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
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
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.
·
: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
'
'!'.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 qua
li-( 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
II
THE .APl?A.:tA
rru
s
A
detailed account of t'.le design and constructionof 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 throughthe 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
Fig. 1.
C<?
N
0&V\
I
~~
l-
L
-B 89 B.,,
+
+ 't'
~
Fig. 2.
..
I
S,
. I .
1'1~ --1
, T
:~
G,
li)1
!
L
IA
t .
-
L
£
+
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 11gun1
• 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 ele
c-/~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)
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•
-9
and Be· The galvanometer, G, had a sensitivity of 8xl0 amp.
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
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 theinsulation about t he lead to collector, C..!, was measured and
found to be of t he order of 101G 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~ col lector was
0
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
-6
the gauge; i.e., less thon 10 cm. of H9. Under favorable
-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 found in thisway, 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 sy
mmetri-cal about the value
(r
9Ji 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
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.
-3
In one instance the pres~u:ce fell f rom 2. 7x10 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 currentre~'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.
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
5
1
6
they were accepted. Atlarge 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
B
e
about 10 volts above E, andob-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 afunction 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
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.
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
[image:16.569.58.515.71.645.2]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
B
p
could be anyvalue 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 curveseimilar 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
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 ofthe 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
40
Shape of /11/ain Beam
£ "/SO//olt"s.
30
2. o. 0
10
c~,..r~1tt i11 lle/,,,.;,.,/tz:. Coils
- J
3. SCATTZRING CURVE3: 'J:he equation:
- _L
f
(e}
=
Ie sin
&
ff
I
9P
( 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 againste
in degrees . 3ecause ofthe 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
/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
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 iPgiven 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 £
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 bee.'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) "1tt K. did not vary a:ppreci ubly 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 ofk
ff&)
Scatferin3 lnAir
-~ //
P = 1.3 X/O mm. rr3.
-tt(e} £,..ISO Jl"lt".s-.
·-
_,,
_90°
/iJ
0
...
0
/()
Scattering inhft!rc/./r.:;.
-4 /J P =I. 8 x ltJ mm. 11.9. £=ISO I/oil's.
( 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 thisif
~
done andf(e)
plotted' the Sm(lO thcurve 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
0
8
0 =Ii:, 7 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.
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
isless t i1an
1
1s
in crossin3 the scat t ering vcilmne. A much more seri0us objection present s itself because of the length ofthe 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 ength3
of
the slit and "d " its dietance from t he scattering volume.
'lfa en
e
==
S"
JCfr
=
I 8 °
Wnich i s qui 'c:e an appreciabledifference. ?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
( 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
Let a current I
0 pass through the first slits
into the chamb0r and. denote by
I
g
tile current collected_ bythe f ixeC: Faraday cage and by
I
e
t hat collected by the rotating cage set aJl:l an anglee
• Let the cur1·ent in the main beam at t he scattering volume be I and the total currentscattered 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 IIwell-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 thefollo1J1.ring relations hold:
-r
e_
o( JO x,.I
=_Lo I~
= -
cl
cl.I
J(f<f ](
I=-
q,?
I
oe
-~p-x.,a
I(,-o.pd.J
-
L
Is
ffa}tfl
/f
3e
-
eI
-olf'r~,
r-dc.J
h
o
e
z.=I,
i
( 1}
( 2)
( 3}
i e. scattered in the direction
e
per unit solid angle andcf
Jl
is the solid angle subt ended at t he scattering VO lumeby 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 ting6'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.
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 andf
{e)
is the probability that an electron will be deflected through
an angle
e
per unit f'Olid angle in going a unit distance inthe 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 contr
i-bution to the integral comee from small angles because of the
exponential term we may write:
f
rr
6.,_,/ =i
2
17f
(81
1ks
e-e;t
cl
&
.'-"- 'l!J a()
()
J
c;z
=
2Trf(S~=
-s;a
e!tJ
4
But :
f{S}
was
measured.denoted by
?.A. .
Let this quanti ty at
t:J ::
0
beThen:
From the graph (Fig. 10)
-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-
2t::... ·~ in order of magnitude at least.