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The gamma rays of radium and its disintegration products Matthews, Frank Samuel 1948

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T H E G A M M A R A Y S O F R A D I U M A N D O F I T S D I S I N T E G R A T I O N P R O D U C T S by Frank Samuel Mathews A Thesis Submitted i n Partial Fulfilment of the Requirements for the degree of MASTER OF ARTS in the Department of PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA September, 19kS>» ABSTRACT A short history of gamma ray investigations i s given. Particular reference i s made to the use of beta-ray spectrometers in these investigations, and a detailed description i s given of the thin-lens beta-ray spectrometer and i t s auxiliary apparatus. The energies of the gamma rays of radium and of i t s equiblibrium disintegration products are determined by measuring the momentum of the photoelectrons ejected by these gamma rays from a lead radiator. These energies agree well with the values reported by E l l i s and Mann, and also agree with most of the previously unconfirmed values reported by Latyshev. Evidence i s given for the existence of a gamma ray (dOk Kev.) previously unreported. The energy calculations are based on a calibration using the F line of thorium B (Ho = 1385.6 gauss-cm.) TABLE OF CONTENTS Page I. HISTORICAL BACKGROUND 1. The Radium Family . . . . . . . . . 1 2. Gamma Rays 3 3 . Beta Ray Spectra k k* Measuring Gamma Ray Energies 6 II. EXPERIMENTAL METHOD 1. The Thin Lens Spectrometer. . . . . . . . . . . . . . 11 2. Spectrometer Alignment Ik 3 . Magnet Current Control 15 U. Radioactive Source Arrangement. . . . . . . . . . . . 18 5. Detector Arrangement • 19 6 . Measurement of Gamma Ray Energies 21 i n . EXPERIMENTAL RESULTS 1. Spectrometer Alignment. 23 • 2. Spectrometer Calibration 25 3 . The Radium Family Gamma Ray Spectrum 2$ k. Comparative Results . . . . . . . . . . 27 IV. CONCLUSIONS 30 V. BIBLIOGRAPHY 32 ILLUSTRATIONS Figures Page 1. The Radium Family 2 2. The Electrostatic Focussing Spectrometer 7 3 . The Magnetic Semi-Circular Focussing Spectrometer 8 1;. The Solenoidal Wound Electron Lens Spectrometer 9 5. The Thin Lens Spectrometer. . . . . . . . 1 2 6 . Magnet Current Control (Block Diagram). . . . . . . 16 7 . Magnet Current Control (Circuit Diagram) 17 8 . Source Arrangement 19 9 . Bell Type Geiger-Mueller Counter. 20 1 0 . Spectrometer Tube Alignment . . 2 3 11. Effect of Compensator Current on Peak Shapes 2k 12. Compensator Coil Efficiency 2k 13. Radium Family Gamma Ray Spectrum . . . . 2 6 Table 1. Comparative Results 28 Plate I. Thin Lens Spectrometer 13 THE GAMMA RAYS OF RADIUM AND OF ITS DISINTEGRATION PRODUCTS I. HISTORICAL BACKGROUND 1. THE RADIUM FAMILY The presence of radioactivity in uranium ores, fir s t detected by Becquerel^in 1896, led Madame Curie(2)to the discovery and isolation of radium in I 8 9 8 . The emitted radiation was found to contain three components: beta rays, separated out by Giesel^)^ and Meyer and von Schweidler^) in 1899j alpha raySj detected by Rutherford^) in 1903j and gamma rays, a penetrating electromagnetic radiation, first discovered by villard^ 6) in 1900 and named by Strutt(7)in 1903. Further investigations showed that this radioactivity was an (1) H. Becquerel. Comptes Rendus, 122, 501. 689. (1896). (2) P. Curie, Mme. Curie, and G. Bemont, Comptes Rendus, 1 2 £ , 1215, ( I 8 9 8 ) . (3) F.O. Giesel, Ann. Phys. Chem., 6 9 , 83!+, ( 1 8 9 9 ) . (U S. Meyer, and E. von Schweidler, Phys. Zeits., 1 , 9 0 , (1899). (5) E. Rutherford, Phil. Mag., 5, 177, ( 1 9 0 3 ) . (6) P. Villard, Comptes Rendus, 13J), 1178, (1900) . (7) R.J. Strutt (afterwards Lord Rayleigh.), Proc.Roy.Soc, 7 2 , 2 0 8 , ( 1903) . 2. atomic phenomenon, and that the rays were emitted when radium atoms (which are slightly unstable) broke up spontaneously to form new elements. It was found that radium i t s e l f emitted only alpha and gamma rays, but that in the process of expulsion of the alpha particles, another radioactive element was formed which in turn decayed into alpha-active or beta-active daughter products, some of which also emitted gamma rays. In 1913, the Law of Radioactive Group Displacement, formulated by R u s s e l l ^ , and in more detail by Fajans^) and Soddy^ 0^, enabled most of the known facts about radium to be correlated, and the complete decay scheme to be worked out, as shown i n Figure 1* THE RADIUM FAMILY. ® so ATOMIC WEIGHT Figure 1* (8) A. S. Russell. Chem. News.. 107, W, (1913). (9) K. Fajans, Phys. Zeits., llj., 131, 136, (1913). (10) F. Soddy, - Chem. News., 10J., 97 (1913). - Jahrb. Radioaktivitat, 10, 188, (1913). 3 . 2. GAMMA RAYS In the Law of Radioactive Group displacement, radioactivity was recognized as an actual disintegration of the nucleus which, i n the alpha ray case, consisted of the emission of a helium nucleus, and i n the beta ray case of an electron from the nucleus. It was not u n t i l 1922, however, that gamma rays were proven to originate i n specifically nuclear processes. In that year, E l l i s ^ ^ attributed regularities i n the energy distribution of the beta rays to the presence of quantum radiations from the nucleus, describable i n terms of nuclear energy levels. These quanta, or gamma rays, i n turn ejected photoelectrons from the electron shells of the atom, with energies, T, calculated from the E i n s t e i n ^ ) photoelectric equation Tehv -Et, where v i s the frequency of the gamma photon and Eb i s the binding energy of the electron i n i t s sh e l l . The reason for the presence of energy levels, and hence of excited states within the nucleus remained unexplained u n t i l 1925 when M e i t n e r ^ ) , and E l l i s and Wooster^-^) showed that gamma rays are only emitted from the nucleus, presumably during a nuclear reorganization, as the result of a previous ejection of an alpha or a beta particle. Finally in 1932, E l l i s p r o v e d that the emission of an alpha particle or beta (11) C.D. E l l i s , Proc.Roy.Sec, A, 101, 1, (1922). (12) A. Einstein, Ann. d. Phys., 17_, 132 , (1905). (13) L. Meitner, Zeits. f. Phys., 3jt, 807, (1925). (IU) C.D. E l l i s and W.A. Wooster, Proc.Camb.Phil.Soc, 22, 8kh, (1926). (15) C.D. E l l i s , Proc.Rpy.S6c, A, 136, 3 9 6 , (1932). particle with less than the normal energy leaves the parent nucleus with an excess energy of excitation which may be emitted afterwards as one or more quanta of gamma radiation. In this way the Law of Conservation of Energy it-Is extended to the nuclear domain. In the radium family, the only alpha-active element mhieh also emits gamma rays i s radium i t s e l f . On the other hand, a l l the beta-emitters of the family except radium C" and radium E emit one or more gamma rays as shown in Figure 1 and Table 1. 3 . BETA RAY SPECTRA Early investigations of the energies of beta rays from a radioactive nucleus revealed a smooth distribution of energies from zero up to a definite maximum which was characteristic of the element considered. Superimposed upon this continuous distribution there were usually a number of sharp peaks which at f i r s t were thought to indicate groups of monokinetic electrons emitted from the n u c l e i i . In 1913, Rutherford and Robinson(l^gh^ed ^ha% these monokinetic groups were, i n fact, a secondary effect originating i n the electron shells, and f i n a l l y in 1922, Ellis^l-'-), as previously mentioned, gave a f a i r l y complete explanation for the whole complex beta distribution. * In the case of beta ac t i v i t y this statement only holds true i f the emission of a neutrino i s postulated. ** An element i s said to emit gamma rays i f i t produces an excited daughter element which emits one or more gamma quanta i n decaying to the ground state. (16) E. Rutherford and H.R. Robinson, Phil. Mag., 26, 717, (1913) Fill i s showed that i n beta ray disintegrations there are only two main phenomena, the emission of the actual disintegration electrons from the nucleus (with a smooth energy distribution), and the consequent emission of one or more gamma photons from the excited daughter nucleus. In addition, however, the beta ray spectrum i s influenced by several secondary effects associated with gamma emission. Chief among them are the following: (a) The relatively frequent conversion of the gamma rays i n the extranuclear electrons of the same atom, and the consequent emission of photoelectrons or "conversion electrons" of characteristic energy T = hv - E D . This phenomenon occurs even i n the thinnest lamina and i s most prominent in materials of high atomic number. (b) Pair production^-'-?) (for gamma ray energies above 1.02 Mev.). A gamma photon may be annihilated i n i t s interaction with matter, and produce an electron positron pair with total combined energy T = h\> - 2 m Qc 2. The cross section for pair production increases with gamma ray energy and also with atomic number. (c) Comp ton scattering. In 1923, Comptonv^) showed that i n their passage through matter, gamma photons eject free or loosely bound electrons from the material, and at the same time lose a part of their own energy. (This process i s completely separate from the photoelectric effect in which orbital electrons are ejected at the expense of the whole quantum). The Compton electrons are ejected most readily by low energy photons and have an energy distribution from zero up to an energy approaching that of (17) CD. Anderson, Phys. Rev., [£, k9k, (1933). (18) A.H. Compton, Phys. Rev., 21, U82, (1923). the incident photon. Compton scattering i s most important i n elements of low atomic number since the Compton scattering cross section increases less rapidly with absorber atomic number than does the photoelectric cross section. k. MEASURING GAMMA. RAY ENERGIES Energy determinations may be made on the gamma photons them-selves, or their energies may be deduced by a study of the photoelectrons, electron positron pairs, or Compton electrons which they eject. In the case of low energy radiations, most of the investigators have used typical X-ray methods. Alvarez^9)applied the methods of " c r i t i c a l absorption l i m i t s " and the "transition effect", and Abelson(2°), (21) (22) T s i e n ' f and F r i l l e y ^ 'made frequency, and hence energy determinations using the bent crystal spectrograph. In this way Tsien discovered six gamma rays of radium D in the range 7-50 Kev., and F r i l l e y discovered twenty-two gamma rays of radium B and C in the range 50-770 Kev, In the study of gamma rays of higher energies, almost a l l the investigations have centred around an electrostatic or magnetic analysis of the photoelectron, electron positron pair, or Compton electron o energies using some type of beta ray spectrometer. The earliest of such spectrometers was one introduced by Baeyer and Hahn( 23) in 1 9 1 0 . Electrons from a s l i t source were deflected i n a magnetic f i e l d , the degree of their deflection being a measure of their energy. (19) L.Alvarez, Phys.Rev., ^ , 1*86, ( 1 9 3 8 ) . ( 2 0 ) P.H.Abelson, Phys.Rev., 5 6 , 7 5 3 , ( 1 9 3 9 ) . ( 2 1 ) S.T.Tsien, Phys.Rev., 6£, 3 8 , (1?1|6). (22) A.R.Frilley, "These", Paris, ( 1928) . (23) H.Baeyer and O.Hahn, Physik., 1 1 , U 8 8 , ( 1 9 1 0 ) . At the present time four main types of spectrometer are i n use: (a) The Electrostatic Focussing Spectrometer shown in Figure 2 . Based on a -theory developed by Hughes and Rojansky(2U)in 192$, i t was used successfully by Backus in 19k5 to measure the low energy gamma rays of Cu^k. i t uses a rad i a l , inverse f i r s t power, electrostatic f i e l d to refocus a diverging bundle of electrons of the correct energy after they have been deviated through an angle of 127° 17'• It i s particularly useful with weak sources, since a f a i r l y large' solid angle i s subtended between the source s l i t and the deflecting plates, but i t i s restricted to use with low energy partieles because of the technical d i f f i c u l t i e s involved i n producing the stronger electrostatic f i e l d needed to focus the more energetic particles. Figure 2 . (2U) A.LW Hughes and V. Rojansky, Phys.Rev., _ t , 2b]*, (1925) (25) J. Backus, Phys.Rev., 6 8 , 5 9 , (19U5) . 8. (b) The Magnetic Semi-circular Focussing Spectrometer shown i n Figure 3* This instrument, developed by Danysz^^in 1912, and sub-sequently improved by Robinson and Rutherford^^and many others, i s similar to the Baeyer and Hahn spectrometer of 1910 but possesses a far higher efficiency. Baeyer and Hahn depended on a narrow s l i t to give them the necessary resolution, tut i n so doing reduced the efficiency to a point where only intense sources could be used. Danysz increased the efficiency tremendously by ins t a l l i n g a far wider s l i t , but maintained the resolving power by focussing the electron beam. A homogeneous magnetic f i e l d i s applied perpendicular to the plane of the figure. Electrons possessing equal velocities describe circles of equal diameter, and i t can be seen from the diagram that, even with a relatively wide s l i t , the particles converge to an approximate focus at the plate or Geiger tube. Figure 3 . (26) J.Danysz, Le Radium, £, 1 , (1912); 1 0 , i i , (1913) . (2?) H.Robinson and E.Rutherford, Phil.Mag., 2 6 , 717, (1913) . 9 . Using this type of instrument and measuring internal conversion and photoelectron lin e energies, E l l i s and associates( 2^)reported f i f t y -four gamma rays of radium, and radium B, C, and D. With the same type of spectrometer and measuring the energies of positrons formed by pair production i n lead, Alichanov and Latyshev^ ^ r e p o r t e d twelve gamma rays of radium C with energies greater than 1.02 Mev. (c) The Solenoidal Wound Electron Lens Spectrometer, f i r s t suggested by Kapitza, and constructed and used by Tricker ( 3 0 ) i n I92I4. i s shown in Figure U. A solenoidal winding, surrounding the whole length of the evacuated cylinder, serves as an electron lens, and focusses electrons of any desired energy on the Geiger tube detector. F a i r l y weak radioactive sources can be investigated with i t ••-•since, i n effect, the Geiger tube subtends a large so l i d angle at the source. It i s more efficient than type (b) but has a lower resolving power. Figure k» (28) CD. E l l i s , Proc.Camb.Phil.Soc, 2 1 , 125, (1922) . CD. E l l i s and H .W.B . Skinner, ProcRoy.Soc, 105A. 165, ( 1 9 2 U ) . CD. E l l i s and W.A. Wooster, ProcRoy.Soc, lHjA"7~276, U 9 2 7 ) . CD. E l l i s and F .W. Aston, ProcRoy.Soc, 129A, 180, (1930) (29) A.I.Alichanov and G.D.Latyshev, CR.Acad.Sci., (U.R.S.S.), 2 0 , 113, (1938) . (30) R.A.Tricker, Proc.Camb.Phil.Soc, 2 2 , U5U, (192U). 1 0 . (d) The Thin Lens Spectrometer shown i n Figure 5 and Plate I. It was f i r s t suggested by KLemperer^^in 1935 and developed to i t s present state by Deutsch, E l l i o t t , and Evans^ 2 ) . A spectrometer of this type, designed by E l l i o t t was used in the present study, and i s described in d e t a i l i n the following section. It has a higher efficiency than type (a), (b), or (c), but a s l i g h t l y lower resolving power. The work with this spectrometer was undertaken i n an attempt to correlate the findings of E l l i s and Wooster, and Alichanov and Latyshev previously mentioned. Similar work with this spectrometer was undertaken in 19k7 by Mann and Ozeroff using a 10 m i l l i c u r i e source, but i t was deemed advisable to repeat the investigation using a 500 m i l l i c u r i e source and a more sensitive magnetic f i e l d control. ( 3 U O.KLemperer, Phil^Mag., 2 0 , 5h5, U 9 3 5 ) . (32) M.Deutsch, L.G.Elliott, and R.D.Evans, Rev.Sci.Instr., l£, 178, (19kh) 11. II. EXPERIMENTAL METHOD 1. THE THIN LENS SPECTROMETER This instrument consists essentially of an evacuated brass tube 8 inches in diameter and hQ inches long, surrounded at its center by a short water cooled magnet coil of number 10 wire, wound in four sections. The system is evacuated to a pressure of 10"^ m.m. Hg. using a Cenco Hypervac pump and a metal, water cooled, 20 liters/second oi l diffusion pump. Pressures are indicated on a Pirani gauge. Inside the tube are five lead baffles (see Figure 5.). Baffles A, D, and E mask the counter from any scattered radiations and hence reduce the normal background count, baffle C prevents gamma radiations of any energy from passing directly from source to counter, and baffle B defines a hollow cone of electrons emitted from the source into the field of the magnet. The spectrometer analyses an electron spectrum using the "chromatic aberration" of a short magnetic electron lens. For a given coil current, electrons of one particular energy in the hollow cone defined by baffle A are focussed by the field of the lens coil on the window of the Geiger counter. Electrons of other energies are focussed at other points on or near the axis of the tube and strike the tube wall or the baffles D and E. Since the focussed electrons always traverse a fixed path, and since a particle can only travel in a curved path of radius o in a magnetic field H i f i t has a momentum mv determined by the formula mv - Hep e being the electron's charge, i t follows that the momentum of -the focussed Figure 5. l i t . electrons i s always directly proportional to the focussing magnetic f i e l d H. Consequently, since the magnet c o i l contains no iron, the momentum of the focussed electrons i s proportional to the c o i l current i t s e l f . The current i through the n turns of the focussing c o i l and the momentum of the focussed electrons are related by the formula: f a, ke mv c n i . where k i s a constant depending on the size and shape of the c o i l , and f i s the focal length, related to u the source distance from the center of the lens, and v the counter distance from the center of the lens by the thin lens formula: ' 1 = 1 + 1 f u v. 2. SPECTROMETER ALIGNMENT Any perturbations or abnormal inhomogeneities i n the focussing f i e l d cause defocussing of the electron beam over i t s long path. Consequently, careful precautions had to be taken to ensure that the axis of the spectrometer tube was symmetrically placed with respect to the focussing f i e l d and that no extraneous magnetic fields were present. (a) The spectrometer tube i s provided with adjusting screws for moving i t relative to the magnet c o i l . Each end of the tube was moved, i n turn, horizontally and ve r t i c a l l y and set at the position which gave a maximum beta particle transmission for a given c o i l current. (b) The perturbing effect of the horizontal component of the earth's magnetic f i e l d was eliminated by choosing the area i n the laboratory where the earth's f i e l d was most constant, placing the spectrometer there, and aligning the axis of the spectrometer tube with the 15. direction of this horizontal component. (c) The spectrometer is provided with two rectangular c o i l s , mounted horizontally above and below the spectrometer tube, and connected as Helmholtz coils. Current from a 250 volt D.C. source was supplied to the coils i n such a way as to compensate for the perturbing effect of the ver t i c a l component of the earth's magnetic f i e l d . The f i n a l criterion for the adjustment of the compensator current was the shape of the photo-electron peaks as measured on the spectrometer. The current was adjusted to give maximum peak height, minimum peak width, and minimum distortion. 3. MAGNET CURRENT CONTROL Since the photoelectron peaks occupy a very small momentum interval, i t i s necessary to hold the magnetic f i e l d steady to at least .1 per cent when any accurate investigation of peak shapes i s made. The control apparatus for this purpose i s shown in block diagram in Figure 6 and schematically in Figure 7. The system.is essentially that used by Dr. L.G. E l l i o t t i n the National Research Council laboratories at Chalk River, with a few modifications to allow the use of a grounded power supply. The D.C. amplifier shown in Figure 7 accepts a l l current fluctuations with frequencies from zero up to about 10 cycles per second, the A.C. amplifier i s sensitive to fluctuation frequencies from 10 cycles per second up to about 1000 cycles per second, and fluctuations more rapid than 1000 per second are shorted out by the i+oOO microfarad condenser across the magnet c o i l . In the D.C. control c i r c u i t the difference between a standard reference voltage obtained from a standardized Rubicon potentiometer, and + 2 2 0 VOLT SUPPLY. 4 6 0 0 MF. RUBICON POTENTIOMETER. CALIBRATION CELL. CALIBRATION GALVANOMETER STANDARD CELL. A . C . AMPLIFIER. • D.C. AMPLIFIER AND PHASE SENSITIVE DETECTOR. 5LS BIAS TUBE. FOR 6AS7 6AS7.s STANDARD RESISTANCE. Figure 6 18. the control c i r c u i t voltage obtained across the .08 ohm manganin standard resistance i s converted into a 60 cycle square wave by means of a Brown converter. This "error signal" i s amplified about 100 db., r e c t i f i e d by means of the "phase sensitive detector", (a f u l l wave detector biased by a 60 cycle sine wave voltage i n order to ensure the correct polarity of D.C. output voltage) and applied to the grids of the regulator tubes. The A.C. control c i r c u i t i s merely a negative feedback loop. A.C. fluctuations across the magnet are amplified by the 6AC7 and the 6L6, and applied directly to the grids of the regulator tubes. One stage of this amplifier i s made insensitive to high frequency fluctuations (over 1000 cycles per second), i n order to eliminate any oscillations i n the circuit which might be caused by a phase s h i f t of the fluctuation signal. The regulator tubes are 38 6AS7 twin triodes connected i n p a r a l l e l , each plate having i t s own 100 ohm 1 equalizing resistance 1, and each grid i t s own 1000 ohm 'grid stopper'. The t o t a l rated plate current i s 10 amperes, but currents of 15 amperes can be drawn for f a i r l y long periods without any serious consequences. Tests with an oscilloscope indicate that the control i s accurate to at least .01 per cent over the current range 0-15 amperes. k. RADIOACTIVE SOURCE ARRANGEMENT The experimental arrangement of the 500 millicurie source i s shown in Figure 8. The thickness of the aluminum capsule i s such that, according to the F e a t h e r ^ ^ r u l e : R(gms/cm2) = .5U3 E (Mev.) - 0.16 (33) N.Feather, Proc.Camb.Phil.Soc., 3ji, 599,. (1938). 19. even the most energetic primary beta particle or internal conversion electron i s absorbed. At the same time' however, gamma rays of each particular energy give rise to a continuous energy distribution of Compton electrons i n the aluminum, and to photoelectrons of discrete energies in the lead radiator, so that p assing into the spectrometer tube there i s a stream of electrons with a very complex energy distribution. Figure 8. The lead radiator i s 3 millimeters i n diameter, and has a surface density of 50 milligrams per square centimeter. This density i s an optimum value, and represents a compromise between a higher value, which would give better photoelectron peak intensity,and a lower value, which would give sharper photoelectron peaks. 5. DETECTOR ARRANGEMENT The focussed electrons are detected by a b e l l type Geiger-Mueller counter shown i n Figure 9. The cathode i s a 0.75 inch diameter copper tube. The anode i s a .005 inch tungsten wire on the end of which is a small glass bead. The window i s of mica and i s sealed to the counter 20. with a cement made from equal parts of beeswax and resin. The mica has a surface density of 2 . 9 milligrams per square centimeter and i s transparent to beta particles with energies greater than 100 Kev. A brass disc with a k millimeter aperture masks the counter window, and improves the spectrometer resolving power by keeping unfocussed electrons out of the counter. Figure 9 . The counter i s f i l l e d with a Trost mixture of 0 . 7 cm. (Hg) of ethyl alcohol vapour and 9 . 3 c.m. of argon. The plateau i f 130 volts long, commencing at 10k0 volts, and has a gradient of 0 . U per cent per volt. A l l counts i n the succeeding investigation were made with a counter potential of 1 0 6 0 volts. The counter potential i s supplied from a high voltage battery pack which has an output that can be varied from 63O volts to 12lj0 volts * The resolving power of a spectrometer i s defined as the momentum interval of the focussed electrons as a percentage of their average momentum* 21. in 22§ volt steps. The current drain through the Geiger tube during discharge i s very low and tests with an electrostatic voltmeter show that the battery output i s extremely stable. This counter supply voltage s t a b i l i t y i s an absolute necessity, since fluctuations in counter voltage cause changes i n the counting rate level and thus distort the results. The output pulse from the G-M counter i s fed into a twin triode, cathode-coupled preamplifier, and via a grounded grid output into a scale of 61i scaling c i r c u i t and a mechanical register. Incorporated in the scaler i s a "pulse size discriminator" which determines the minimum pulse size which can cause a count. Since the discriminator i s very sensitive to line voltage fluctuations, power for the scaling c i r c u i t i s obtained from a Sola constant voltage transformer. 3h this way, changes in the counting rate level due to a shi f t in discriminator bias are eliminated. 6. MEASUREMENT OF GAMMA RAY ENERGIES Projected into the spectrometer tube from the source and radiator Is a stream of electrons with a complex energy distribution. The focussing f i e l d current i s varied and the momentum spectrum plotted, f i r s t with the lead radiator in place, and then with i t removed. The f i r s t plot shows a series of photoelectron peaks superimposed upon a continuous Compton background, and the second plot shows only the Compton background. The difference between these two curves thus shows the momentum distribution of the photoelectrons alone. The energies of the photoelectrons, and consequently the energies of the original gamma rays themselves can then be calculated. As was previously mentioned, the momentum of the focussed electrons i s proportional to the f i e l d c o i l current. The current required 22. to focus photoelectrons of a known momentum i s therefore determined, and this one-point calibration serves for the whole spectrum. Once the photoelectron" momentum i s known, the photoelectron energy can easily be calculated from the formula: Hy • /y/T(T* 1.02) where = mv i s the electron momentum in gauss-cm. and T i s the kinetic e energy i n Mev. The gamma ray energy and the associated photoelectron energy are related by the formula: h» = T 4- E D where hv i s the gamma ray energy and E^-, i s the binding energy of the photoelectron i n i t s particular shell. The binding energies for the K, L, M, and N shells of the lead r a d i a t o r a r e as follows: E^ K = 87.6 Kev. E _ = 15.8 Kev.-bL E b M = 3.85 Kev. E - 0.89 Kev. M l (3U) J«M. Cork, Radioactivity and Nuclear Physics, loc. c i t . , 301. 23. III. EXPERIMENTAL RESULTS 1. SPECTROMETER ALIGNMENT (a) Adjustment of the spectrometer tube, relative to the magnet c o i l i s shown i n Figure 10. Counting rates, accurate to within 1.5 per cent are plotted for various tube positions recorded relative to an arbitrary i n i t i a l setting. The f i n a l position of both source and counter, end i s indicated by the broad arrow. Figure 10. (b) The effectiveness of the earth's f i e l d compensator i s shown in Figures 11 and 12. Figure 11 shows how variations i n compensator current affect the plotted shape and intensity of the 0.162 Mev. K line of radium. The optimum current setting was taken as 1050 milliamperes. 1050 UA COMPENSATOR CURRENT 1000 MA 0 . 4 0 0 .45 P O T E N T I O M E T E R  SETTING. Figure 1 1 . 2U. Figure 12 shows the degree of earth's f i e l d compensation at various points along the spectrometer tube axis when the optimum compensator current i s flowing. The incomplete compensation near the ends of the spectrometer tube does not result in' any serious defocussing. The focussing f i e l d perturbation at the source end can be neglected since i t only affects unfocussed electrons, and the "counter end" perturbation i s not serious since the electrons travel only a short distance after being perturbed, and are therefore deviated only slightly from their intended path. ORIGINAL VERTICAL FIELD VERTICAL FIELD H AFTER COMPENSATION. MAGNET POSITION. DISTANCE ALONG SPECTROMETER . Figure 12 . 2 5 . 2. SPECTROMETER CALIBRATION In the determination of the c o i l current required to focus line of thorium B ( Ho = 1385.6 gauss-cm.)^ . Since a thorium B source was not available, the spectrometer was calibrated against the 1.77 Mev. line of radium C, which in turn was calibrated against the F line of thorium by Mann and Ozeroff ^ 6 ) ^ 2$k7» The 1.77 Mev. l i n e was chosen because i t has the highest intensity of a l l the radium lines, and because i t i s the radium line on whose value E l l i s , Alichanov, and Mann agree most closely. The potentiometer reading which corresponds to the Ho value of 7116.2 gauss-cms for the 1.77 Mev. l i n e was found to be 0 .77 i i volts. From this, by direct proportion, a l l the other Ho values are determined. 3 . THE RADIUM FAMILY GAMMA RAY SPECTRUM Figure 13 shows the graph of the photoelectron peaks and Compton background over the momentum range O-96OO gauss-cm. The momentum scale i s logarithmic so that the momentum interval at any point i s a constant fraction of the total momentum at that point. Each point on the composite curve and on the Compton background curve represents an average total count of at least "U0,000. The s t a t i s t i c a l accuracy of each of these curves i s therefore * \ per cent. The s t a t i s t i c a l accuracy a of the difference curve i s given by the formula: (35) C.D.Ellis. ProcRoy.Soc, 138. 318. (1932) . K.C.Wang, Zeits. f. Phys., 8 7 , 6 3 3 , (193U). (36) K.C.Mann and M.J.Ozeroff, "Thesis", U.B.C, (l ? U 7 ) . • - - 27. where b and c are the s t a t i s t i c a l errors i n the composite curve and the Compton background curve. The photoelectron peaks i n the difference curve therefore have a s t a t i s t i c a l accuracy of 0.7 per cent. The gamma ray energies shown are calculated on the assumption that a l l the peaks are due to photoelectrons ejected from the K shell of the lead atom (E^ K 87.6 Kev.). It w i l l be seen later that i n the case of the 650 Kev. and 688 Kev. peaks this assumption may not be ju s t i f i e d . The bracketed gamma ray energy values i n Figure 13 are values which are considered doubtful or unreliable because of the poor shape or low s t a t i s t i c a l weight of the plotted photoelectron peaks. They are therefore not included in the following discussion. k. COMPARATIVE RESULTS Table I shows a comparison between the values found by previous investigators and those found i n this present study. Relative intensities of the lines are also included. The intensities measured i n this present discussion have been corrected for the decrease i n cross-section for photoelectron production with increasing gamma ray energy, using recently ( 3 7 ) published w''cross-section curves. U37J CD.Coryell, M.Deutsch, R.D.Evans et a l , "The Science and Engineering of Nuclear Power," (Addison-Wesley), p. UO. TABLE 1 E l l i s and Constantinov Alichanov and Mann and Mann and associates & Latyshev(38) Latyshev Ozeroff Mathews' Gamma-ray Gamma^ray Gamma-ray Relative Gamma-ray Relative Gamma-ray Relative Energy Energy Energy Intensity Energy Intensity Energy Intensity -OL72 .0536 .0589 M89 .197 .205 0.6** .209 .21*5 .237 .250 .260 .275 .289 11 s* .295 .297 .332 .35U .314; 28 3 e i .359 .389 .391 .U29 . U 2 8 6 . U 2 8 9.1 .UU8 2.2 • U71 .U78 11 .1*98 .503 13 .518 25 .612 . 6 0 6 .598 55 .608 76 .773 .766 .768 11 . 7 7 9 36 .80I4 30 M .933 78 .91*0 I U 1.13 1.12 1.10 1.11 1.11 5o 1 .2U8 1.23U 1.21 23 1.22 33 1 . 2U 21 1.29 18 1 .33 3 . 7 1.390 1.370 1.39 h9 I.I4O 22 1.U1 18 1.U26 l.l+lli 1.53 2U 1.52 29 1.62 22 (continued on Page 29) TABLE 1 (cont'd) E l l i s arid- Cons tantinov '. Alichanov and - - - . Mann and Mann and associates & Latyshev(38) Latyshev Ozeroff Mathews Gamma-ray Gamma-ray Gamma-ray Relative Gamma-ray Relative Gamma-ray Relative Energy Energy Energy Intensity Energy Intensity Energy Intensity 1.69 : i 7 1.68 6 1.778 1.761 1.75 100 , 1.77 100 1.77 100 1.82 17 1.87 31 2.09 15 2.09 2k 2.219 2.200 2.20 ia 2.19 22 2.2k 20 2.5 2.1*2 21 (2.U) - ' 2.1*3 18 (2.8) — Not corrected for photoelectric cross-section. (38) A.A.Constantinov and G.D.Latyshev, J.Phys.U.S.S.R., 5, 21*9, ( 1 9 U U . ~ £ 30. IV. CONCLUSIONS The comparative chart i n Table I shows twenty-three gamma rays (energies between .209 Mev. and 2.J4.3 Mev.) found i n this investigation. The lower end of the spectrum i s cut off at 100 Kev. because of absorption in the counter window, and therefore gamma rays with energies below 188 Kev. (100 Kev. plus the lead K shell binding energy of 88 Kev.) are undetected. At the upper end of the spectrum the Compton background end point at 2.2*6 Mev. indicates the presence of a gamma ray of energy 2.8 Mev., which i s apparently too weak to show as a photoelectron l i n e . This value i s calculated from the formula: hi) (Mev.) = ... ' " -.51T T - <\| TtT+ 1.02; cos $ where T i s the maximum Compton rec o i l energy (in Mev.) and 0, the scattering angle i s taken as 0 . The twenty-three gamma rays reported here agree very closely with the values reported by E l l i s , Mann and Latyshev. At low energies, the agreement with the values reported by E l l i s i s very good. Qrie.notlceably/ different value, (reported here as 250 Kev.) may well be an unresolved pair (.245 Kev. & .260 Kev.). Consideration of the peak shape (very broad compared with neighbouring peaks) makes this suggestion plausible. At higher energies, the agreement with the findings of Latyshev i s even more noticeable. A l l but one of his previously unconfirmed values are reproduced here. The 1.1*26 Mev. gamma ray reported by E l l i s , however, . 3 1 . i s noticeably absent i n these results and in the results of the other (19) investigators. This absence has been explained by Theboud v J 7 'as being due to the fact that this particular gamma ray i s almost t o t a l l y internally converted. In view of this fact, detection of this gamma ray cannot be expected i n an instrument such as the thin lens spectrometer which meas-ures energies of the secondary electrons. In the middle of the spectrum the results are less conclusive. The .650 and .688 Mev. lines shown i n Figure 13 may actually be caused by the L and M lines associated with the strong .608 Mev. K li n e . The separation between the K (.608 Mev.) and the M (.688 Mev.) i s appreciably correct, but the separation between the K and the L (.650 Mev.) i s considerably i n error. One new li n e i s reported in this region. It has an energy of .80I4. Mev. and i s f a i r l y intense but may have been missed previously because i t l i e s on a very steep portion of the composite curve. (39) G.D.Theboud, "These", Paris, (1925). 32. V. BIBLIOGRAPHY P. H. Abelson A. I. Alichanev and G. D. Latyshev L. Alvarez C. D. Anderson J. Backus H. Baeyer and 0 . Hahn H. Becquerel A. H. Compton A. A. Constantinov and G. D. Latyshev J. M. Cork C. D. Coryell, M. Deutsch, R. D. Evans et a l P; Curie, Mme. Curie, and G. Bemont J. Danysz M. Deutsch, L. G. E l l i o t t , and R. D. Evans A. Einstein CD. E l l i s Phys.Rev., 3 6 , 753, (1939). C.R. Acad.Sci.,(U.R.S.S.),20, 113, (1938) Phys.Rev., 5 k , U86, (1938) . Phys.Rev., i ^ , 494, (1933). Phys.Rev., 6 8 , 5 9 , (1945) . Physik., 1 1 , 4 8 8 , (1910) . Comptes Rendus, 122. 501 , 6 8 9 , (1896) . Phys.Rev., 2 1 , 1*82, ( 1923) . J.Phys. U.S.S.R., £, 21*9, (1941) . Radioactivity and Nuclear Physics, loc. c i t . , 301. "The Science and Engineering of Nuclear Power", (Addison-Wesley) Comptes Rendus, 1 2 J , 1215, (1898), Le Radium, 9 , 1 , (1912). Le Radium, 1 0 , 1*, (1913) . Rev.Sci.Instr., 1 5 , 178, (1944) . Ann. d. Phys., 17, 132, (1905. ProcRoy.Soc, A, _101, 1, (1922). Proc.Camb.Phil.Soc, 21, 125, (1922). ProcRoy.Soc, I38, 318", (1932). 33. C. D. E l l i s and F. W. Aston C. D. E l l i s and H. W. B. Skinner C. D. E l l i s and W. A. Wooster K. Fajens N. Feather A. H. F r i l l e y F. 0. Giesel A. L. Hughes and V. Rojansky 0. KLemperer K. C. Mann and M. J. Ozeroff L. Meitner S. Meyer, and E. von Schweidler H, Robinson and E. Rutherford A. B. Russell . E. Rutherford E. Rutherford and H. R. Robinson E. Rutherford, J. Chadwick, C. D. E l l i s J. D. Main Smith F. Soddy L. F. Stranathan R. J. Strutt Proc.Roy.Soc, 129A, 180, (1930). Proc.Roy.Soc, 105A, 165, (1921*). Proc.Camb.Phil.Soc, 22, 81*1*, (1926). Proc.Roy.Soc, III4A, 2?6, (192?). Phys.Zeits, IU, 131, 136, (1913). ProcCamb.Phil.Soc, 3ji, 599, (1938). Reports on Progress i n Physics, 2, 66, (19U0). "These", Paris, (1928). Ann.Phys.Chem., 69, 83I4, (1899). Phys.Rev., 3jt, 281;, (1925). Phil.Mag., 20, 51*5, (1935). "Thesis", U.B.C., (191*7). Zeits. f. Phys., 3j*, 807, (1925). Phys.Zeits., 1, 90, (1899). PhilMag., 26, 717, (1913). Chem.New., 107, 1*9, (1913). Phil.Mag.,_5, 177, (1903). Phil.Mag., 26, 717, (1913). "Radiations from Radioactive Substances", (Cambridge), (1930). "Chemistry and Atomic Structure", (Ernest Benn), London, (192ii). Chem.New., 107, 97, (1913). Jahrb. Radioaktivitat, 10, 188, (1913). "The Particles of Modern Physics", (Blakiston), Philadelphia, (191*2). Proc.Roy.Soc, 7_2> 208, (1903. 34. G. D. Theboud R. A. Tricker S. T. Tsien P. Villard K. C. Wang "These", Paris, ( 1925) . Proc.Camb.Phil.Soc, 22 , 454, (1924) . Phys.Rev., 6£ , 3 8 , ( 1 9 4 6 ) . Comptes Rendus, 130, 1178, ( 1 9 0 0 ) . Zeits, f. Phys., 8 7 , 6 3 3 , (1934) . 0O0 ACKNOWLEDGEMENTS The beta-ray spectrometer and auxiliary apparatus for this study were provided out of a Grant-in-Aid of Research to Dr. K. C. Mann from the National Research Council of Canada. The auther i s indebted to Dr. S. E. Maddigan of the Br i t i s h Columbia Research Council, who made available a 500 m i l l i c u r i e Radium sourcej to Mr. J. Bryden of the Consolidated Mining and Smelting Company of Canada Limited, who arranged for a g i f t of 1|060 pounds of lead which was used i n the construction of baffles for background reduction, and castles for personnel protection; and to Mr. A. W. Pye, who aided i n the construction of end window beta counters and their associated f i l l i n g system. The author wishes to express his special thanks to Dr. Mann for the expert advice and inspiring encouragement he has given while supervising the project. 

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