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Measurements of Radioactivity Measurements of Radioactivity United States Department of Commerce National Bureau of Standards Circular 476 UNITED STATES DEPARTMENT OF COMMERCE • Charles Sawyer, Secretary NATIONAL BUREAU OF STANDARDS • E. U. Condon, Director Measurements of Radioactivity by Leon F. Curtiss National Bureau of Standards Circular 476 Issued October 15, 1949 For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington 25, D. C. Price .Q^ Preface This publication is a compilation of information intended to be useful to those starting out in research on problems in radioactivity and nuclear physics. An effort has been made to provide, in brief form, most of the essential background for all phases of experimental investigations in this general field. The number of topics involved limits the space that could be given to each, and the author is aware that for many items this has resulted in the elimination of important information. This defect may be corrected in future revisions, when criticisms and suggestions have indi- cated the direction of most useful expansion. This Circular is issued in its present form to provide a convenient source of the information contained and to provide an opportunity for those interested in this field to offer critical comments that can serve as the basis of an improved compilation. E. U. Condon, Director. Conlents Preface 11 VI. Radioactive radiations 37 1. Neutrons — 37 I. Introduction 1 2. Production of neutrons 37 1. Discovery 1 3. Mass of the neutron 37 2 . Statistical nature 1 4. Measurements of neutrons 38 3. Radioactive radiations 5 5. Fast neutrons 38 4. Artificial radioactivity 6 6. Slow neutrons 38 7. Counting alpha particles produced by II. Detection and measurement of radioactive neutron-induced distintegration 38 radiations 8 8. Counting gamma rays resulting from 1. Photographic emulsions 8 neutron capture 38 2. Crystals 9 9. Induced activities 39 3. Ionization of gases 10 10. Cross sections for reactions with 4. Measurement of charge transported by neutrons 39 alpha and beta rays 12 11. Radioactivity produced by neutrons 40 5. 12 Counting methods 12. Proton 41 6. Ionization chambers 12 13. Production of protons 41 7. Proportional counters 14 14. Detection and measurement of protons 41 8. Geiger-Muller counters 15 15. Radioactivity produced by proton 9. Electron multiplier 18 bombardment 42 10. Wilson cloud chamber 18 16. Deuterons 43 11. Calorimetric methods of measuring 17. Deuteron reactions 43 radioactive radiations 19 18. Alpha particles 44 III. Measurement of ionization currents 20 19. Range of alpha particles 44 1. Electroscopes 20 20. Bragg curve 45 2. Quartz fiber electroscopes 21 21. Stopping power 46 3. Electrometers 21 22. Geiger-Nuttall law 46 4. String electrometers 23 23. Scattering of alpha particles 47 5. Portable electrometers 23 24. Emission of alpha particles from the nucleus 47 6. Electrometer tubes 24 25. Beta particles 48 7. Vibrating reed electrometers 24 26. Measurement of beta rays 49 8. Ionization chambers 25 27. Measurements of beta rays with end window counters 49 IV. Radioactive substances 26 28. Beta-ray standards 50 1. Natural radioactivity 26 29. Electroscopes 50 2. Artificial radioactivity 28 30. Ionization chambers 51 3. Disintegration by protons 29 31. Beta-ray spectra 51 4. Disintegration by deuterons 30 32. Magnets for semicircular beta-ray 5. Disintegration by alpha particles 30 spectrographs 52 6. Distintegration by neutrons 30 33. Magnetic electron lens spectrometer 53 7. Disintegration by photons 30 34. Continuous beta-ray spectra 53 8. Alternate methods for producing a given 35. Neutrino 55 radioisotope 31 36. Fermi theory of beta-ray decay 55 9. Decay of artificially radioactive sub- 37. Absorption of beta particles 56 stances 31 38. Scattering of beta particles 56 10. Positron emission 31 39. Range of beta particles 56 11. Electron capture 31 40. Absorption method for determining 12. Isomeric transitions 31 energies of beta rays 57 41. Beta-ray energies by magnetic deflec- V. Equipment for producing artificially radio- tion 57 active isotopes 32 42. Positron 58 1. Voltage multiplier 32 43. Annihilation radiation and pair pro- 2. Cascade transformers 33 duction 58 3. Van de Graaf generator 34 44. Mesotrons 59 4. Linear accelerator 34 45. Artificial production of mesotrons 59 5. Cyclotron 35 46. Gamma rays 59 6. Betatron 35 47. Disintegration schemes 61 7. Synchrotron 36 48. Coincidence measurements 62 8. Uranium reactors 36 49. Absolute calibration of gamma-ray 9. Fission products 36 sources by coincidence 63 iii 50. Measurement of gamma radiation..... 64 4. Neutron standards 76 51. Counting gamma rays 65 5. Units used in radioactive measurements 76 52. Fission particles 65 in geology 79 53. Measurement of half-value periods 67 IX. Radioactivity ratio 79 54. Counter measurement of short half- 1. Uranium lead value periods 68 2. Helium content 79 55. Measurement of half-value periods with 3. Age of terrestial matter 79 counters 69 4. Determination of radium and thorium in 56. Determination of very long half-periods 70 rocks 80 57. Half-periods from true coincidence 5. Pleochroic halves 80 measurements 71 6. Generation of heat in the earth 80 58. Statistical error in measurement of half-value periods with counters 71 X. Health protection 81 1. Nature of radiation injuries 81 VII. Radioactive tracers 72 2. Genetic effects of radiation 81 1. Preparation and measurement of tracer 3. Visible evidence of injury from radiation 82 samples 73 4. Tolerance limits 82 2. Absolute measurements of tracer tolerance levels 82 samples 73 5. Measurements of 6. Alpha radiation 82 7. Protective precautions for substances VIII. Radioactive standards and units 74 emitting alpha rays 83 1. Alpha-ray standards 74 8. Protection from gamma rays 83 2. Beta-ray standards 74 3. Gamma-ray standards 75 XI. References 84 IV MEASUREMENTS OF RADIOACTIVITY I. INTRODUCTION 1. Discovery the limit of which, as x approaches zero, is e. Therefore The discovery of radioactivity illustrates how q'=e-^K 1 an incorrect hypothesis may stimulate experi- ( ) ments that lead to the discovery of new phenom- If at the time t—0 there is a large number No ena. After Roentgen had announced the dis- of radioactive atoms present, the number N, covery of X-rays in 1895, a search was insti- at any subsequent time t, is given by tuted by other physicists for substances that might emit naturally a similar radiation. Bec- N=No (2) querel concluded that since X-rays stimulated certain substances to a strong phosphorescence, This relation expresses the law of exponential such substances would be likely to emit a radia- decay so widely established experimentally in tion having the properties of X-radiation. Ac- the study of radioactivity, where A is the dis- cordingly, he exposed photographic plates, integration constant. wrapped in black paper, to a number of phos- Differentiating eq. 2 with respect to t, we ob- phorescent substances with uniformly negative tain for the rate of disintegration results until he tried salts of uranium. The suc- cess of this trial, announced in 1896, marks the dN discovery of radioactivity. =aNo e-^*=-AN, (3) dt 2. Statistical Nature the negative sign indicating that the number The fundamental nature of radioactivity can of unchanged atoms is decreasing. be described as a probability that the atoms of It has become customary to identify the rates a substance will undergo a transmutation spon- of disintegrations of radioactivity atoms by taneously into atoms of another element with a specifying the time required to decay to one- release of energy in the form of various types half the initial activity. This time is known as of radiation. If this probability is very small the half-value period, T. This period is the time, the substance is either stable or weakly radio- T, required for A/’/N(,=l/2=e“^^; or loge 2= active. If it is large it is strongly radioactive. -\T, from which r=0.693/a. To test this view, let us assume that the prob- Another constant that may be derived from ability that an atom of a given substance will the fundamental equation is the mean life, L, of disintegrate in an interval of time A is p, which the whole group of atoms. The number of atoms is the same for all atoms of the substance and transformed in time dt is given by \Ndt= independent of their age. For very small values xNq 6“^* dt. Each atom has a life t, hence the of A the probability, p, will be proportional to average life of all of them is the length of the interval so that p=AA, where A is a constant representing the probability that t\N(, dt an atom will disintegrate in unit time. Now the L=of oo =0/ 00 t\e-\* dt=l/\. probability, q, that an atom will not disinte- No grate in an interval A is q'=1-p= 1-AA. For a finite time t=/cA, the probability that an atom . (a) . Successive transformations —It is of in- will not be transformed is g'=(l-AA)*'= terest to determine the relative amounts of ( 1-AA ) which may be written radioactive substances when atoms of one type disintegrate successively into other types. These q'=[(l-AA) can be determined from the relation N=No for a number of conditions that are important Now let A become infinitely small while keep- in practice. To derive these relations we will ing the product A: A constant, that is t constant. assume that we have a radioactive chain con- sisting of three types of atoms. A, B, and C, in which A disintegrates to form B, which in turn disintegrates into C with the respective disin- tegration constants A^, A 2 , and Ag.
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