~amsauGr u.

5.

~. Kbllath, Ann. d. Physik,

i,

^{91; T.} J. Jones, Phys. Rev. , 32, 459; R. B. Brode, Pro. '3..oy. ::)o c. ,

!§.~_, 134.

E. G. Dymond, Phys. ~ev., <;:> 0 ,1 '7, r:z.

~' :tv""'•

J . ·J. : . :ra::c:i.rT8ll, I::.:·c,. l.at. Acad. of ;.;:.ciences, 14, 564.

7. G. 2. ]arr1well, Phys. ::lev., 34, 661; Dymond and "Iatson, Pro. Roy. Soc., 122, 571.

8. J. k. :Pearson, Journ. Optical Soc., ];2, 371.

9. 1i\Thiddington, Nature, 124, 758.

10. P. L. Cor)eland, Phss. ~ev., 35, .982.

11. JI'. 1. Arnot, Pro. Ro;y. Soc., 125, 660.

12. I. Langr:rni1· ancl H. A. Jones, :Phys. ~ev., 31, 357.

·

:rflE l?ROBLEM

In the studies of the atom, as a structure made up of r:uclei and electrons, a great deal of inforrnstion l1ae been obtained from experiments a_ealing vvi th energy r oJ.ations.

Iv1odern s~~:ectroscopy has revealed an enonnou.s complexity of 'lexci ted states¹¹ to which the atom may r)e r8i:::ed, and the quantum theory has given a ver'j satisfacto::cy description of the phenomena. The problem hae also been attacked by ob-

servin~ the ener~y losses suffered by electrons in their ir.teraction v.ri 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 attack ias been to observe the effective cress-sectional area presentec 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 results are e:x:presP.ed by a qua.nti ty ^O(' w'.1ich is the area in sg. cm. presented to a moving electron 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 electron hap, collided with an a tom if it suffere an apprecieble <.;11c::.116 e in energy or momentwn.

'!'.Te shall call t~-iost: coJ.li' ~;ions in wb.ic[1 t!1e en·.;rg~' dot::f· not chant;e appreciably nelastic ^1' coll.is ions and al 1 others

change whic~ is comparable to the lowest resonance potential of ti~1e atom, and. a corres:ponciing change in momentum ·will be defined b.>1 the geometry of the apparatus in an~,r particular care.

In an,y theory prof esPing to give a complete picture of the atom as an electrical structure i t will be necef:Fary to know t'ie fie la. of force in its neighborhood. 'nle can hope to do t n.i f' only b~/ invePtigating t hese momentum tru.nsfers in detail. Because o:f' the enormous diBpari ty i.r~ masses , it is obvious that the electron alone need be followed. This problem of dete.cmininb' t he angular dif·.tribution of electrons Ecc:.ttered by atomf' has only recentls claimed attention. The early experi-

( 5) ( 0)

ments of Dymond a.nd Harnwell were in disag:ceement, but some of the difficulties of t ae problem were made clear. Both obser- vers have since reported results which seem to be in quali-

( 7)

tative agreement with the present theories. A series of experirnentf' waP. begun at t r1is Institute by Mr. John I>ear;::.on and the author in an attempt to improve t :1e tecb.nique and to mea,pure the scatterins at large angles. An account of the

first result::c obtained was given by Mr • .Pearson in his Doctor's Thesis at this Institute (1930). It if with the further

development of the experiment and the reFults obtained that this thesis will deal.

II

THE .APl?A.:tA rru s

A detailed account of t'.le design and construction of t he apparatus has been given by Mr. Pearson, but for com- pleteness t ern essential points oi' construction and further modifications are given here.

FI~~T: The scattering chamber should be free from

electric and magnetic fields. The early experimentf' already

(5),(6)

referred to showed t~at this 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 earth's magnetic field. Storage batteries furnished the current for these and a potentiometer mersured very accurately the current which neutralized the vertical component. The chamber was a cylinder 5 inches in diameter and

4t

^inches deep. A vertical cross-sectional :plan through the slits 3

1 and S;z , which were in optical alignment, is shown in Figure 1. The pumps and pressure cauge were con:nec- ted to the chamber by pyrex glasf' tubes at two diametrically opposite openings not shown in the figure.

SECOND: The source of electrons wr.s an 8 mil tungsten wire bent in the form of a narrow hairpin about as long as

the slits and heated with A.O. throu£:h an insulating trane- former. The filament was spot-we1a.ed t o leads which led through the glass stopper, Q, as shown. Later filaments were firmly fa~tened to these leads by twisting tightly and

Fig. 1.

C<?

0&V\ N

~~

I

l- L

^-

B 89 B.,,

+ ^'t' +

~

Fig. 2.

..

I

S,

. I .

1'1~ --

1

, T

:~

li)1

G,

!

L

^I

A t .

- L

£ + I I I I

I

seemed to work just as well. The emission waP controlled by manual operation of resistances in the filE.ment heating cir- cuit. The loop in the filament was supported by a nickel wire which served as the cathode lead. The inhomogeneity

because of the "I Rn drop in the filrment was thu:::: cut down and in most cases the spreed because of this effect Was less than 3 v0lts. An accelerating grid, A, of fine mei=h nickel gauze bent in the form of a semi-circle with its axis paral- lel to the slits and convex toward the filament was part of the electron ¹¹gun^1• and served to focus a large part of t he emission on the slits and thence to the chamber as a narrow beam. The stopper, Q, fitted into t he glaPs tube, T, which in turn fastened to t'.'le chamber as shown. The various ground glass joints were made vacuum tight with picf~ wax and those near t i e hot filament were water cooled. The dimensions in

the electron gun were made small so that arc discharges would not occur. Sputtered tungsten on the glass near the elec-

/~eu/s

trode/\sometimes caused insulation troubles but it was found possible to burn this out by applying high voltages.

THIRD: In order to interpret the results as single scattering it i s necessary that the mean free path of the electron shall be larger than the dimensions of the chamber • .According to the kinetic theory this is given by 4 f f times tne mean free path of the g8s atoms. Direct measurements of electronic mean free paths have given values in most cases

( 2)

larger t han this, so it can safely be talcen to calculate an

upper limit to t he pressures which csn be used. This limit is approximately 10-l mm. for the gases used. In all the

~

scattering experiments underk'ken, thiF condition was amply satisfied.

FOU~Tq: In the results of t hi s experiment first rep- orted, an anomalous loss of energy of the electronP in the main be2m w~s described. In order to i~vestiga.te this point more closely, an auxiliary grid of nickel wire was mounted between the fixed Faraday cage and the last slit. Thi s grid, which could be maintained at any desired potential, i e shown

in Fig. 2, but t hrough an error was left out of Fig. 1.

Results showed that this formed a fairly good equipotential surface.

E'IFT]: A schematic diagram of the electrical connections is shown in 1t'ig. 2. The filament, F, was maintained at a

negative potential, E, with respect to ground and the acceler- ating grid at a positive potential, A, with respect to, F. All the other potentials were with respect to ground. The

V"'

milliam~ter, M, measured the current to t he slits and chamber. Gz, is the retarding grid and its potential will be called,

Bg.

The potentials, E, A, and B9, were obtained from potentiometerE'.

fed by a D.C. mot or generator set and batteries supplied, Bp•

and Be· The galvanometer, G, had a sensitivity of 8xl0 amp. -9

per cm. and was provided with shunts in order to read larger currents. A Dol azalek electrometer shunted with a large re-

sist~nce, R, measured t he current to the rotating collector C.3. It was regularly 01)(::1·8.tcJ Bt a sensitivity of 2000 mm.

per volt. An analysis of the theory of the instrument and a

( 8)

method of obtaining greater sensitiveness i s given by Pearson. The resistanc~, R, was a narrow line of india ink drawn on drawing pap0r, boiled in par~ ffin , and sealed in a glass tube. After many trial s one was made which had a constant resistance

If 9

of 2xl0 ohms. Another resistance (2xl 0 ohms) was used to read larger curr ent s. Thus it was possible t o measure currents

_,,,.

as small as 10 amp. It is interesting t hat these high re- sistances should be as constant as t i1ey were found to be.

Even at high voltages (2000 volts) the resi stance decreased less than

!

^of its value at 1 volt. The resistance of the insulation about t he lead to collector, C..!, was measured and found to be of t he order of 10^1G ohms at 200 volts and so a correction to the el ectrometer readings because of this was not large enough to be considered.

All t he slits were 13 mm. long and 1 mm. wide except S"° 3 , whici1 were .8 mm. wide. The slits ;:) , I ' were . 1-₄¹ "

apart, S _2. were Z_<.-n _' and _. S ₃ l". The rotatin~ ₀ col lector was

mounted in a ground met 1 joint in the cover, which was sealed to the chamber with picien wax. The index, P, attaci1ed to the rotator gave the angular position on the engraved scale <9.

A two stage mercury pmnp backed by an oil pump was used to evacuate the apparrtus. Liquid air traps i solated

the pumps and Mcl eod gauge from the ci1amber. With the pumps in operation, t he pressure was lower than could be read on the gauge; i.e., less thon 10 -6 cm. of H9. Under favorable

running conditionR, the system wouJd hold ~ vacuum of

-S"

5xl0 cm. for a couple of days without pumping, shovving that it was quite tight for ² metal apparatus. Because the chamber was constructed of brass, it was impossible to bake out, but

it was found that after several days of pumping and inter- mittent bombardment with an intense electron beam, the vacuum conditions were very good.

III PROCEDURE

The value of the current necessary to neutralize the horizontal component of the earth' s magnetic field had been determined with a magnetic pendulum before the apparatus was mounted in position. It was found that comparatively

large variations in thie current had no effect on I!/, the current to t he galvanometer, s0 this adjustment was never critical. The current in these coils was set at t his value and then, with the el ectron gun furnishing a steady current to the slits, the current in t he other pair of coils was varied until the galvanometer deflection was a maximum.

Experiments showed that this current was slightly different when Bg and ^Bp were zero, thr,n when the ^pot en ti Els were ad-

justed so that only full speed electrons could rePch the collector. This difference is due to t he formation of slow speed secondaries at or nesr t he slits. The voltage, A, was then varied in order to get as intense 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 this

11rt11.

way, runs were taken obs8rVing, _{I 9 ,} as a function of Bp, or Bg, as will be described later. Also, 19 , as a function of the vertical magnetic field ^w1s investigated. This gave the , nshapen of t he main beam. In general this was not symmetri- cal about the value

(r

₉^Ji when a new filament was being tried

"'4lC,

out, :-:-nd so it was necessary to again line up the filament with the slits. This wns a slow process, but when it was

done carefully, the readings at positive and negative angles checked very well. Fortunately for the experiment a good filament would last some time.

Mercury vapor was the most convenient gas to investigate and so most of the work was done with it. A mixture of ice and water was placed about the "liquid air trapn near t he chrunber which contained a small quantity of liquid mercury. The temperFture of this ^b~)th determined the pressure of mercury vapor in the chamber when equilibrium was reached, as long as the bath was below room temperature.

The other liquid rir trap next to the McLeod gauge was con- nected to the chamber by a long narrow glass tube and conse- quently had little to do with the pressure in the chamber.

Liquid air was usually left on this trap as 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 temperature was checked with a

thermometer. The International Critical Tables gives the

-~ 0

value l.8xl0 mm. for the pressure of mercury vapor at 0 C.

which was used in the calculations.

Experiments were attempted with hydrogen but it was found impossible to keep the pressure constant long enough

to take a run because of some kind of a "gette:.cn action re- moving the gas. Electrolytic hydrogen was introcluced into

the vacuum tight apparatus through a liquid air trap and

allow'ea to come t o equilibrium. I¹hen the filament was turned on and observationsstarted. It was noticed that the pressure steadily diminished as long ^PS t he .::l :::ctron gm1 was ope·rating. In one instance the pres~u:ce fell f rom 2. 7x10 -3 cm. to

-':1

1. 2x10 cm. in half an hour and then remained constant for over three hours after t~e filament was turned off. This phenomenon was observed several times and so ^wor~ with this gas was given up. With air in t he apparatus at similar

pressures the phenomenon ^wrs not noticed.

In making scattering mea2urements the current t o the rotating collector, r.,was obs·3rvecJ. as a function of the angular position

fJ •

ExperimentF showed t irnt no current

re~'ched the collector

c

₃ in vacuurn when9was greater than 15°. Thie ab~ence of scatterin8,' at large:c angles was used as a

criterion for good vacuum conditi ons. Because of the inhomo- g0neity in t he main beam it was considered :practical to

mear:mre elastic scatte:cing only, and so the value .of Be was always adjusted t o collect the full speed electrons. At

angle~ greater t han 30° sirnultane..::,us readin.gs of Ie and

~~ were made. At times the main beam wouli vary considerably mer.

due to variable slit ecattering or filament variations, but

the ratio I~ for a given angle and prePsure was remarkably constant. In

'

genc::.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 diffused into the collector. This was conveniently done by raising the bias Be about 10 volts above E, and ob- serving the current to the collector. ^:B1or very large angles the positive ion current was often greater than the electron current.

Fluctuations in the line vol~age 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 curves showing

r

₉ as a function of Bp before the introduction of the ret1:1rd.ing grid are shown. The initial drop at small v::lues 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, to a decrease in ionization as t he electrons

I

2

0

0

P < 10-s;,.m, l!g, E • ISO V./ts.

0

Fig. 3.

0

p = 2.s xto-⁴111m 119 Vqrcr.

£ =I SO Ve Ifs.

:&'ig. 4.

were slowed up. This part of the curve wss very unsteady when gas was present, while in vacuum the curve was quite

flat. The most interesting feature is the early 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 G

2 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 thfln 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

ID

40

P <. 10·5",,,,,,.115.

£ •200 Volts.

120

Fig. 5.

of electrostatic interpenetration of fields and as the effect seemed independent of current densities, ordinary space ch£·r 3e does not help. Further, it was found that Bp could be any value between zero and about 30 vol ts po Pi ti ve with re!:'.'pect to B

9 and the retardation curves would not drop off below the bias E. But when Bp was made less positive with respect to B

9 the drop off occured below E and when Bp

=

Bg curves

eimilar to the lower curve in Fig. 5 were obtained. It should be notice6 that in this case there is supposedly no field

between collector and grid but, nevertheless, a curve simi- ( 10) lar to Fig. 3 was found. Some direct experiments ^by Copeland on "Secondary Electrons from Contaminated Surfaces¹¹ have

shown the effect of coating the collector, in this case a tungsten wire, wita an oil f ilm. This produced an insulating layer which very efficiently reflected the incident electrons when there was no field at the surface of the collector tend-

ing 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 contaminE.tes very

easily, it is easy to see ^~ow the collector at 140 volts can reflect 150 volt electrons. The incident electrons will collect on the surface of the film until the potential due to space charge becomes sufficiently negative with respect to the plate so electrons can pasP to the plate. But, as the plate is made more and more negative, a point is finally reached where ~he surface cf t hB film i s at a potential E

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 obtf"ined. Further experiments with other co2.-

lectors are being conducted to test this point more carefully.

It seems at least in 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

r

9 ^w s observed 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. The "half width" iP indicated in both cases. To obtain the resultant magnetic field in gauss, multiply the difference in abscissa of any point with the abscissa for(r,Ji by 1.10. 'rhis effect

lr14X.

has been observed in cathode ray oscillograph tubes and has been qualitatively explained as due to positive ions of low mobility, compared to electron speeds in the electron beam.

The effect varied with current density, pressure, and velocity of electrons but was not studied 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.

40

Shape of /11/ain Beam

£ "/SO//olt"s.

30

2. o. ⁰

10

c~,..r~1tt i11 lle/,,,.;,.,/tz:. Coils

- J

Fig. 6.

3. SCATTZRING CURVE3: 'J:he equation:

- _L

f ^(e} =

^{Ie sin}

^&

ff I

₉

P

^{( 1)}

was us0d in interpreting the results (appendix I) . Ie i s the scattered current reaching t he collector

c

₃ , r

9 the main beam, e the angle of setting andP the pressure. f(fJ) is the

probability per unit solid angle of an electron being ^sc~ttered through an angle

e

^{in going· 1 cm. t} nrou,:;·;;_ the gas considered, at a pressure of l mm. of mercury. 'i1he curves- show ~

f (B}

plotted in arbitrary units against

e

^{in degrees . 3ecause of}

the very small currents scattered at large 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 densities. Results in a typical case are shown in Figure 7. The smooth curve is drawn through the crosses, which were ts.ken when the focusing effect was very pronounced.. The value of

( r

₁ ^\

flntlX,

with gas was 5 time2 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 ,},

^{was in}

"'4X.

,_, .

LdllS case but 10% greater in gas than in vacuum. In plotting this

curve the "K¹¹ in the ab0ve equation hud to be adjuF:ted by a small factor to bring th8 curves together. 'i1his ''K" which includes the slit scattering and some of the geometry of the chamber VJas ^D lway s found t o vary from day to day and some- times during the progress of a run. ]:ow ever, quali tr ti ve results were all that were hoped for End it can be seen that

/0

8

6 0

; f(B)

'

4

2

so

Scattering /17 fi'!ercttr'j

_.,.

P=l.Bx/o mm.I-lg.

£ =IS-O Volts.

0

70

Fig. 7.

the two curves are almost identical. l ll of the scattering curves taken in mercury at lar~e angle~ appeared as if t hey would be qu.Lte monotonic except for a definite minimum, as

if the scattered current at a particular angle we.s entirely mi rsing. Because ~f the spre~d of electron valocitieR a~d

the finite resolvinc power of t~e slits this appears as a rather broad minimum whose l ocation is a definite function of the speed of the el ectrons. Curves were taken for

E

=

^{100 to E}

=

200 vol tf' a~1d t ':e surnms1~y of the resul tP iP given in Fig. 8. It was impossible to work with slower elec- trons b·ecause t .fiG slit scattering increc'Peli very fast for these and practically no current reached tha collectors.

;;l1ove 20C vol tP. t he minimum 'appears in t he st dep part of the curves ~nd so is smoot hed out. ~n interePting correlation

/,

1,0

Cat8,.;~ .8

E. l:il.· •. .4~4f'

/(JO 6$'. J ClfrYt!S

!2S S7 3 ..

,6 IS'O so 7 ..

17S 44 ³ "

200 ,,,.0 I "

04/()() 12S 00 l't'.r

£

Fig. 8.

the electrons in vo 1 ts. 'fi1L_-; iP someti1ing lil::--; •H'.1a t would be expected if t:1e scattering followed an inverse square law of force. .:.¹he ag:ceement should not b0 empha:=:iz ·cl too much,

ho~3ver, a2 it may b ' only fortuitoue.

Jcattering measurements et lG.:cge anelef' were taken with air a2 the scattering gas and Fig. S give2 t~e results

for E= 150 volts. It was necessary to use slightly b.ic:·her prePsures to obtain large enoug~ scattered currents to measure but the condition for single scattering was still s&tiPfiedo In contra~t to the curves for mercp.ry , t hiP one F~10¹.1.1s a

sim:yle monotonic decrease as

e

^{increases. ~:'.:.i!='} curve can be

e.'1own t o agree very closely with an inverse squa·re lmv of :force but not 0nough curveP were talcen with oir to rna~>::e thj_s ver:.; certain, r::: i t wa F thout; ht that the P-catte.ring iin•3 to a mixture of gases would be hard t o int erpret. Very little focusing effect Tuns fcunc~ ¹.ni th ~::ir.

~oward the completion of the work the large

resist~nce R (Fig. 2) developed an e.m.f . and a~ it u2uully tool:: 2evert1J. monthc fer a new resisb_rnce to become const;:;,~1t ,

it vvas decided to tr~¹ to meef'n:re the scattering at :::r'.lal l 1::..~1gl ·es

fo~ la~~e &nglee except that low filament ~nisricDs were used.

I t WO.'' founa. thc. t the v2lue of

( r

₉) did not vary a:ppreci ubly

"1tt K.

under the~'condi. tions. :''.ie rJain b earn war. m ec:.Pur ed at t be be-

s

^inning of the run ~ma_ c~ecked at t:1e end. 'I'l~e value of

k ^ff&)

wap computed a~ before and the reeults are s~own by the circles

Scatferin3 lnAir

-~ //

P = 1.3 X/O mm. rr3.

-tt(e} £,..ISO Jl"lt".s-.

·-_,, ^_

90°

~ ig. 9.

/iJ

...

0

0

/()

Scattering inhft!rc/./r.:;.

-4 /J

P =I. 8 x ltJ mm. 11.9.

£=ISO I/oil's.

Fig • . 10.

( 2)

ir.. Fig. 10. qecently La;.gmuir hus s:iown t(iot :r:.:cactically all the mecsuremJnt s of the scattering fm1ction for elect rons

em I' ir/c "I

&t sr::ic:::.11 an:;·12E' can be expresse,l b;y the

11equation:

- e2.

f ^{(fl} =} f (e~:o ^e

^{s;i '2)}

where ~ i~' t~1e "rnean equare angle of a.efl ection". Using the data obtained in thif experiment , t he constants in t his

equation can be obtained graphically b,y plot tins log

f

^(fJ}

ags inst

e

^{2 • When this}

if~

^{done and}

f(e)

^{plotted' the Sm(lO th}

curve t';1own in t'ig. 10 is obtained. The experimental :points ( 11)

fi t thiE: equation quite ¹.vell. Arnot has recently reported d.irect meapurem;;nts of the angula:c· scattering of 82 volt el ectrone in mercury. 1an5muir h.as P i1own that t hen: results

e. ^{= /.''· 30 .}

are consistent with equation (2) where ₀ ~ A value of

8

₀ =Ii:, 7 0 was fcund in the ·oresent ex·oeriments f or 150 volt

~ ( 12) ~

electron2. langmuir and Jones ho.ve meosurGd t'.le small angle scattering in mercµry Oi,' an indirect metr:od r.nd they find

J.:'.)D -- 100

~ , approximately , f0r 150 volt el actronA . 'l'he ir mathod does not distinguish sharply between losr of energ~ and

loss of for;rrnrd r:iomentum, Ci0ir.¹ever. It i~- impossible tc cc<.lcu- late t~1e value of

f(B)

from the present ex1Jeriment s because of the unc er ta in ty in

'.'K" {

^equation 1) . Ar.; was mentioned,

111{" vvould va.ry from day t o day as much as a factor 5. All

that can be said is the.t t b.e va.lue of the total :probability of scatt~ring ~ as computed from this data i s in agreamant 1Pit'.1 the value found by other. observers iri order of me.gni tude.

The cal cul a t i on is shovm in .Appendix II.

It has been objected that since the ~cattering

volume increap·as rapidly at small angl 8E, tl1e:ce is 8Jl llll-

certainty in the interpretation of the results as the main beam doeP not remain const4'nt t'.1.rouc;hout the scattering volume. Jo•vever, at t be 2.ov.r :pressures used in tL1is ex1)cri- ment, t l:.i f' is not a seriou;:-· objection becn1ee i t i € easily

"

computed that th.e change in t he main beam w'.len

e

⁼

s

^is

less t i1an

1 1s

^{in crossin3 the scat t ering vcilmne. A much more}

seri0us objection present s itself because of the length of the slits. j t these angles , an el ectron may enter the collector haviDci b8G11 deflected aE littl e as

e

^{Or as much.}

IL- Iv

e d3

as T where cos

r =

^{cos -}

1Jiq,z

+-A z. 'lh" i s the l ength

3

of

the slit and "d " its dietance from t he scattering volume.

'lfa en

e

⁼⁼

^S"

^J

^{Cfr = I 8 °}

^{Wnich i s qui 'c:e an appreciable}

difference. ?urt.her work may justify a correction for this effect.

v

CONClU:...IONS

I t i s found

(1) That the angular distribution function of

el~ctronf' scattere:l in m'2rcury i f not a monotonic Junction of t he angl e, but h~;e a rninimum wi10 ee an0ul a:c position iE an inverse cot 2ngent function of the ene~gy of the electrons.

(2} That th0 angular distribution function of el ectrons ecattered in air is a monotonic function of the angle within the rs.nge investigat ed.

( 2) Th.at measur3nHnt2 of small arigl s 2cattering in mercury are in qualitative agreement wi th t~e work of other observer::~.

During the courPe of the experiment th·3 following ,phenomena were observed:

1. The apparent loss of energy of the electrons in the main ^{be~ m} as measured by retarding :potentials.

2. Focusing effect.

3. The "getter" action which prevented work with hydrogen.

In conclusion the author would like to express his appreciation and ind.ebtedness to Professor R • .A. · Millikan for his ;interest, advice and encouragem0nt in the work, to

Mr. S.elby Skinner for his patient assistance in taking readings and to Mr. Juli us Pears on and J.,1r. William Clancy for the

technical assistance which they so kindly contributed.

Let a current ^I ₀ pass through the first slits into the chamb0r and. denote by

Ig

^{tile current collected_ by}

the f ixeC: Faraday cage and by

I e

^{t hat collected by the}

rotating cage set aJl:l an angle

e

• Let the cur1·ent in the

main beam at t he scattering volume be ^I and the total current scattered in th.is volume I s • The currents are diminished by scattering in passing through the gae according to the

I ""/

^{-C(1)f 11 II}

well-known relation =- ^-L0

e

where

- r

i s the current

" "

in the beam after traversing a distance 1 in a gas at pressure

II II

"'p"when the absorption coefficient is ^{0( •} Let (l-k₂) be t he

fract ion of the current scatt0red ^by slits ^s2 and (1-k ) _~ the fraction scattered by

s

₃ • With these notati ons the follo1J1.ring relations hold:

-r

e_

^{o( JO x,}

.I

^{=_Lo I}

~ ^{= -} cl.I <f ]( ^I

^-~p-x.,

a

cl

^{J(f I}

^=- q,?

^o

e

^I(,

-o.pd.J - L

Is ^{ffa}tfl /f}

3

e -

e

I

^-olf'

r~, r-dc.J h

o

e

z.

=I,

i

( 1}

( 2)

( 3}

( 4)

i e. scattered in the direction

e

^{per unit solid angle and}

cf Jl

is the solid angle subt ended at t he scattering ^VO lume by the collector. ^By using equations ^{(2), (3) ,} and ⁽⁴⁾ we can

for

This equation contains correcting factors for finite solid angle

~.fl.),

^{scattering volume}

{o "X,) ,

^{density of gas ( p),}

and for difference in path l ength

{c/z. - ^~} .

S.ubsti tu ting

6'x,::

_s

~$ ^,,

^"

/J? where W is the width of slits

s

₃ we have:

wher-e:

o(

It i E obvious from the definition Of

f(e}

^that:

ff(&) c/SL "' "(

Il..

o(

E..,,.

( 7)

,, ,,

This can be solved for 0( provided the constant C is known.

i i

If the scattering of electrons

( 2)

through 8mall angles i e properly described by the

f ^(&J

⁼

f(e~=O

equation,

(9.

- ea

e

^o _{( 1)}

where

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'Oli}d angle in going a unit distance in the gas at ^{1 mm.} of mercury pressure, ^we may calculate the total eca.ttering produced by the gas.

( 2)

Combining (1) and (2) and noticing that most of the contri- bution to the integral comee from small angles because of the exponential term we may write:

f ^rr

^6.,

_,/ =i

2

₁₇

f (81

^1k

s ^e-e;t cl ^&

.'-"- 'l!J a()

()

^{= 2Trf(S~=} J

⁴

^{-s;a c;z e!tJ}

But :

f{S} was

^measured.

denoted by

?.A. .

Let this quanti ty at

t:J ::

0 be

Then:

From the graph (Fig. 10)

i i i

-o<f' (

el2 -tf 5)

K b0comes

61 3

_e _ _ _ _ _ _

. o(

The exponential t erm i s practically unity so we have:

I

I I

o(:::

23, 3

( 4) This result agrees with t he v:c:lue obtained by Brode

-:::;, 7

e-²

t::... ·~ in order of magnitude at least.

c,,.,

^z

iv