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A cloud chamber study of the radiations from zinc65 Parry, Kenneth John 1949

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$0 A CLOUD CHAMBER STUDY OF THE RADIATIONS FROM ZINC 6 1 by KENNETH JOHN PARRY A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS IN THE DEPARTMENT OF PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA . APRIL, 19k9 A CLOUD CHAMBER STUDY OF THE RADIATIONS FROM ZINC 6^ I ABSTRACT The primary object of t h i s research project has been to construct a Wilson cloud chamber f o r nuclear physics investigations, i n p a r t i c u l a r , suitable f o r use with the high voltage Van de Graeff generator now being erected i n the Physics "Department of the University of B r i t i s h Columbia. The chamber design i s based on drawings obtained from the Chalk River Laboratories of the National Research Council, and i s b a s i c a l l y s i m i l a r to the design developed by various people through the period 1935 - 19U0 at the Cavendish Laboratory, Cambridge. The control unit design i s e s s e n t i a l l y the same as that developed at the Chalk River Laboratories, N. R. C., and provides f o r automatic operation of the chamber. The whole u n i t has been assembled on a movable t r o l l e y so that the chamber may be used i n conjunction with the ion beam from the e l e c t r o s t a t i c generator. The whole of the machine and assembly work was carried out i n the Physics Department at U. B. C., using castings obtained from a l o c a l Vancouver firm. I t was intended had time permitted to check c a r e f u l l y the performance of the chamber by conducting a b r i e f experiment involving the photographing of numerous electron tracks. To t h i s end a source of Zinc^5 was obtained, which i s a positron emmitter, but only a very preliminary examination of the radiations from i t has so f a r been possible. ACKNOWLEDCMENTS The author wishes to express h i s appreciation to Professor J . B. Yferren f o r his guidance and assistance i n carrying out t h i s work, To the s t a f f of the Physics Department shop f o r t h e i r help i n the construction of the cloud chamber, i n p a r t i c u l a r to Mr. M. J . Symonds f o r his assistance, To Mr. J. W. Parry f o r the use of his camera while waiting f o r the Kine-Exacta f o r the cloud chamber, and, To Mr. H. D. Dendy f o r h i s assistance i n processing the pri n t s appearing i n t h i s paper. The author i s also grateful f o r the funds provided by the Defence Research Board f o r the establishment of a Nuclear Physics Techniques laboratory, thus making t h i s work possible, and f o r the information on the cloud chamber i n use at the Chalk River Laboratory supplied by the Physics Division of the National Research.Council. TABLE OF CONTENTS Page I Abstract . . . . . . . . . . 1 I I Apparatus 2.1 Construction d e t a i l s of the cloud chamber . . 2 2.2 Details of l i g h t i n g system . . h 2.3 Camera system and method of measuring curvature of tracks 6 2. h Details of cloud chamber magnets . . . . . . . 7 2.5 Cloud chamber control c i r c u i t 8 I I I Theory of cloud chamber operation • 3.1 Adiabatic expansion and supersaturation . . . 12 3.2 The condensation process 15 3.3 The difference i n the action of p o s i t i v e and negative ions upon condensations 19 • 3. U Drop growth 21 3.5 Sensitive time of a cloud chamber . . . . ... 22 3.6 Optical system of cloud chamber . . . . . . . 2k IV Operating characteristics of apparatus U'.l Procedure i n setting up the chamber 28 U.2 Some observations with the cloud chamber using anrU source . 2 9 V Measurement of the energies of /3 p a r t i c l e s by cloud chamber method . 33 PLATES To face page -I Cloud chamber apparatus . . . . Front I I Cloud chamber, f i e l d c o i l s and camera 6 • . ILLUSTRATIONS 1. Calibration of expansion r a t i o screw 2 i 2. Crossection of cloud chamber 2 3. Cloud chamber valves . . 3 k. Lens system and mounting of cloud chamber l i g h t s . . . h 5. Power supply f o r l i g h t s . . . . . . . . . . . . . . . & 6. Camera and mirror stand f> 7,. Helmholtz c o i l s • . . 7 8. Switching c i r c u i t of Helmholtz c o i l s . 7 8a Flux density of Helmholtz c o i l s 7 9. Cloud chamber control c i r c u i t ....... 8 10. Calibration of cloud chamber l i g h t delay 11 11. Variation of the saturated vapor pressure oyer a drop with the radius of a drop l6 12. Growth of a drop i n H2 and the vapour from 95% C^cjOH where percent expansion i s 12.6 . . . . . . . . • 22 13. E f f e c t of variation of expansion r a t i o 30 Ik. Effect of variation of l i g h t delay 31. 15. E f f e c t of va r i a t i o n of clearing f i e l d . 32 16. Positron tracks from Zinc65 . 3$ TABLES I Variation of supersaturation produced with several gas| and vapours l a I I Variation of ^ and S with total.pressure P j . . . . . 1$ I I I Variation of i^.and S with i n i t i a l temperature . . . . . . 1$ IV Rates of growth of drop (cm2/sec x 10°) i n the vapour from.95$ C2H5OH 22 I I APPARATUS 2.1 CONSTRUCTION DETAILS OF THE CLOUD CHAMBER The chamber i s the rubber diaphram type o r i g i n a l l y used by C. T. R. Wilson, the expansion being effected by suddenly opening the back of the diaphram to a very low pressure. The chamber i s designed to operate at pressures up to three atmospheres. A l l parts are of brass to avoid d i s t o r t i o n of the magnetic f i e l d , except f o r the c y l i n d r i c a l walls which are of ^ " thick p l e x i -glass and the §" thick glass plate top which must stand 1 5 0 0 pounds when working at 3 atmospheres i n the chamber. Twelve clamping bolts are provided f o r working at pressures greater than one atmosphere but only s i x are required when working at one atmosphere or l e s s . The base and the two clamping rings are of cast brass, the perforated plate which constitutes the bottom of the chamber was machined separately and soldered to the bottom clamping r i n g . The black velvet background was sewn to an aluminum r i n g 3/32" thick of diameter suitable to make a snug f i t with the walls of the chamber. The velvet makes an excellent background f o r photography as w e l l as providing a means of eliminating the eddy currents set up i n the chamber by the sudden expansion. Plexi-glass was used f o r the transparent walls of the chamber because a suitable glass cylinder was not available at the time. The advantage of plexi-glass when working at high pressures i s that i t w i l l not shatter. However, i t does have the tendency to lose some of i t s transparency since i t i s e a s i l y scratched and smeared by some solvents. Two black rings are painted around the walls leaving a f " clear space to a s s i s t i n collhnating the l i g h t s . Aquadag was used f o r t h i s since i t may be removed by washing with water without harming the plexi-glass cylinder. A f " aquadag rin g was painted around the periphery of the inside of the top glass plate. This i s used to provide a clearing f i e l d i n the chamber when UOO vo l t s i s applied to i t . The ring i s painted out to the edge i n two places, and an aluminum shim of about .00U" i s used to make a contact with one of these and the other serves as a means of checking the f i e l d with a v o l t meter. The diaphram presently used consists of two layers of No. 20 dental dam. This has the advantage of being very l i g h t and offering l i t t l e resistance to a change i n i t s position., The two layers are used to insure a good seal where they are clamped. A piece of 1/8" t h i c k synthetic rubber has also been used and found to be satisfactory. The expansion r a t i o , i . e . , the r a t i o of the f i n a l to the i n i t i a l volume of the chamber, may be altered by a screw extending through the base casting. This screw has eight threads per inch, one complete turn advances the screw 1/8 of an inch. There are 2J> d i v i s i o n s on the drum and the zero position corresponds to an expansion r a t i o of approximately 1.0. The expansion r a t i o has been very c a r e f u l l y measured and a graph has been drawn (Fig. l ) showing the reading of the expansion r a t i o screw and the corresponding expansion r a t i o . The vacuum tank was made from an old mercury b o t t l e . I t i s of cast i r o n and i s painted on the outside to prevent any leakage. The pipe which connects to the vacuum tank contains two valves. The f i r s t one i s the expansion valve and the second i s the b u t t e r f l y valve. The main expansion valve i s the most important working mechanism on the chamber. I t has a double function,' i . e . , i t opens the back of the diaphram to the vacuum, closing o f f the atmosphere fo r expansion, and closes o f f the vacuum tank opening, the back of the EXPANSION VALVE . BUTTERFLY VQLVE i Figure 3. Cloud chamber valves. diaphram to the atmosphere f o r compression when working with pressures below 1 atmosphere i n the chamber. The valve i s electromagnetic, the solenoid and iro n c i r c u i t being made from a Hammond 1J>8 choke. A Schrader valve serves to admit the atmospheric pressure when the chamber i s being compressed. The b u t t e r f l y valve i s used to effect a slow expansion f o r clearing the chamber of dust and o l d ions between main expansions. Slow expansions are used f o r clearing because i n t h i s case the temperature w i l l not f a l l so f a r as a f t e r a main expansion, hence the chamber w i l l recover fast e r . Figure 2 shows the cloud chamber, and the valves are shown i n F i g . 3. 2.2 DETAILS OF LIGHTING SYSTEM Ample l i g h t i s supplied f o r photography by two G.E. FT-126 repeat f l a s h lamps. The lamps are ar g o n - f i l l e d , approximately 5>" i n length and ^ " i n diameter. T h i r t y - s i x microfarads at 2000 v i s maintained continuously across the lamps i n serie s , and they are flashed when desired by discharging 8 Mfds at U00 v through the primary of a spark c o i l , the secondary of which i s clipped to the back of each lamp. This high voltage pulse ionizes the argon s u f f i c i e n t l y to permit a discharge of the 36 Mfds. The fl a s h duration i s thus very short since the resistance of the lamps when conducting i s very small. The lens system consists of two l u c i t e lenses of index of ref r a c t i o n l.Ul. An immersion lens i s fastened d i r e c t l y to each lamp and a second p i a n o - c y l i n d r i c a l lens focusses the l i g h t . The back half of the l i g h t s i s silvered. With t h i s system, advantage i s taken of the fa c t that when a source i s placed i n a c i r c u l a r l y bounded LIGHT B« 5 END V I E W LUC Ut MM.41 IMMERSION ! CONTACT Fo«T«^G6««NG PLAN VIEW Figure k\• Lens system and mounting of cloud chamber lights. FIG 5. TOWER. SUPPLV POR. LIGHTS medium of radius R and index of refraction N at a distance JJ from the center, a v i r t u a l image free of aberration i s formed at a distance NR. Sixty per cent of the l i g h t from the source i s used by t h i s method. £l} The lenses were machined as clo s e l y as possible and then polished, f i r s t with a very f i n e emery paper and f i n a l l y with j u s t "Brasso" and a piece of f l a n n e l . The whole system i s mounted i n a bakelite box with special safety connections i n s t a l l e d . The p i a n o - c y l i n d r i c a l lens may be set ahead or back to adjust the focus. Black tape was used after the adjustment was made to stop the intense l i g h t from leaking through the seams of the box, and also along the outer face of the piano-c y l i n d r i c a l lens to further collimate the l i g h t . The l i g h t boxes are set upon special mountings which allow the Helmholtz c o i l s to be i n s t a l l e d and the l i g h t s set i n between them. Details of the lens system and the lens boxes with t h e i r mountings are shown i n F i g . k. Figure 5 i s the c i r c u i t diagram of the power supply and spark c o i l trigger mechanism. Figure 6. Camera and mirror stand. Kine-Exacta Image obtained k 7" i Chamber clamping ring 2.3 CAMERA SYSTEM AND METHOD OF MEASURING CURVATURE OF TRACKS The apparatus f o r photographing the tracks stereo-graphically i s shown i n F i g . 6. I t consists of two p a r a l l e l front-surfaced mirrors fastened r i g i d l y to a frame which supports the camera mechanism 21" from the. cloud chamber. The mirrors are 6" x 12" x ^" s i l v e r e d plate glass. The camera shown i n the same figure i s a Kine-Exacta 35 mm Reflex, f i t t e d with a Zeis Tessar f :3.5 lens. Yfith t h i s arrangement 36 exposures may be taken continuously. Kodak Super XX Panchromatic recording negative i s used f o r photographing electron tracks, and orthochromatic recording negative i s used f o r heavier p a r t i c l e s . To measure ranges and angles between tracks i n nuclear disintegrations, the developed negatives are replaced i n the camera and the image re-projected through the same o p t i c a l system. This avoids any error being introduced due to the o p t i c a l parts. The curvatures of electron tracks are found by comparing the images with a series of c i r c l e s drawn on a card and placed i n a plane the same distance as the cloud chamber o r i g i n a l l y was from the camera. 2.U DETAILS OF CLOUD CHAMBER MAGNETS A very uniform magnetic f i e l d i s provided by a p a i r of Helmholtz c o i l s of 12^ 2 turns each. The mean diameter of the c o i l s i s 39.2 cm, the depth i s 8.5 cm, and they are accordingly spaced 19.6 cm apart. The f i e l d strength has been measured using a f l u x meter across a diameter and up and down the center l i n e and found to have a maximum of 59.9 gauss/amp. This compares with the calculated value of H - *^ f f o r a Helmholtz arrangement, which 10 r gives i n our case 57.2 gauss/amp. The search c o i l used to measure the f i e l d strength was 5.31 sq. cm i n area and consisted of 150 turns of 16 gauge copper wire of resistance 1.5 ohms. Brass castings were used f o r the forms, and around the inside face of each was wound a single layer of % n copper pipe through which water i s cir c u l a t e d to keep the chamber side of the c o i l s cool. This avoids unnecessary turbulence due to heat convection i n the chamber. The walls and' bottom were then completely covered with an in s u l a t i n g material, the wire wound, and f i n a l l y a lay e r of 1/8" sash cord f o r protection. The exact procedure used was as follows: 1. 0.01" s t r i p of brass wound over the copper tubing. 2. h layers of .01" empire cloth. 3. 12h2 turns of ffH Formel copper wire with 1 layer of .01" empire cloth between each layer of wire. The j o i n t s of the cloth were staggered around the periphery. (No joins were necessary i n the copper wire.) k. h layers of .01" empire cl o t h . 5. 1 layer of 1/8" sash cord. 6. 2 coats of gl y p t a l varnish. F ) G 7 . . H E I M H O L T Z . C O I L * SCflu£ ~ I M C H E S Rheostat Coil 1 n o ^ Switch T).£, Coil 2 "X-2 r Selenium rectifiers (8 plates) in series arrangement Figure 8. Switching circuit of Kelmholtz coils. 10 inches':; • i • i i .1 ; ; • • i i i . - • > 1 • 1 ' 1. i . .. i inches : Figure '8a! ,FIux i density of Helmholtz" c o i l s : ;l:i:t. A selenium r e c t i f i e r is'connected across each c o i l f o r switching the c o i l s o f f . 7flien the current i s broken, the back emf of the c o i l i s e f f e c t i v e l y short c i r c u i t e d i n t h i s manner. Figure 7 shows the d e t a i l s of the c o i l s themselves, and Fig . 8 shows the switching c i r c u i t , and F i g . 8a shows f l u x density on a diameter and v e r t i c a l l y along central axis of c o i l s . 2.$ CLOUD CHAMBER CONTROL CIRCUIT A control c i r c u i t f o r completely automatic operation of the cloud chamber was b u i l t and found to operate s a t i s f a c t o r i l y . I t consists of a series of resistance-capacity delay c i r c u i t s f i r i n g thyratrons and hence relays i n suitable sequence, and has been designed to carry out the following operations. 1. To carry out three slow cleaning expansions between main expansions. 2. To carry out a main expansion cycle as follows: (a) Helmholtz c o i l s switched on (relay l ) . (b) After an adjustable delay of from 0 to 10 sec. to give time f o r the magnetic f i e l d to b u i l d up to a steady state, the chamber expands and the e l e c t r i c clearing f i e l d i s switched o f f (relay 2). (c) Relay 3 closes a p a i r of contacts that can be used to synchronize a source or operate a shutter. A variable delay of from 0 to 0.2 sec a f t e r the closing of the expansion relay (relay 2) i s provided. (d) At a time variable from 0.015 to 0.2 sec aft e r the operation of the expansion, relay h flashes the l i g h t s . After the main expansion, the three clearing expansions are carried out and the chamber resets i t s e l f f o r another main expansion which.will be carried out automatically i f desired or w i l l remain set u n t i l the expansion button i s pressed. The relays mentioned above are shown on control c i r c u i t diagram, F i g . 9. Continuous automatic operation i s made possible by the telephone selector switch which i s driven by thyratrons 6 and 7. This p a i r of thyratrons acts as a "long period" multivibrator, i . e . , current passes f i r s t through one then through the other. As soon as the H. T. i s switched on, U00 v appear on the anodes of thyratrons 6 and 7 by contacts h and 5 of relay 7. Voltage on the g r i d of thyratron 6 i s slowly b u i l t up through i t s R.C. network and eventually f i r e s the thyratron which energizes relay 6 grounding the g r i d of thyratron 6 by contacts 3 and 2, and removing the 1;00 v o l t s by contacts h and 5. This tube continues to conduct and by so doing puts the v o l t s onto the R. C. network of thyratron 7 by contacts $ and 6 of relay 6. At the same time, contacts 1 and 2 of t h i s relay disconnect the g r i d of thyratron 7 from ground. Thyratron 7 eventually f i r e s and i n so doing energizes relay 7 removing the volts from both plates of thyratron 6 and 7 by contacts h and 5. This quenches both valves and the whole operation i s repeated. This multivibrator drives the selector switch around which stops positions 9, 10, 11 i n which contacts are made which operate clearing expansions. F i n a l l y on reaching contact 18 the chamber i s ready f o r the main expansion. The functions of the switches on the control c i r c u i t are as follows: (a) H. T. - power on or off (b) F u l l - P a r t i a l Expansion - f a s t or slow clearing expansions (c) Automatic - Manual - continuous or single main expansions (d) Press to expand (e) Lights on - o f f (f) Camera on - o f f (g) Clearing f i e l d (h) Light delay ( i ) Helmholtz c o i l s ( j ) Source delay (k) Light duration ( l ) Expanded time 16 - To be used when automatic-manual switch i s on manual - Operations w i l l be carried out with or without cloud chamber l i g h t s - Operations w i l l be carried out with or without camera - Allows a clearing f i e l d of from 0 to iiOO volts to be selected - Allows the time at which l i g h t s f l a s h to be selected from 0.015 sees to . 2 seconds a f t e r expansion. This switch has been calibrated using a triggered oscillograph. Time delays against numbers on the switch are shown i n Fig. 10. - Allows time of from . 0 to 1 0 seconds f o r the f i e l d to b u i l d up - Allows a time of from 0 to 0 . 2 sees a f t e r the main expansion i n which to either operate a camera or source shutter - This switch cannot be used with the FT - 1 2 6 f l a s h lamps. However, i t can be used to produce a longer f l a s h duration with suitable l i g h t s . - Allows time i n which chamber i s compressed to be varied from 0 to UO seconds Compressed time Allows time in which chamber is expanded to be varied from 0 to kO seconds. <0.6? - i . Figure'10 ^  Calibration of ' k cloud chamber l i g h t , delay. .: -i I l l THEORY OF CLOUD CHAMBER OPERATION 3 . 1 ADIABATIC EXPANSION AND SUPERSATURATION when the pressure on a volume of gas i s suddenly and hence ad i a b a t i c a l l y decreased, the r e s u l t i n g lower temperature may be obtained as follows: Suppose the i n i t i a l volume,pressure, and temperature of a non-condensible gas are V^, P-^ , and T^, and immediately a f t e r the expansion the volume, pressure and temperature are given by V 2, P^and • T n e n *"or 3 1 1 adiabatic expansion we have Pi v* = P 2 1 V 2 V (1) where )f i s the r a t i o of the s p e c i f i c heats of the gas, Cp/Cv. Using Boyle's Law PV = nRT, ( l ) becomes, ^ v / " 1 - T 2 1V 2 V~ 1 (2) Equation (2) allov/s a determination of the new temperature T2^ lower than the o r i g i n a l temperature T j . I f the i n i t i a l volume of the gas was saturated, a f t e r an adiabatic expansion, supersaturation w i l l e x i s t , and the degree of S can be obtained i n the following way: Let the volume of the incondensible gas be saturated with a vapour at a d e n s i t y / ^ = where M]_ i s the mass of vapour present i n V^. Then immediately af t e r expansion but before condensation the vapour density i s n M2 / 2 = . Since supersaturation produced i s the r a t i o of the density of vapour immediately after expansion before condensation to the saturated japour density a f t e r condensation, we have 3 -fa (3) As the saturated vapour pressure depends upon temperature alone, the degree of supersaturation w i l l depend upon the temperature difference produced. Supersaturation i s an unstable condition, and condensation w i l l take place i f suitable nuclei f o r condensation are present u n t i l the saturated vapour pressure at the f i n a l temperature T 2 i s reached. The temperature T2 i s s l i g h t l y higher than the temperature T2^ " e x i s t i n g immediately a f t e r expansion because some heat i s l i b e r a t e d by the condensation of the vapour. After t h i s the gas i n the chamber w i l l slowly warm up to the temperature of the room. An expression f o r the supersaturation produced by the expansion considered above as a function of expansion r a t i o V^/V^ i s found as follows: s = _ M-±-/ll m ^ cu) fit V 2 1 V 2 M 2 W J Now we have, o r i g i n a l l y , Mn P 1 V 1= -5- R T 1 ( 5 ) and a f t e r expansion, before condensation, -1 M-l T P 2 1V 2 = - i - RT2 (6) and f i n a l l y , Mo P 2 V 2 = l f R T 2 Using Equations(5)and (7) we get p l T 2 V l and by Equations (6) and (7), S ^ T 2 (9) P 2 T ? T Assuming TJ-= T ? i n Eq. (2) and substituting f o r — i n (8) , we get s A v^ Z L ! I_ A ? 1 P 2 V ^ I v 2 " P 2 \ ; = ^ < i f e > (10) Vp where ( l +£ ) i s the expansion r a t i o defined as The supersaturation expressed by (10) i s actually s l i g h t l y l e s s than that defined by (8) and (9) because of the assumption T 2"^T 2 made above. I t should also be noted that i n (10) ^ i s not the r a t i o of the s p e c i f i c heats of the incondensible gas, but of the gaseous mixture e x i s t i n g , and i s given by J f - i - P T | y g . i K T - i J where P j , Pg, P v, J^g, ^ v are the total " pressure, the pressure of the non-condensible gas and vapour, and r a t i o of s p e c i f i c heats of gas and vapour respectively. In general f o r n gases [ 2 ] i n the chamber . /£ p 7V - pf 2. ($r=i) ( n ) From Equation (11) i t i s seen that V depends upon i n i t i a l temperature (volume constant), pressure and nature of the gases, hence supersaturation depends upon these factors also. Numerical examples of the variations of these various quantities with gas mixtures commonly used are given i n Tables I , I I , I I I below: GAS VAPOUR T2°K s 1 A H 20 1.66. 252.8 15.6 A i r H 20 l.kO 267.2 4.2 co2 H20 1.31 273.U 2.8 . A i r C^OH 1.37 269.8 3.1a Table I : Showing v a r i a t i o n of supersaturation produced with several gases and vapours commonly used. Expansion r a t i o =1.25 and the i n i t i a l temperature i s 20°C. J5~ A i r and Alcohol P T 111*0 380 111* 76 36 20 10 6cm Hg 1.396 1.387 1.361 1.31*5 1.302 l . 2 l a 1.180 1.125 2.703 2.61*8 2.1*39 2.38 2.0l*9 1.706 1.1*22 1.206 A i r and Water 1.1+00 1.399 1.398 1.396 1.392 1.385 1.372 1.351* 3.018 3.017 3.016 3.016 3.011* 2.889 2.772 2.572 Table I I : Showing va r i a t i o n of V and S with t o t a l pressure P T. o V 2 I n i t i a l temperature i s 29b A, =— = 1.21 PT cm Hg 1*0°C 30° * 25° 20° 10° 111* 1.322 1.35 1.361 1.370 1.383 2.08U 2.31*5 2.U3 9 2.523 2.651* 38 1.232 1.280 1.302 1.322 1.356 1.592 1.912 2.01*9 2.156 2.355 Table I I I : Showing v a r i a t i o n of % and S with i n i t i a l temperature. Expansion r a t i o - 1.2. 3.2 THE CONDENSATION PROCESS I t i s impossible f o r condensation to occur i n the absence of suitable n u c l e i , except at extremely high supersaturation, and . the d i s t i n c t character of condensation i s due to the action of certain d e f i n i t e n u c l e i . I t i s known that the vapour pressure of a l i q u i d can be changed by curving i t s surface, convex surfaces having a higher and concave surfaces a lower vapour pressure than a plane sheet of l i q u i d at the same temperature. Hence condensation occurs more re a d i l y upon concave surface than upon a convex one, and f o r t h i s reason nucl e i of i r r e g u l a r shape act most r e a d i l y as condensation nuc l e i . (Irregular shape would most l i k e l y be porous and present a large t o t a l concave surface). This i s demonstrated . by the ease with which a cloud can be formed i n a chamber •containing d u s t - f i l l e d a i r , and the d i f f i c u l t y experienced when the a i r i s dust-free. Lord Kelvin £ 3 ] showed that the vapour pressure over a plane surface p and over a sphere pjs of radius r i s given by l n ^ = ^ (12) P ??RT where (f i s the surface tension of drop, p i s the density, R i s the gas constant and T i s absolute temperature. Figure 11 shows the values of — f o r various water drops of r a d i i r at a temperature 291°A, i . e. 18°C. The value of ?£, i . e . , the r a t i o of the vapour pressure over a drop of radius r i n equilibrium with a sheet of l i q u i d of vapour pressure p i s numerically equal to the super-saturation necessary to maintain the drop. By Equation (12) i t i s seen that to maintain a drop of radius 2 x 10 cm a supers at uration of the order of 235 i s required. A supersaturation of t h i s magnitude i s almost impossible to obtain. I f a drop should e x i s t of t h i s radius i n ordinary degrees of supersaturation, i t would probably immediately evaporate. The curve of F i g . 11 indicates that as the drop radius increases the supersaturation required decreases, hence the higher the supersaturation the smaller i s the nucleus required upon which a drop w i l l form. Experimentally, f i n e drops are formed on molecular aggregates as nuclei f o r extremely high supersaturations of the order of 8, produced when the expansion ra t i o i s larger than 1.38. This.was f i r s t demonstrated by Wilson {h\ i n 1897. On the other hand very small supersaturation of the order of 1.2 are necessary to form condensation on dust p a r t i c l e s as nuclei since the size of a dust p a r t i c l e varies from 10"^ to 1 0 ~ 6 cm, I I I I « I I 1 I I . I I . I.,.-. I I t \ I I t I Uncharged drop " : Charged drop . - r Pr/p • r - Pr/p 1x10"^ 1.001 l . 9 5 x l o _ y i o " i y 1x10-5 1.01 3.9x10-8 1.00 l x l O " 6 1.12 U.25x]0~8 2.00 2 . 3 x l O - 7 1.60 5 .8xio~ 8 U.op 1.9x10" 7 1.78 5-85x]0"8" h.oQ 1.6xlO~ 7 2.00' 6.U5xL0- i 8 U.oo l x l O - 7 • 3.00 8.8QclO- 8 3.36 2.8xlO~ 8 U.oo 15.6XX)-8 • 2,09 6.8x10" 8 5.oo 23.Uxlcr 8 1.6a • 5.6x10- 8 7.00 ii.7xlO" 8 10.0 2 x l O - 8 ' 235.0 l o g 1 0 r (cm) I 7 Figure 11. Variation of the saturated vapor pressure over a drop with-the radius of the drop.. • ,-''••" thus presenting a large surface to condensation. This may be seen i n F i g . 11. After condensation has taken place, the drops yd.ll Pr grow rapidly to the v i s i b l e size reducing the supersaturation to unity. R. Von Helmholtz Q>) was one of the f i r s t to observe condensation with ions as n u c l e i , during the time when condensation was thought to occur only on dust p a r t i c l e s . C. T. R. Wilson [6] demonstrated that condensation on ions as condensation n u c l e i was possible, confirming S i r J. J . Thompson's [7] theory, which i s discussed below. Consider a drop of radius r carrying a charge e. The potential energy of t h i s drop w i l l then be J e ^ / k r , where k i s the s p e c i f i c inductive capacity of the d i e l e c t r i c surrounding the drop. Should the drop evaporate, i t s radius would diminish while the charge remains the same, hence the potential energy would increase. On the other hand the po t e n t i a l energy of an uncharged drop lt7&*(f, due to i t s surface tension (fwould decrease (provided the surface tension remained constant) as r decreased. Since i t would require work to evaporate a charged drop, a charged drop w i l l be i n equilibrium when the vapour pressure around i t would not be s u f f i c i e n t to prevent the evaporation of an uncharged one. Thomson showed that i n the case of a charged drop Equation (12) becomes _ P r M , 20- e 2 . . . . 10 T " w>{ — ' a s ? ) : ( u ) which reduces to Equation (12) i f e = 0. Equation (13) shows that a charged drop w i l l grow u n t i l - unity, or ( - e^/S^kr^) s 0, 2 1^/3 '-'< d r c r r " ~ ( 1 U ) The graph of Equation (13) i s shown i n F i g . 11 with that of Equation (12) f o r comparison. Equation (lU) defines the c r i t i c a l radius r c , determining the size of the drop when p r - p, or when the space around the drop i s just saturated. If we use £ = 76 dynes/cm (true for thick water films), for singly charged ion e = U.7 x lO'^esu, k = 1 for air , then r c = ( )V3, h x ^ - B ^ Thus i n saturated air each ion would be surrounded by a drop of water of radius h x 10_^cm. (Limit of unaided vision i s around 5 x 10"^ cm.) Now i f we set x = then Equation (13) becomes 2J* S i i & . i a ^ ) ci5) 2oM p Using r c s h x 10-^cm, R • 8.3 x lo7ergs/mole°K, for water at 10°C, i.e., T = 283,/'= l,cf = 76 dynes /cm, and M = 18 gms, we have .33 hi - = x ( l - x 3) (16) P (Note: If the expansion ratio i s set at 1.2 and the chamber i n i t i a l l y at 20°C, then resulting temperature due to sudden expansion would be about 10°C, as i s seen from Equation (2). ) Equation (l£) allows one to determine the size of drop corresponding to any supersaturation, and Equation (16) shows that in a space far from saturated, where a drop could not exist on an uncharged particle, drops of a f i n i t e size w i l l exist with ions as condensation centres. It can also be seen that to reduce the drop r x* ID to half the c r i t i c a l radius (x = — • = 2, .331n — = - l U , p r s r c P hence - 2.5>6 x 10~^ 8) i t would be necessary to produce a relative humidity of 2.5 x 10"^^. Hence i t can be seen that, i n any a i r space where ions are present small drops w i l l also be present. Now as the radius of a drop, r, increases from 0 to r c i n f i n i t y x = — goes from i n f i n i t y to zero and at both of these limits the right hand side of Equation (16) vanishes, and reaches where ^  (x ["l - x^J ) - 0, or when k x 3 = 1, i.e . , d a maximum when x • ( 4 ) " ^ «= -.629. Supersaturation corresponding to t h i s value of x would be 4.1 The above calculation indicates that a supersaturation of the order of k w i l l result i n the best development of drops formed upon ions, and hence best tracks. 3.3 THE DIFFERENCE IN THE ACTION OF POSITIVE AND NEGATIVE IONS UPON CONDENSATIONS From the simple theory given i n section 3.2 there would be no difference i n the degree of supersaturation required to form droplets on positive or negative ions. In practice i t i s found that the splashing of water drops through a i r produces a lay e r of charge on the surface of the drop, and a layer of the opposite charge i n the gas surrounding the drop. I f such charged layers existed around the drops formed on ions, the a b i l i t y of p o s i t i v e and negative ions to produce condensation would be influenced. / \ 2(J From Equation ( 1 3 ) i s the pressure at the surface e 2 of the drop due to surface tension and Q^^, i s the tension due to the e l e c t r i c charge, i . e . , the e l e c t r i c tension i s given by kE 2 e where E = — S h o u l d there be a double layer of charge at 87T kr* the surface of the drop, then the expression f o r the e l e c t r i c tension w i l l be dif f e r e n t . This theory was f i r s t b u i l t up by S i r J . J . Thomson J.&3 as given below. Assume V to be the potential difference between these k V 2 charged layers, then f o r a non-ion drop a tension given by would e x i s t , so that Equation (12) would become pr M ( ?£ _ k X ! ) p ~ Wty> K r 85fd? ;  Should the drop have formed on an ion of charge e we would have for the drop, from Equation (13), _ p r M ..2<f k , V e >2 ,, ^ F ^ ^ - r ^ d 4 ^ 3 ) } ( 1 8 ) Expanding the term i n the brackets we then have, p = RT/O V r " e l d 2 " Hifdr^ " Blkr* J U 9 J which shows the effect of the charged surfaces and the charge V e carried by the ion. Equation (19) has the term 7 the sign of which i s determined by the direction of the f i e l d due to the charged surfaces and the sign of the ion charge. If this term i s positive then the right hand side of(1?) i s less by this amount and less supersaturation would be required to maintain a given drop radius, but i f this term i s negative more supersaturation would be required. Thus the sign of the term i s determined by the sign of the charged ion and the direction of the f i e l d which i s produced by the charged surfaces. In the case of the electrification of water drops, the water surface i s negative and the a i r surface positive, hence the direction of the f i e l d i s into the drop. This i s the same direction as the f i e l d produced when the drop has formed upon a negative ion, V e hence i s positive. Thus where the condensible gas i s water IflTdr2 vapour a negative ion w i l l act as a better condensation centre,i.e., need a lower expansion ratio than a positive ion. In some liquids, for example alcohols, the el e c t r i f i c a t i o n produced i s positive on the drop surface and negative i n the a i r layer around i t . In such a case the positive ion would act as a better condensation centre than a negative ion. W. E. Hazen [9} has shown, by photographing the drops formed on positive and negative ions separated by a strong electric f i e l d , that condensation actually does favour negative ions i n the case of water drops. This effect has been used by R. B. Brode to measure the s p e c i f i c i o n i z a t i o n of cosmic ray p a r t i c l e s . Errors have arisen i n cloud chamber work involving drop counting to measure the s p e c i f i c i o n i z a t i o n of an i o n i z i n g p a r t i c l e from incorrect adjustment of the expansion r a t i o giving r i s e to conden-sation on droplets of one sign only. 3.U DROP GROWTH In order to have photographs of undistorted cloud tracks, the exposure must be made as soon as possible a f t e r the expansion i s completed. The f a l l of drops, the swirling motion of the gas, a i r currents set up by heat convection into the chamber, and other effects inherent i n the design of the expansion chamber make i t impossible o r d i n a r i l y to photograph tracks undistorted l a t e r than ^ second a f t e r the expansion i s completed. On the other hand, an exposure should not be taken too early a f t e r an expansion, i . e . , time must be allowed f o r the drops to grow to v i s i b l e s i z e . R. M. Langer [ l l j and W. E. Hazen [ 1 2 ] have succeeded i n deducing from t h e o r e t i c a l considerations the rate at which a drop w i l l grow. Their calculations are based on the latent heat cbn. o clT equation A(g^) = Uflr^k (g-) and the d i f f u s i o n equation * l = U n r 2 D ( 3£ ) where A i s the l a t e n t heat of evaporation, m the dt dr mass, r the radius of the drop, and and ^  are the temperature gradient and density gradient within the drop respectively. Hazen has determined the rate of growth of the drop by photographing the motion of the drops i n the gr a v i t a t i o n a l f i e l d , and found a reasonable agreement with the values calculated from the above equations. Some of the re s u l t s of Hazen's work are shown i n Table IV where the rate of growth i n a 95% C^^OH vapour, using chamber pressures between 1 . 1 and 1 . 2 atmospheres, i s shown f o r N 2, H2, and He, and i s compared with the values obtained by calc u l a t i o n . These results indicate that the surface area of the drop increases l i n e a r l y with time, which can be seen most c l e a r l y from F i g . 12 also from Hazen. Permanent gas N2 H 2 He Percent Expansion 15.2 16.8 11*. 6 16.9 10 Experimental result 5.25 5.95 17.3 18.9 17 Theoretical re s u l t 5.2 5.65 27.5 31 Table IV. Rates of growth of drop ( cm 2/ s e c x 1 ° ) i n t h e vapour from 9$% C2H£0H. Figure 12.. Growth of a drop i n H2 and the vapour from 95$ C2HCJOH where percent expansion i s 12.6. 3.5 THE SENSITIVE TIME OF A CLOUD CHAMBER In many cloud chamber experiments i t i s necessary to know the sensitive time of the chamber, i . e . , the length of time i n which supersaturation remains s u f f i c i e n t to cause condensation on ions after the expansion has been completed. The sensitive time may be determined experimentally by observing the tracks formed on ions l e f t by p a r t i c l e s which are projected into the chamber at various times a f t e r the expansion. W. E . H a z e n h a s m e a s u r e d t h e s e n s i t i v e t i m e b y p e r i o d i c a l l y p h o t o g r a p h i n g a n e l e c t r o n s o u r c e t h a t was moved t h r o u g h t h e chamber a f t e r e x p a n s i o n . The t i m e i n w h i c h t h e c h a m b e r was s e n s i t i v e was d e t e r m i n e d b y e x a m i n a t i o n o f t h e d e n s i t y o f t h e t r a c k s f o r m e d a t t h e d i f f e r e n t t i m e i n t e r v a l s . E . J . W i l l i a m s [l3j h a s b e e n s u c c e s s f u l i n d e r i v i n g a r e l a t i o n f o r t h e s e n s i t i v e t i m e o f a c l o u d c h a m b e r b y a c o n s i d e r a t i o n o f t h e r a t e a t w h i c h h e a t moves i n t o t h e c h a m b e r . T h i s e q u a t i o n i s T - l T T F ^ < I >2<T-'>2 . ( 2 0 ) w h e r e t i s t h e s e n s i t i v e t i m e o f a chamber w i t h volume. V a n d w a l l a r e a S . The d e n s i t y o f t h e g a s , i t s t h e r m a l c o n d u c t i v i t y a n d s p e c i f i c h e a t a t c o n s t a n t p r e s s u r e a r e r e s p e c t i v e l y P , K , s , a n d y i s t h e r a t i o o f t h e s p e c i f i c h e a t s . The p e r c e n t e x p a n s i o n j u s t n e c e s s a r y t o p r o d u c e t r a c k s i s £ a n d b€ i s t h e maximum i n c r e a s e i n t h e p e r c e n t e x p a n s i o n w i t h o u t p r o d u c i n g a f o g . E q u a t i o n (20) assumes a n e x p a n s i o n t i m e w h i c h i s s m a l l c o m p a r e d t o t h e s e n s i t i v e t i m e . H o w e v e r , W i l l i a m s showed t h a t i f t h e e x p a n s i o n t i m e i s " n o t t o o many t i m e s " g r e a t e r t h a n t h e s e n s i t i v e t i m e , t h e n t h e s e n s i t i v e t i m e may be i n c r e a s e d , a n d w i l l be g i v e n a p p r o x i m a t e l y b y ? + (2t ) w h e r e X i s g i v e n b y E q u a t i o n (20) a n d t i s t h e t i m e o f t h e e x p a n s i o n . I n g e n e r a l , t h e r e f o r e , one may i n c r e a s e t h e s e n s i t i v e t i m e o f a chamber b y i n c r e a s i n g ( a ) t h e r a t i o o f v o l u m e t o w a l l a r e a ( b ) t h e . d e n s i t y o f t h e g a s i n t h e c h a m b e r b y i n c r e a s i n g t h e p r e s s u r e .(c) the expansion r a t i o ;(d) the time of expansion. For computing the source strength needed to obtain tracks a knowledge of the sensitive time i s obviously es s e n t i a l . For t h i s chamber the sensitive time i s about l/f>0 of a second, hence a source of i o n i z i n g p a r t i c l e s should project i n t o the . v i s i b l e region of the chamber approximately 10 p a r t i c l e s within t h i s time to obtain a useful picture. The source a c t i v i t y necessary f o r t h i s i s given by A - —k__ZI ^ !L micro-curies (3.71 xlO»)T 0 where N i s the number of tracks desired, i s the sensitive time and 0 i s the s o l i d angle subtended by the source i n the v i s i b l e region of the chamber, for . example, when N = 10, 0 = ^, and f = then source strength necessary would be A = 0.8 micro-curies. 3.6 OPTICAL SYSTEM OF CLOUD CHAMBER The low i o n i z i n g a b i l i t y of some radioactive p a r t i c l e s , such as electrons, makes t h e i r tracks very d i f f i c u l t to photograph. To obtain good clear pictures of these tracks adequate l i g h t must be scattered from the cloud drops to the camera system. This illumination of the image i n the camera can be increased by making certain adjustments on the camera. The theory of these adjustments i s considered below. The amount of l i g h t which passes through a lens from an object at a distance u i s proportional to I j the i l l u m i n a t i o n of the 2 object,- the s o l i d angle subtended by the lens (where a i s the diameter of the lens aperture); and the area of the object surface A. I f the area of the image i s A-'- then the i l l u m i n a t i o n on unit area of the image i s IA1 = j j ^ j I assuming no l i g h t i s l o s t by r e f l e c t i o n . The magnification factor m i s given by m A1 ^ = - = ( j ) 2 where v i s the image distance. The r e l a t i v e apertvire F or f-number of the lens system i s given by f = -, where F i s the f o c a l length of the lens system. Introducing both of these factors we then have f o r the illu m i n a t i o n on unit area of the image T , * ? * L (21) Now from the lens formula F = we have v = F ( 1 + m), hence u+v ( 2 1 ) becomes . " ( 2 2 ) From ( 2 2 ) i t would appear that i n order to increase the i l l u m i n a t i o n on the image we should decrease the f-number of the lens, i . e . , we should increase the aperture. However, t h i s i s l i m i t e d by the desired depth of focus as can be seen from the following equation. The depth of focus u i s given by A u = 2 A f 2 ( ^ E ) 2 ( 2 3 ) This equation permits, a calculation of the f-number which should be set on the camera to obtain best conditions of i l l u m i n a t i o n of the image f o r a given depth of focus and magnification. The substitution of the r e l a t i v e aperture set by Equation (23 ) i n t o Equation ( 2 2 ) shows that il l u m i n a t i o n i s l i m i t e d by the magnification f o r a given depth of focus, i . e . , * • £*\ - <2W Thus so f a r as il l u m i n a t i o n i n t e n s i t y i s concerned reducing m and hence f from (23 ) increases the l i g h t reaching the f i l m . However, • the magnification can not be reduced i n d e f i n i t e l y due to the resolving power of the f i l m emulsion used. For a given f i l m there i s a l i m i t to the smallness of the magnification used and hence to the smallness of the f number used ( i . e . to the largeness of the aperture used). The breadth of the image track i s equal to the sum of the width of d i f f r a c t i o n pattern due to a l i n e source and the width of the. geometrical image of the track. The width of the d i f f r a c t i o n 2vA pattern due to a l i n e source i s given by — — which upon substitution of v - F(l+m) becomes 2 F A o r 2fA(l-*m), and the width of the - a geometrical image i s simply DQm where DQ i s the actual width of the track. Therefore i f D i s the breadth of the image track we have D = 2f^(l*m) + D m,' and substituting f o r f from Equation (23) we have D = m | (2AAu^ 4 D0)j (25) For Kodak Super XX Panchromatic f i l m the resolving power i s 90 l i n e s per mm so that D can be as small as 1/900 * .001 cm. The width D 0 of electron tracks i s approximately .01 cm, the wave length of l i g h t from the argon lamps i s ~ U x 10"^cm, and the depth of focus used i n the chamber i s 1 cm. Hence by Equation (25) the smallest magnification that i s useful i n t h i s case i s m = approx-imately. The r e l a t i v e aperture i s calculated by substitution of these conditions into Equation (23) and found to be f:5.5. I t has been shown experimentally ^ l i * ] that f o r water drops the i n t e n s i t y scattered at 20° to the beam of l i g h t i s about 100 times as great as when the angle i s 90°. Thus the contrast of the image on the negative may be increased by: (a) using a stronger l i g h t source (b) i n c l i n i n g the axis of the camera so that a smaller angle exists between the l i g h t source and the camera axis (c) using the smallest magnification compatible with the resolving power of the f i l m emulsion (d) using a small depth of focus having r e l a t i v e aperture set by equation (23) (e) using fastest possible f i l m compatible with f i n e s t grain s i z e . IV • OPERATING CHARACTERISTICS OF APPARATUS U.l PROCEDURE IN SETTING UP THE CHAMBER T/ftien the apparatus i s being re-assembled, great care must be taken to keep a l l foreign materials out and to make the chamber vacuum t i g h t . The chamber should not o r d i n a r i l y be stripped beyond the bottom plate. However, when i t i s necessary to inspect or replace the diaphram, the bottom plate may be removed by withdrawing the s i x clamping bolts and disconnecting the vacuum l i n e at the f i r s t rubber hose connection d i r e c t l y below the chamber. The bottom plate can then be l i f t e d straight up u n t i l the vacuum l i n e i s clear. Should t h i s be done, the opportunity should be taken to inspect the f i l l i n g pipe where i t i s sealed into the plate since i t i s not possible to wax t h i s j o i n t properly a f t e r the plate i s on. Af t e r a l l the parts have been c a r e f u l l y cleaned with suitable solvents, the assembly i s carried out as quickly as possible. The clamping bolts are tightened i n pairs working across the diameter rather than i n succession around the r i n g to avoid unnecessary strains being put on the top glass plate and the cylinder. The chamber i s then pumped down and sealed o f f to check f o r leaks by use of the vacuum gauge. I f t h i s gauge shows no appreciable change i n pressure f o r a period of roughly two hours, vacuum conditions may be considered satisfactory. I t i s absolutely essential f o r a l l leaks to be eliminated since these give r i s e to eddies within the chamber and so to d i s t o r t i o n of the tracks. Dust-free a i r i s then admitted through the glass wool f i l t e r column to bring the pressure up to the required value, about UO cms pressure i s convenient f o r most purposes. The required l i q u i d i s next admitted by the f i l l i n g tube, and the chamber sealed o f f by a vacuum tap provided at the bottom of the f i l l i n g tube. The volume of the l i q u i d admitted i s just i n excess of the amount necessary to saturate the gas i n the chamber since too much l i q u i d w i l l render the velvet a poor background f o r photography. The chamber should then be allowed to run continuously at an expansion r a t i o just below the l i m i t at which a " d r i z z l e " of f i n e drops would set i n i f the chamber were free from dust p a r t i c l e s and ions. The expanded time should be set at about 30 seconds during t h i s period so that cloud drops formed on dust p a r t i c l e s w i l l have time to s e t t l e before the chamber i s re-compressed, Following t h i s "cleaning" phase the expansion r a t i o should be reduced slowly u n t i l the desired conditions e x i s t within the chamber. To prevent any moisture from condensing on the top glass plate or on the chamber walls while operating the chamber i t was found necessary to keep the base casting about 1°C below the temperature of the glass plate and the wa l l s . This was done by c i r c u l a t i n g cold water through a rubber hose which made two turns around the base casting. U.2 SOME OBSERVATIONS WITH THE CLOUD CHAMBER USING AN e( SOURCE The following series of pictures were taken using a bellows camera and a 3^" x hi" Kodak Super XX Panchromatic f i l m pack. The d. tracks are from a polonium source about 1 m i l l i c u r i e i n strength. The other source d i r e c t l y opposite i s Zinc^5 and i s approximately the same strength as the polonium. The non-condensible gas i n the chamber i s a i r , and the vapour consists of 2 parts of 20 ethyl alcohol to 1 part of water. Series A : These pictures show the effect of varying the expansion ratio from the ion limit to the cloud limit. A clearing f i e l d of hOO v i s used between expansions. The exposures are made 0.115> seconds after the expansion. The expansion ratios are indicated beside each picture. Pressure i n the chamber when compressed i n each case i s g atmosphere. F1C-. 15 E F f e c r OF VARIATION »F £*P*»iMSiotf RATIO, 1-145 JITS' _ F|0_ I 5 _ ( ( O H T ' D . ) 3 1 Series B; These pictures show the effect of varying the light delay from 0.0a seconds after the expansion to 0.115 seconds. The expansion ratio i s 1.155 i n each case and the clearing f i e l d used between main expansions i s hOO volts. Pressure i n chamber when compressed i s j atmosphere. Series G; Here the source i s polonium of strength approximately 1/20 of 1 m i l l i - c u r i e . The expansion ratio i s 1.15 and the ligh t delay i s 0.115 seconds. The pressure of the compressed chamber is 2/3 atmosphere. These pictures show the effect of varying the clearing f i e l d from 0 to hOO v. V MEASUREMENT OF THE ENERGIES OF/9 PARTICLES BY CLOUD CHAMBER METHOD The cloud chamber has been extensively used to study the /Sray spectrum of radioactive elements. This i s evident from the Seaborg 15 table of isotopes where the maximum energy of approximately one-quarter of the/9 emitters i s shown as having been measured by use of the cloud chamber» The cloud chamber does, however, have several disadvantages. These are: (a) A large number of tracks must be examined to get good s t a t i s t i c s f o r the spectrum, and t h i s requires a great deal of time. (b) I t i s impossible to eliminate completely the secondary electrons produced either from the gas i n the chamber or from the walls by the action of )( rays which usually accompany^ rays, or from the primary./? rays themselves, and (c) The^# rays are scattered frequently by the gas causing errors i n the measurements of curvatures. H. A. Bethe £l6} has shown that the error due to multiple scattering may be considerably reduced by using a gas i n the chamber of low atomic number, i . e . , hydrogen or helium. In spite of these objections the method has been widely used and i s s t i l l s p e c i a l l y useful f o r spectrum measurements on gaseous radioactive substances. The energy of the p a r t i c l e i s measured d i r e c t l y by observing i t s deflection i n a magnetic f i e l d perpendicular to the direction of motion of the p a r t i c l e s . The radius of curvature of a p a r t i c l e i s given by ar = =£ (*> . where H i s the magnetic f i e l d strength i n gauss, e i s the e l e c t r o -s t a t i c charge of the p a r t i c l e of mass m, andp i s the radius of curvature i n centimeters. From (26) we may write, p . = IJT (T + 2 m 0c 2) (27) tint cj/ where p i s momentum given by' p = 5 ^ (28) c In Equation (27) T i s the k i n e t i c energy i n ergs r e l a t i v i s t i c a l l y expressed as T = mc2 - m 0c 2 p o raQc^ 2 - moc'-ft? where m0 i s the rest mass of the p a r t i c l e . Hence from (27) and (28) we may write He^= !^T(T+2m0c2) (29) and solving t h i s f o r the k i n e t i c energy, we get 1' -°2[(1 " 4 (30) The maximum energy of t h e j $ p a r t i c l e s from Z i n c 6 ^ i s l i s t e d i n the Seaborg tables as 0.1+ Mev, hence i t can be seen from Equation (30) that i n a f i e l d of 1;00 gauss the maximum radius of curvature ^ > o f the p a r t i c l e would be 6 . I 4 . cm approximately. The shape of thejfy spectrum i s found by p l o t t i n g the measurement of the energy of the p a r t i c l e s from the cloud chamber photographs against the number of p a r t i c l e s of the same energy. The end point of the^ spectrum i s determined by use of the Fermi I—T~~ theory, by p l o t t i n g / -y ^- against the corresponding energy, 7 (w^-l^'w where w i s t o t a l energy of the electron i n 'mc2* uni t s . I t i s of course necessary to use a t h i n source to avoid any disturbance i n the d i s t r i b u t i o n function due to s e l f absorption of the softer electrons within the source. In addition to studying the positron spectrum i t was hoped to obtain further evidence of the annihilation of the positron 35 while i n motion, by finding the occasional track which stopped while the positron was obviously s t i l l well above thermal energies. Also i t was hoped to obtain some further stat i s t i c s of positron-electron collisions as Mgr. Ho Zah-Hei fl?} has described, and to compare these with trie theory piven by Bhabha . In this way, and as far as present theory indicates, only in this way can one distinguish between a positron as a hole or negative energy state of an electron or a positron as an independent positively charged r>article i n a state of -positive energy whose behavior i s described by the Dirac equation. In conclusion, the following photographs are included to show the stage which has been reached in photographing electron tracks to date. The camera and film used i s the same as that described in Section IV. The Kine Exacta camera now being set up w i l l no doubt give better definition of the electrons from the zinc source mainly because of the reduced image size. Fl<rl(». POSITRON ^dftcui Ftov\ £N REFERENCES 1. E. F. Lofgren, E. P. Ney and F. Oppenheimer, Rev. Sci. Inst. 19, h; 271, 191+8. 2. F. Richarz, Ann. Physik 19, 1*57, 1908 3. Poynting and Thomson, The Properties of Matter, p. 166, 1907. h. C. T. R. Wilson, P h i l . Trans. 189, 265, 1897. 5. R. v. Helmholtz, Wied, Ann. 32, 1, 1887. 6. Ibid, p. 6. 7. J. J. Thomson, Conduction of E l e c t r i c i t y through Gases, p. 11*9, • 1903. 8. J . J . Thomson & G. P. Thomson, Conduction of E l e c t r i c i t y through Gases, 1928. 9. W. E. Hazen, Phys. Rev. 65, 259, 19hh. 10. R. B. Brode, Rev. Mod. Phys. U , 222, 1939. 11. R. M. Langer, Phys. Rev. 56, p. 851, -1938. 12. W. E. Hazen, Rev. Sci. Inst. 13, 21*7, 19l*2. 13. E. J. Williams, Proc. Camb. Phil. Soc. 35, 512, 1939. 11*. C. G. Webb, Phi l . Mag. 19 , 927, 1935. 15. G. T. Seaborg, Rev. Mod. Phys. 16, 1, 191*1*. 16. H. A. Bethe, Phys. Rev. 69, 689, 19l*6. 17. Mrs. Ho Zah-Wei, Phys. Rev. 70, 221*, 19l*6. 18. H. J. Bhabha, Proc. Roy. Soc. 195, 151*, 1936. BIBLIOGRAPHY Bethe, H. A., "Influence of multiple scattering on curvature measurements." Phys. Rev. 69, 19U6. Bhabha, H. J., Proc. Roy. Soc. 195, 1936. Brode, R. B., "Specific ionization of high speed particles." Rev. Mod. Phys. 11, 1939. Das Gupta, N. N., and Ghosh, S. K., "A report on the Wilson cloud chamber and i t s application i n physics." Rev. Mod. Phys. l8,19U6. Hazen, W. E., "Average energy loss of mesotrons i n a i r . " Phys. Rev. 65, 19kh. Hazen, W. E., "Some operating characteristics of the Wilson cloud chamber." Rev. Sci. Inst. 13, 19U2. Helmholtz, R. v., Wied. Ann. 32, 1887. Mrs. Ho Zah-Wei, "Single scattering and annihilation of positrons." Phys. Rev. 70, 19h6. Langer, R. M., "Growth of droplets i n Wilson chamber." Phys. Rev.56, 1938. Lofgren, E. F., Ney, E. P., and Oppenheimer, F., "A cloud chamber illumination system." Rev. Sci. Inst. 19, h, 19kB. • Poynting and Thomson, The Properties of Matter, 1907. Rayleigh, J. W. S., Collected Scientific Papers 1899 - 1920, Vol. 1, Cambridge University Press, Cambridge, 1920. Richarz, F., Ann. Physik 19, 1908. Seaborg, G. T., '"Table of isotopes," Rev. Mod. Phys. 16, 191+U. Thomson, J. J., Conduction of E l e c t r i c i t y through Gases, Cambridge University Press, Cambridge, 1903. Thomson, J. J., and Thomson, G. P., Conduction of E l e c t r i c i t y through Gases, Cambridge University Press, Cambridge, 1928. 

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