(147):53280,12:53281,00""T 11)"***********************"x( 11)"* *"2 11)"* RADIOACTIVITY *"< 11)"* *"F 11)"***********************"P::Z 12)" A PHYSICS PROGRAM"d""/n16)"PREPARED BY"9x""V 14)"PAUL W. MCDANIEL"r 14)"4295 WARREN WAY" 14)"RENO, NV 89509":13)"ALL RIGHTS RESERVED" 12 (147):"":53280,2:53281,216)"NOTICE":u6)"WHEN FLASHING CURSOR AND A QUESTION MARK APPEAR PRESS RETURN WHEN READY TO PROCEED. GRAPHICS CONTINUE ""AFTER 20 SECONDS WITHOUT ANY ACTION BY THE STUDENT.":(147)6)"THE PRECEEDING PROGRAMS IN THIS SERIES ARE:":10)"INTRODUCTION TO PHYSICS"::10)"MATTER IN BULK":_10)"ATOMIC STRUCTURE-PART I":10)"ATOMIC STRUCTURE-PART II":10)"ATOMIC STRUCTURE-PART III": "6)"COPIES OF THESE PROGRAMS CAN BE PURCHASED FROM THE AUTHOR AT A PRICE OF $10.00 FOR EACH PROGRAM FROM": ,12)"DR. PAUL W. MCDANIEL 4295 WARREN WAY RENO, NEVADA 89509": 6 (147):"":53280,1:53281,0 @14)" RADIOACTIVITY "::(147):"" J(147)y!T6)"IN THE 1880'S MANY PHYSICISTS THOUGHT THAT THEY HAD NAILED DOWN ALL THE FUNDAMENTAL QUESTIONS ABOUT NATURE.":!^6)"FOR EXAMPLE, JOHN TROWBRIDGE, HEADOF THE PHYSICS DEPARTMENT AT HARVARD UNIVERSITY, WARNED BRIGHT GRADUATE "u"h"STUDENTS AWAY FROM PHYSICS BY TELLING THEM THAT THE ESSENTIAL BUSINESS OF SCIENCE WAS FINISHED AND THAT ALL THAT""r"REMAINED WAS TO DOT A FEW I'S AND CROSS A FEW T'S.":)#|6)"ALBERT MICHELSON, A NOBEL PRIZE WINNER FROM THE UNIVERSITY OF CHICAGO, SAID IN 1894, 'THE FUTURE TRUTHS OF"t#"PHYSICS ARE TO BE LOOKED FOR IN THE SIXTH PLACE OF DECIMALS'.":#6)"HOW WRONG THEY WERE! BEFORE MICHELSON'S WORDS WERE IN PRINT THE PHENOMENUM OF RADIOACTIVITY WAS DISCOVERED.":$(147):""$6)"THE PHENOMENON OF RADIOACTIVITY HAS PLAYED A MAJOR ROLE IN THE DEVELOPMENT OF ATOMIC AND NUCLEAR " %"PHYSICS. OUR EVERYDAY LIFE IS STRONGLY AFFECTED BY THIS PHENOMENON, AND MOST PEOPLE HAVE AT LEAST SOME UNDERSTANDING "F%"OF THIS PROPERTY OF CERTAIN TYPES OF MATTER.":]%(147):""%6)"A NUCLEUS MAY DECAY SPONTANEOUSLY BY THE EMISSION OF AN ALPHA PARTICLE (THE NUCLEUS OF A HELIUM ATOM),A BETA "U&"PARTICLE (AN ELECTRON), OR A GAMMA RAY (A PHOTON), THEREBY RIDDING ITSELF OF EXCESS NUCLEAR EXCITATION ENERGY OR"&"ACHIEVING A CONFIGURATION THAT IS OR WILL LEAD TO ONE OF GREATER STABILITY.":&(147):""@'6)"WE HAVE SEEN IN OTHER PARTS OF THIS STUDY THAT THE NUCLEUS OF AN ATOM IS AN AGGREGATE OF PROTONS AND NEUTRONS"'"MOVING VERY CLOSELY TO ONE ANOTHER UNDERTHE STRONG FORCES THAT GIVE THEM EXCEEDINGLY HIGH SPEEDS.":' (147):""E(6)"THE NUCLEI OF SOME ISOTOPES ARE UNSTABLE AND THEY SPONTANEOUSLY EMIT CHARGED PARTICLES OF HIGH ENERGY AND "("ELECTROMAGNETIC RADIATIONS.THESE NUCLEI ARE SAID TO BE RADIOACTIVE. SOME OF THESE ISOTOPES ARE NATURALLY RADIOACTIVE")&"AND OTHERS ARE MANUFACTURED IN NUCLEAR REACTIONS.":)0 (147):""):6)"SOME NATURALLY RADIOACTIVE SUBSTANCES EMIT ALPHA PARTICLES, THE NUCLEI OF HELIUM ATOMS.)D*N6)"IN 1895 ROENTGEN SHOWED THAT A PENETRATING RADIATION WAS EMITTED WHEN CATHODE RAYS STRUCK THE GLASS WALLS OF A DISCHARGE TUBE.":3*X (147):""*b6)"THESE AND OTHER EXPERIMENTS INSPIRED CONTINUING RESEARCH WHICH LED TO THE DISCOVERY BY BECQUEREL IN 1896"/+l"THAT URANIUM IS A NATURAL SOURCE OF PENETRATING RAYS. HE COINED THE WORD 'RADIOACTIVE' TO DESCRIBE THIS PROPERTY.":H+v (147):""+6)"THE CURIES AND THEIR CO-WORKERS IN1898 DISCOVERED THAT RADIUM, THORIUM ANDSEVERAL OTHER ELEMENTS WERE RADIOACTIVE."E,"BY 1918 NEARLY 40 RADIOACTIVE ISOTOPES HAD BEEN FOUND WITH ATOMIC NUMBERS GREATER THAN 80. IN ADDITION IT HAD BEEN","OBSERVED THAT SOME OTHER ELEMENTS, LIKE POTASSIUM AND RUBIDIUM ARE RADIOACTIVE.":, (147):""+-6)"LET US EXAMINE ONE RADIOACTIVE ELEMENT IN SOME DETAIL IN ORDER TO MORE FULLY UNDERSTAND RADIOACTIVITY."5-""-6)"WHEN A SOLUTION OF A RADIUM SALT IS PLACED IN A CLOSED GLASS VESSEL IT ISFOUND THAT THE AIR ABOVE THE SOLUTION"/."SHOWS A FAINT GLOW WHEN EXAMINED IN THE DARK. WHEN THE AIR IS REMOVED BY PUMPINGIT OUT OF THE FLASK THE GLOW DISAPPEARS."{."SOMETIME LATER THE GLOW REAPPEARS WHEN THE FLASK IS LEFT TO REST.":. (147):"" /6)" THIS SHOWS THAT RADIUM MUST DISINTEGRATE INTO A GAS AND THAT THE GAS ITSELF IS RADIOACTIVE. THIS GAS WAS"b/"ORIGINALLY CALLED'RADIUM EMANATION'. LATER THE NAME WAS CHANGED TO 'RADON'.":/6)"NOW RADIUM HAS CHEMICAL PROPERTIESLIKE THOSE OF BARIUM. WE NOW KNOW THAT RADIUM HAS 88 PROTONS IN ITS NUCLEUS."[0"AND THAT THE DISINTEGRATION PROCESS CONSISTS OF THE EMISSION OF AN ALPHA PARTICLE, WITH A CHARGE OF 2E, FROM THE"0 "NUCLEUS. THEREFORE THE CHARGE OF THE RESIDUAL NUCLEUS MUST BE 86E (SO TWO PLANETARY ELECTRONS MUST BE LOST)"S1"THE REASONING ABOVE LEAD US TO THE CONCLUSION THAT THE RESIDUAL NUCLEUS MUST BE A RARE GAS. ALL CHEMISTRY TESTS"|1 "HAVE CONFIRMED THIS CONCLUSION.":1* (147):""246)"IT HAS BEEN OBSERVED FROM STUDYINGTHE RADIOACTIVE PROCESS THAT WHEN A RADIOACTIVE ATOM EMITS AN ALPHA PARTICLE"2>"THAT THE ATOMIC NUMBER IS REDUCED BY 2 AND THE MASS NUMBER REDUCED BY 4, SINCE THE ALPHA PARTICLE IS A HELIUM NUCLEUS"2H"WITH A CHARGE OF 2 UNITS AND A MASS NUMBER 4.":2R (147):""]3\6)"ON THE OTHER HAND, WHEN A BETA PARTICLE IS EMITTED THE ATOMIC NUMBER ISINCREASED BY ONE BUT THE MASS NUMBER"3f"REMAINS THE SAME, SINCE THE EMISSION OF A NEGATIVE ELECTRON IS EQUIVALENT TO A NEUTRON IN THE NUCLEUS CHANGING INTO A"3p"PROTON.":4z (147):""46)"THE EMISSION OF A GAMMA RAY, WHICHMAY ACCOMPANY EITHER ALPHA OR BETA EMISSION, LEAVES BOTH THE ATOMIC NUMBER"4"AND THE ATOMIC MASS UNALTERED.":4 (147):""44)"STATISTICS OF RADIOACTICE DECAY ": 5(147):""56)"THE NUMBER OF RADIOACTIVE NUCLEI IN ANY SAMPLE OF RADIOACTIVE MATERIAL DECREASES CONTINUOUSLY AS SOME OF THE"5"NUCLEI DISINTEGRATE. THE DECREASE RATE VARIES WIDELY FOR DIFFERENT NUCLEI.":5 (147):""p66)"IF N IS THE NUMBER OF RADIOACTIVE ATOMS IN A SAMPLE AT TIME T, AND DN IS THE NUMBER THAT DISINTEGRATES IN TIME DT"6"THEN SINCE THE RATE OF CHANGE OF N IS PROPORTIONAL TO N , WE HAVE":6 (147):""616)"THE EQUATION"6""712)"DN"712)" = -L * N"2712)"DT "<7$""7.6)"REPRESENTING THE DISINTEGRATION RATE, WHERE L (LAMBDA) IS A CONSTANT."78""8B6)"THEREFORE IT FOLLOWS THAT THE NUMBER OF RADIOACTIVE NUCLEI DECREASES EXPONENTIALLY WITH TIME.": 8L (147):""L8V6)"IF N IS THE NUMBER AT TIME T = 0"\8`6)" 0"b8j8t6)"THEN THE NUMBER OF NUCLEI REMAINING AT A LATER TIME T IS"8~""816)" -LT"816)"N = N E (1)" 916)" 0 "9""96)"THE PROPORTIONALITY CONSTANT L (THE GREEK SYMBOL FOR LAMBDA IS USUALLY USED) IS CALLED THE 'DECAY CONSTANT' AND":"HAS A DIFFERENT VALUE FOR EACH RADIOISOTOPE. THE CONNECTION BETWEEN THEDECAY CONSTANT L AND HALF LIFE T IS ">:"EASY TO ESTABLISH. 1/2" :V: (147):""|:6)"THE 'HALF-LIFE', T ,OF A":6)" 1/2"4;"RADIOACTIVE ISOTOPE IS DEFINED AS THE TIME AT WHICH THE NUMBER OF RADIOACTIVE NUCLEI HAS DECREASED TO ONE-HALF THE NUMBER AT TIME T = 0." :@;(147);6)"AFTER ONE HALF LIFE HAS ELAPSED, THAT IS, WHEN T = T , THE ACTIVITY N 1/2"; "DROPS TO 1/2 N BY DEFINITION. HENCE 0":<12)" E-LT"<12)"N = N E ",<(12)" 0":F<210)" -LT"c<<10)"1/2 N = N E 1/2"{6)"SINCE THE PHENOMENON OF RADIOACTIVITY IS STATISTICAL IN NATURE THERE IS NO WAY OF KNOWING IN ADVANCE ">"WHICH NUCLEI WILL ACTUALLY DECAY IN A PARTICULAR TIME SPAN. THE STATEMENT THATA CERTAIN RADIOISOTOPE HAS A HALF LIFE "'?"OF 1 HOUR SIGNIFIES THAT EVERY NUCLEUS OF THE SAMPLE HAS A 50 PERCENT CHANCE OFDECAYING IN ANY 1 HOUR PERIOD. THIS"?"DOES NOT MEAN A 100 PERCENT PROBABILITY OF DECAYING IN 2 HOURS. THE DECAY CONSTANT L IS THE SAME AS THE "?"PROBABILITY PER UNIT TIME FOR THE DECAY OF A NUCLEUS OF THAT ISOTOPE.":@(147):""P@6)"THE HALF LIFE OF A RADIOISOTOPE ISNOT THE SAME AS ITS":k@10)" "@10)"MEAN LIFETIME T":""@"WHICH IS DEFINED AS THE RECIPROCAL OF ITS DECAY PROBABILITY.":"@"10)" 1"@,10)"T = "A610)" L":)A@10)" 1 T"OAJ10)"T = =1/2 = 1.44 T "xAT10)" L 0.693 1/2":A^(147)Ah""Br6)"FOLLOWING IS A CHART SHOWING THE DECAY CURVE FOR THE RADIOACTIVE ELEMENT POLONIUM (T = 140 DAYS)"B|6)" 1/2":#B (147)-B 1,1FB 1,66,110 280,110pB 1,8,14," "B 1,66,110 66,10B 1,8,15,"0 140 280 420 560 700"B 1,8,16," TIME, DAYS"B 1,6,1,"1-"B 1,104,50,3,3 C 1,4,6,"1/2-"C 1,4,8,"1/4-"1C 1,145,65,3,3DC 1,4,9,"1/8-"WC 1,185,75,3,3iC 1,66,10,3,3C 1,66,10 104,50 145,65 185,75 220,80 300,84C& 1,0,0,"ACTIVITY"C0 1,6,22,"DECAY CURVE FOR POLONIUM": 20: 0 D: (147):53280,1:53281,2DD""DN6)"THE FACT THAT RADIOACTIVE DECAY FOLLOWS THE EXPONENTIAL LAW IS STRONG EVIDENCE THAT RADIOACTIVITY IS" EX"STATISTICAL IN NATURE. THUS, WHILE EVERYNUCLEUS IN A SAMPLE OF RADIOACTIVE MATERIAL HAS A CERTAIN PROBABILITY OF"Eb"DECAYING THERE IS NO WAY OF KNOWING IN ADVANCE WHICH NUCLEI WILL ACTUALLY DECAYIN A PARTICULAR TIME INTERVAL. IF THERE" Fl"IS A LARGE NUMBER OF NUCLEI IN A SAMPLE THE ACTUAL FRACTION OF IT THAT DECAYS INA PARTICULAR TIME INTERVAL WILL BE VERY"WFv"CLOSE TO THE PROBABILITY FOR ANY INDIVIDUAL NUCLEUS TO DECAY."]FuF(147):""F6)"THE USER OF A RADIOACTIVE MATERIALIS OFTEN MORE INTERESTED IN THE NUMBER OF DISINTIGRATIONS PER UNIT OF TIME THAN"kG"IN THE TOTAL NUMBER OF ATOMS PRESENT IN THE SAMPLE. EXPERIMENTS HAVE SHOWN THAT IN ONE GRAM OF THE ELEMENT RADIUM"qGG16)" 10"G16)"3.71 X 10 "GG10)"ATOMS DECAY EACH SECOND"GG (147)G""H16)"DEFINITION" H""AH 6)"ANY RADIOACTIVE SOURCE THAT UNDERGOES"XH16)" 10"H 16)"3.71 X 10 DECAYS PER SECOND"H*H46)"IS SAID TO HAVE AN ACTIVITY OF"H>12)"1 CURIE.":HH (147):""0IR" THE NATURALLY RADIOACTIVE ELEMENTS ":[I\(147):"": 53280,3:53281,2If6)"WE HAVE DISCUSSED THE PRODUCTION OF THE ELEMENT RADON BY THE DISINTEGRATION OF THE ELEMENT RADIUM."TJp"THE ATOMIC MASS OF RADIUM IS 226, AND ITS DAUGHTER ATOM OF RADON IS 222 BECAUSE AN ALPHA PARTICLE OF MASS 4 HAS"Jz"BEEN LOST. THIS TRANSFORMATION FITS INTOA VERY INTERESTING SCHEME WHICH HAS BEENWORKED OUT FROM MANY EXPERIMENTS.":;K6)"LET US NOW EXAMINE THE GENETIC RELATIONS IN THIS CHAIN OF THE NATURAL RADIOACTIVE ELEMENTS.":SK(147):""yK12)" THE URANIUM SERIES ":K(147):"" L6)"THE URANIUM SERIES ARISES FROM AN ISOTOPE 238 OF URANIUM. IN THE NEXT FIGURE, THE VARIOUS MEMBERS OF THIS"~L"FAMILY ARE SHOWN. HERE THE ATOMIC NUMBERIS PLOTTED HORIZONTALLY, AND THE ATOMIC MASS IS PLOTTED VERTICALLY.":L (147)L 1,1L 1,10,170 320,170L 1,1,22,"81 82 83 84 85 86 87 88 89 90 91 92"M 1,1,23,"TL PB BI PO AT RN FR RA AC TH PA U"LM 1,0,1,"-------------------------------------240 "M 1,0,2,"-------------------------------------238 "M 1,0,3,"-------------------------------------236 "M 1,0,4,"-------------------------------------234 ",N 1,0,5,"-------------------------------------232 "dN$ 1,0,6,"-------------------------------------230 "N. 1,0,7,"-------------------------------------228 "N8 1,0,8,"-------------------------------------226 " OB 1,0,9,"-------------------------------------224 "DOL 1,0,10,"-------------------------------------222"|OV 1,0,11,"-------------------------------------220"O` 1,0,12,"-------------------------------------218"Oj 1,0,13,"-------------------------------------216"$Pt 1,0,14,"-------------------------------------214"\P~ 1,0,15,"-------------------------------------212"P 1,0,16,"-------------------------------------210"P 1,0,17,"-------------------------------------208"Q 1,0,18,"-------------------------------------206"Q 1,156,10 156,1606Q 1,179,10 179,160OQ 1,202,10 202,160hQ 1,225,10 225,160Q 1,248,10 248,160Q 1,275,10 275,160Q 1,133,10 133,160Q 1,106,10 106,160Q 1,83,10 83,160Q 1,58,10 58,160R 1,35,10 35, 160*R 1,10,10 10,160;R 1,34,2,"1"RR( 1,28,4,"2 3 4"cR2 1,28,6,"5"tR< 1,22,8,"6"RF 1,16,10,"7"RP 1,10,12,"8"RZ 1,4,14,"9 10 11"Rd 1,0,16,"12 13 14 15"Rn 1,3,18,"16"Sx 1,4,4,"THE URANIUM SERIES": 20: 0S (147)|S 6)"THE FOLLOWING TABLE WILL HELP THE STUDENT IDENTIFY THE ISOTOPES ON THE URANIUM SERIES CHART"S S (147)S 6)"# ON ISOTOPE PARTICLE PRODUCT"S 6)"CHART OR NAME EMITTED NUCLEUS"S T 6)" 1 U-238 ALPHA TH-234"\T 6)" 2 TH-234 (A)BETA PA-234 (U-X1)"T 6)" TH-234 (B)BETA PA-234 (U-X1)"T 6)" 3 PA-234 BETA U-234 (U-Z)"!U 6)" PA-234 BETA U-234 (U-X2)"MU 6)" 4 U-234 ALPHA TH-230"U 6)" 5 TH-230 ALPHA RA-226 (IONIUM)"U 6)" 6 RA-226 ALPHA RN-222"U 6)" 7 RN-222 ALPHA PO-218"*V" 6)" 8 PO-218 ALPHA PB-214 (RA A)"lV, 6)" 9 PB-214 BETA BI-214 (RA B)"rV6 V@ (147)VJ 6)"# ON ISOTOPE PARTICLE PRODUCT"VT 6)"CHART OR NAME EMITTED NUCLEUS"W^ 6)" 10 BI-214 (A)BETA PO-214 (RA C)"GWh 6)" (B)ALPHA TL-210"Wr 6)" 11 PO-214 ALPHA PB-210 (RA C')"W| 6)" 12 PB-210 BETA BI-210 (RA D)"X 6)" 13 BI-210 BETA PO-210 (RA E)"PX 6)" 15 PO-210 ALPHA PB-206 (RA-F)"X 6)" 16 PB-206 STABLE STABLE (RA G)":X (147)X ""+Y 6)"THE ACTINIUM SERIES ARISES FROM ANISOTOPE 235 OF URANIUM. THE NEXT CHART AND TABLE SHOW THIS SERIES."::(147)4Y 1,1MY 1,10,170 320,170Y 1,1,22,"81 82 83 84 85 86 87 88 89 90 91 92"Y ""Y 1,1,23,"TL PB BI PO AT RN FR RA AC TH PA U"Y 1,0,1,"-------------------------------------241 ",Z 1,0,2,"-------------------------------------239"dZ 1,0,3,"-------------------------------------237 "Z 1,0,4,"-------------------------------------235 "Z 1,0,5,"-------------------------------------233 " [& 1,0,6,"-------------------------------------231 "D[0 1,0,7,"-------------------------------------229 "|[: 1,0,8,"-------------------------------------227 "[D 1,0,9,"-------------------------------------225 "[N 1,0,10,"-------------------------------------223"$\X 1,0,11,"-------------------------------------221"\\b 1,0,12,"-------------------------------------219"\l 1,0,13,"-------------------------------------217"\v 1,0,14,"-------------------------------------215"] 1,0,15,"-------------------------------------213"<] 1,0,16,"-------------------------------------211"t] 1,0,17,"-------------------------------------209"] 1,0,18,"-------------------------------------207"] 1,156,10 156,160] 1,179,10 179,160] 1,202,10 202,160^ 1,225,10 225,160)^ 1,248,10 248,160B^ 1,275,10 275,160\^ 1,133,10 133,160u^ 1,106,10 106,160^ 1,83,10 83,160^ 1,58,10 58,160^ 1,35,10 35, 160^ 1,10,10 10,160^ 1,34,4,"1"^* 1,28,6,"2 3" _4 1,24,8,"4 5"_> 1,22,10,"6"/_H 1,16,12,"7"A_R 1,10,14,"8"X_\ 1,4,16,"9 10 11"m_f 1,1,18,"11 12"_p 1,4,6,"ACTINIUM SERIES"_z 20: 0:(147)_ 6)"# ON ISOTOPE PARTICLE PRODUCT"_ 6)"CHART OR NAME EMITTED NUCLEUS"` ,` 6)" 1 U-235 ALPHA TH-231"n` 6)" 2 TH-231 BETA PA-231 (U-Y) "` 6)" 3 PA-231 ALPHA AC-227"` 6)" 4 AC-227 BETA TH-227 (AC) " a 6)" 5 TH-227 ALPHA RA-223 (RD-AC)"ba 6)" 6 RA-223 ALPHA RN-219 (AC-X)"a 6)" 7 RN-219 ALPHA PO-215 (ACTINON) "a 6)" 8 PO-215 ALPHA PB-211 (AC-A)+b 6)" 9 PB-211 BETA BI-211 (AC-B)"b 6)" 10 BI-211 (A)BETA PO-211 (0.32%) (AC-C) 10 BI-211 (B)ALPHA TL-207 (99.68%) (AC-C)"c6)" 11 PO-211 ALPHA PB-207 (AC-C')"-c6)" 12 PB-207 STABLE"::(147)c6)"NOTE: IN THE ACTINIUM SERIES THE DECAYS OF AC-227 AND BI-211 MAY PROCEED EITHER BY ALPHA EMISSION AND THEN BETA"c$"EMISSION OR IN REVERSE ORDER.":Kd.6)"THE STUDENT IS ADVISED THAT AN INTERESTING QUIZ ON THE ACTINIUM DECAY SERIES IS AVAILABLE FOR DOWNLOADING ON "`d8"Q-LINK.":""dB6)"NAMES LIKE IONIUM, MESOTHORIUM, ACTINON, ETC (SHOWN IN PARENTHESIS IN THE TABLES) ARE SURVIVORS OF OUR EARLY"dL"STUDIES OF RADIOACTIVITY.": eV (147)e`6)"MOST OF THE RADIOACTIVE ELEMENTS FOUND IN NATURE ARE MEMBERS OF FOUR RADIOACTIVE SERIES CONSISTING AS WE HAVE"fj"SEEN OF A SUCCESSION OF DAUGHTER PRODUCTS ALL ULTIMATELY DERIVED FROM A SINGLE PARENT NUCLIDE. THE FACT THAT"ft"THERE ARE EXACTLY FOUR SUCH SERIES FOLLOWS FROM THE FACT THAT ALPHA DECAY REDUCES THE MASS NUMBER OF A NUCLEUS BY 4."f~6)"THUS THE NUCLIDES WHOSE MASS NUMBERS ARE ALL GIVEN BY":f14)"A = 4N (1)":og"WHERE N IS AN INTEGER, CAN DECAY INTO ONE ANOTHER IN DESCENDING ORDER OF MASS NUMBER. RADIOACTIVE NUCLIDES WHOSE MASS"g"NUMBERS OBEY EQUATION (1) ARE SAID TO BEMEMBERS OF THE 4N SERIES. THE FOUR RADIOACTIVE SERIES ARE SHOWN ON THE NEXTTABLE"::(147) h""6h6)"THE FOUR RADIOACTIVE SERIES":""dh"MASS SERIES PARENT HALF STABLE"h"NUMBER LIFE END"h" YEARS PRODUCT"h"" i" 232 10 208"Oi"4N THORIUM TH 1.39 X 10 PB "zi" 90 82"i" 237 6 209"i "4N+1 NEPTUNIUM NP 2.25 X 10 BI "j" 93 83"4j" 238 9 206"cj("4N+2 URANIUM U 4.51 X 10 PB "j2" 92 82"j<" 235 8 207"jF"4N+3 ACTINIUM U 7.07 X 10 PB "kP" 92 82"JkZ"":bkd(147):""kn12)" ALPHA DECAY ":kx(147)l6)"THE TOTAL BINDING FORCE IN A NUCLEUS IS APPROXINATELY PROPORTIONAL TOITS MASS NUMBER BECAUSE THE ATTRACTIVE"l"FORCES BETWEEN NUCLEONS ARE OF SHORT RANGE. THE REPULSIVE ELECTROSTATIC FORCES BETWEEN PROTONS ARE, HOWEVER, OF "l"UNLIMITED RANGE, AND THEREFORE THE TOTALDISRUPTIVE FORCES IN A NUCLEUS IS APPROXIMATELY PRPORTIONAL TO" m14)" 2"m14)"Z":m6)"NUCLEI CONTAINING 210 OR MORE NUCLEONS ARE SO LARGE THAT THE SHORT RANGE NUCLEAR FORCES THAT HOLD THEM" n"TOGETHER ARE JUST BARELY ABLE TO COUNTERBALANCE THE MUTUAL REPULSION OF THEIR PROTONS. ALPHA DECAY OCCURS IN"hn"SUCH NUCLEI AS A MEANS OF REDUCING THEIRSIZE AND THUS INCREASING THEIR STABILITY.":tn(147)n6)"BUT THE STUDENT MAY ASK, WHY ARE ALPHA PARTICLES EMITTED RATHER THAN, SAYPROTONS OR OTHER NUCLEI? THE ANSWER IS"oo"TO BE FOUND IN THE HIGH BINDING ENERGY OF THE DAUGHTER NUCLEI AND THE KINETIC ENERGY Q RELEASED WHEN VARIOUS PARTICLES"o"ARE EMITTED BY A HEAVY NUCLEUS. THIS IS GIVEN BY":o10)" 2"o10)"Q = (M - M - M )C "p10)" I F A" p"WHERE"Bp"6)"M = MASS OF THE INITIAL NUCLEUS I"wp,6)"M = MASS OF THE FINAL NUCLEUS F"p66)"M = MASS OF THE ALPHA PARTICLE A":p@(147)6qJ6)"WE FIND THAT ALPHA PARTICLE EMISSION IS THE ONLY ENERGETICALLY POSSIBLE DECAY MODE BECAUSE OTHER DECAY"qT"MODES REQUIRE THAT ENERGY BE SUPPLIED FROM OUTSIDE THE NUCLEUS. FOR EXAMPLE ALPHA DECAY IN URANIUM-232 RESULTS IN "5r^"THE RELEASE OF 5.4 MILLION ELECTRON VOLTS (MEV), WHILE 6.1 MEV WOULD HAVE TOFURNISHED IF A PROTON IS TO BE EMITTED "prh"AND 9.6 MEV IF A HELIUM-3 NUCLEUS IS TO BE EMITTED."rr6)"THE KINETIC ENERGY T OF THE EMITTED ALPHA PARTICLE IS NEVER QUITE EQUAL TO THE DISINTEGRATION ENERGY Q "cs|"BECAUSE MOMENTUM MUST BE CONSERVED. THE NUCLEUS MUST RECOIL WITH A SMALL AMOUNT OF KINETIC ENERGY WHEN THE ALPHA "s"PARTICLE IS EMITTED. IT IS LEFT TO THE STUDENT TO SHOW THAT":s10)" A-4"s10)"T = Q"s10)" A":s(147):""|t6)"THUS IN THE DECAY OF RADON-222 WHERE THE ENERGY OF THE EMITTED ALPHA PARTICLE IS 5.486 MEV THE TOTAL KINETIC "t"ENERGY RELEASED IS Q = 5.587 MEV.":t(147)t""t12)" THEORY OF ALPHA DECAY ":fu6)"THE ATTRACTIVE FORCES BETWEEN NUCLEONS ARE OF SHORT RANGE, THUS THE TOTAL BINDING FORCE IN A NUCLEUS IS "u"APPROXIMATELY PROPORTIONAL TO ITS MASS NUMBER A, THE NUMBER OF NUCLEONS IT CONTAINS. THE REPULSIVE ELECTROSTATIC"^v"FORCES BETWEEN PROTONS, HOWEVER, ARE OF UNLIITED RANGE, AND THE TOTAL DISRUPTIVEFORCE IN A NUCLEUS IS APPROXIMATELY"xv" 2"v"PROPORTIONAL TO Z ." w6)"NUCLEI WHICH CONTAIN 210 OR MORE NUCLEONS ARE S0 LARGE THAT THE SHORT- RANGE NUCLEAR FORCES THAT HOLD THEM "w&"TOGETHER ARE BARELY ABLE TO COUNTERBALANCE THE MUTUAL REPIULSION OF THEIR PROTONS. ALPHA DECAY OCCURS IN "w0"SUCH NUCLEI AS A MEANS OF INCREASING THEIR STABILITY BY REDUCING THEIR SIZE.":w:(147):""xxD6)"THE NEXT FIGURE IS A PLOT OF THE POTENTIAL ENERGY V OF AN ALPHA PARTICLE AS A FUNCTION OF THE DISTANCE R FROM THE"xN"CENTER OF A HEAVY NUCLEUS.":xX(147)xb1,1xl1,0,21,"T = KINETIC ENERGY OF ALPHA PARTICLE"yv1,0,22,"R = NUCLEAR RADIUS":1,0,23," 0"2y1,20,20 20,144 280,144Ay1,2,1,"V"Ry1,38,17,"R"qy1,20,120 60,120 60,40y1,220,30,160,110,180,265y1,7,18,"":1,8,19,"R":1,9,20,"0"y1,12,4,"POTENTIAL ENERGY"y1,13,5,"OF ALPHA PARTICLE"z1,14,7," 2".z1,14,8," 2ZE "Kz1,14,9,"V(X) = "jz1,14,10," 4(PI)E X"z1,16,11," 0"z1,10,9,"_"z 1,20,12," 2"z1,20,13," 2ZE"z 1,20,14,"R = "{*1,20,15," 4(PI)E T"{41,24,16," 0"2{>1,107,107 150,115C{H1,13,15,"T"{{R1,13,14,":":1,13,13,".":1,13,16,":":1,13,17,":"{\ 20:(147): 0{f""|p6)"NOTE THAT THE HEIGHT OF THE POTENTIAL BARRIER FOR THE ALPHA PARTICLEIS ABOUT 25 MILLION ELECTRON VOLTS. THIS"|z"IS EQUAL TO THE WORK THAT MUST BE DONE AGAINST THE REPULSIVE ELECTROSTATIC FORCE TO BRING AN ALPHA PARTICLE FROM"}"INFINITY TO A POSITION ADJACENT TO THE NUCLEUS BUT JUST OUTSIDE THE RANGE OF THE STRONG ATTRACTIVE NUCLEAR FORCES."}"WE CAN THEREFORE REGARD AN ALPHA PARTICLE IN A NUCLEUS AS BEING INSIDE A BOX WHOSE WALLS REQUIRE AN ENERGY OF 25"~"MEV TO BE SURMOUNTED. HOWEVER WE KNOW THAT ALPHA PARTICLES OF ONLY ABOUT 4 TO 9 MEV ENERGY DO ESCAPE FROM THE NUCLEID ";~"INVOLVED. HOW IS THIS POSSIBLE?":G~(147)~6)"ALPHA DECAY CANNOT BE EXPLAINED ONTHE BASIS OF CLASSIC ARGUMENTS. HOWEVER GAMOV AND GURNEY IN 1938 WERE ABLE TO"9"SHOW THAT ALPHA DECAY CAN BE EXPLAINED BY QUANTUM MECHANICS. THE BASIC NOTIONS OF THIS THEORY ARE THAT AN ALPHA""PARTICLE IS IN CONSTANT MOTION AND IS CONTAINED IN THE NUCLEUS BY THE SURROUNDING POTENTIAL BARRIER, AND THAT "7"THERE IS A SMALL LIKELIHOOD THAT THE PARTICLE MAY PASS TRHOUGH THE BARRIER EACH TIME A COLLISION OCCURS. THUS THE"|"DECAY PROBABILITY PER UNIT TIME LAMBDA CAN BE EXPRESSED AS":12)"LAMBDA = FP":6)"WHERE F IS THE NUMBER OF TIMES PERSECOND AN ALPHA PARTICLE WITHIN A NUCLEUS STRIKES THE POTENTIAL BARRIER "v"AROUND IT AND P IS THE PROBABILITY THAT THE PARTICLE WILL BE TRANSMITTED THROUGHTHE BARRIER.":(147)6)"LET US SUPPOSE THAT THERE IS ONLY ONE ALPHA PARTICLE IN THE NUCLEUS AND THAT IT MOVES BACK AND FORTH ALONG A "" V"<$"NUCLEAR DIAMETER, F = "^." 2R":҂8"WHERE V IS THE ALPHA-PARTICLE VELOCITY WHEN IT EVENTUALLY LEAVES THE NUCLEUS AND R IS THE NUCLEAR RADIUS."B6)" 7"%L6)"TYPICALLY V = 2 X 10 METERS PER SECOND"FV" -14"m`6)" AND R = 10 METERS":j" 21"t"HENCE F = 10 PER SECOND":~(147)56)"IN QUANTUM MECHANICS A MOVING PARTICLE IS REGARDED AS A WAVE, AND THE RESULT IS A SMALL BUT DEFINITE VALUE FOR P.":F(147):1,11,6,20,"A BEAM OF PARTICLES CAN LEAK THROUGH A FINITE BARRIER"1,4,6,"":1,4,5,"^":1,4,4,"V"1,80,40,50,100,134,225:1,154,173,50,100,310,351,2,10,"WAVE":1,2,11,"FUNCTION"71,219,22,50,100,186,225T1,275,210,50,100,330,30q1,231,30,50,100,155,2041,40,119 320,1191,190,120 190,10 200,10 200,1201,40,55 191,55 191,11 201,11 201,55 320,551,20,3,"T--". 1,27,10,"EXPONENTIAL":1,195,110 220,90q1,16,18,"SINUSOIDAL":1,126,90 146,135:1,192,135 219,1261,23,15,"0 L"( 20: 0:(147)2""<6)"WHILE THE ALPHA PARTICLE IN A NUCLEUS MAY STRIKE ITS CONFINING WALLS ": F12)" 21".P12)"10 TIMES PER SECOND"\Z" 10"هd"IT MAY HAVE TO WAIT AN AVERAGE OF 10 YEARS TO ESCAPE FROM SOME NUCLEI! THUS THE PROBABILITY OF THE ALPHA PARTICLE"on"ESCAPING FROM A NUCLEUS IN A QUANTUM MECHANICAL TREATMENT IS NOT EXACTLY ZEROAS CLASSICAL THEORY PREDICTS BUT IS, INSTEAD, VERY SMALL.":x(147):""12)" BINDING ENERGY ":(147).6)"STABLE NUCLEI HAVE SMALLER MASSES THAN THE COMBINED MASSES OF THEIR CONSTITUENT PARTICLES. THE NUCLEUS OF""LITHIUM-6, FOR EXAMPLE, HAS A MASS OF 6.01697 ATOMIC MASS UNITS, WHILE THE THREE NEUTRONS AND THREE PROTONS OF "&"WHICH IT IS COMPOSED HAVE A TOTAL MASS (AS FREE PARTICLES) OF 6.05140 ATOMIC MASS UNITS. THE MISSING MASS IS ""THEREFORE 0.03443 ATOMIC MASS UNITS, WHICH IS EQUIVALENT TO 32.1 MEV. IN ORDER THAT A LITHIUM NUCLEUS BREAK UP " "INTO INDIVIDUAL NUCLEONS, THEN, 32.1 MEVOF ENERGY MUST BE SUPPLIED TO IT FROM ANEXTERNAL SOURCE."6)"THE ENERGY EQUIVALENT OF THE MASS DISCREPANCY IN A NUCLEUS IS CALLED ITS BINDING ENERGY AND IS A MEASURE OF THE ""STABILITY OF THE NUCLEUS.":(147)1,11,43,20 43,163 300,163 I 0 27 3 :1,5I,20,"":I31,5,21," 20 60 100 140 180"z1,5,22," 40 80 120 160 ":1,12,24,"MASS NUMBER A" J 0 18 2 :1,4,2J,"-": J "1,2,2,"9":1,2,4,"8":1,2,6,"7":1,2,8,"6":1,2,10,"5":1,2,12,"4":1,2,14,"3":1,2,16,"2":1,2,18,"1"|,1,47,145,3,2:1,50,48,3,2:1,52,75,3,2:1,63,36,3,2:1,83,26,3,2:1,108,23,3,2:1,140,25,3,2:1,265,36,3,261,2,1,"BE/NUCLEON (MEV)"@1,47,145 50,48 52,75 63,36 83,26 108,23 140,25 265,36 320, 40J1,18,12,"BINDING ENERGY VERSUS"/T1,18,13,"ATOMIC NUMBER"D^ 20: 0:(147)Th""rr12)" BETA DECAY ":~|(147)6)"NUCLEI CONTAIN INTERNAL ENERGY THAT IS QUANTIZED, AND THUS THE NUCLEUS HAS ENERGY LEVELS BETWEEN WHICH "r"TRANSITIONS CAN OCCUR. ONE OF THE PROCESSES BY WHICH NUCLEI CAN MAKE THESETRANSITIONS IS BETA DECAY, IN WHICH AN ""ELECTRON (POSITIVE OR NEGATIVE) AND A NEUTRINO ARE EMITTED. THE BETA DECAY PROCESS CAN BE EXPLAINED BY ASSUMING"?"THAT A NEUTRON TRANSFORMS ITSELF INTO A PROTON, ACCORDING TO THE SCHEME":U8)" -"{8)"N -> P + E + ANTINEUTRINO":(147)6)"HENCE WHEN A NUCLEUS EMITS A BETA PARTICLE (A NEGATIVE ELECTRON), THE ATOMIC NUMBER OF THE NUCLEUS INCREASES "e"BY ONE UNIT, BUT THE MASS NUMBER DOES NOT CHANGE. FOR EXAMPLE, WHEN THE NUCLEUS ":x12)" 234"12)" TH "12)"90":ב"EMITS A BETA PARTICLE, THE RESIDUAL NUCLEUS IS":12)" 234"12)" PA " 12)"91":&(147)06)"SOME NUCLEI, INSTEAD OF EMITTING NEGATIVE ELECTRONS, EMIT POSITIVE ELECTRONS (POSITRONS), WHICH CARRY A":"POSITIVE CHARGE +E, THEREFORE THE RESIDUAL NUCLEUS, AFTER POSITRON EMISSION, HAS A SMALLER ATOMIC NUMBER BY"BD"ONE UNIT. FOR EXAMPLE WHEN THE NUCLEUS":TN12)" 13"dX12)" N"ub12)" 7":l"EMITS A POSITRON (AND A NEUTRINO), THE RESIDUAL NUCLEUS IS":̓v12)" 13"ܓ12)" C"12)" 6"::(147)46)"THE TWO TYPES OF BETA-DECAY ARE DESIGNATED":T14)" - +"u14)"(BETA) AND (BETA)":6)"IF WE DESIGNATE THE PARENT NUCLEUSBY X AND THE DAUGHTER NUCLEUS BY Y, WE MAY WRITE THE EQUATIONS FOR THE TWO " "KINDS OF DECAY AS":&6)" A A -"Q6)" X -> Y + E + ANTINEUTRINO"f6)"Z Z+1"q"AND"6)" A A +"6)" X -> Y + E + NEUTRINO"̕ 6)"Z Z-1":ؕ(147) ""*12)" THE NEUTRINO "::(147)4"">6)"IT HAS BEEN OBSERVED THAT THE ELECTRONS AND POSITRONS IN THESE DECAY MODES ARE EMITTED WITH A WIDE RANGE OF "H"KINETIC ENERGIES FROM ZERO TO A MAXIMUM COMPATIBLE WITH THE TOTAL ENERGY AVAILABLE. THE NEXT FIGURE SHOWS HOW "R"THE DISTRIBUTION OF ENERGY AMONG BETA PARTICLES VARIES WITH THE ENERGY OF THE BETA PARTICLES IN THE DECAY OF RADIUM E":\(147)f1,1Ηp1,0,1,"# OF BETA PARTICLES"z1,43,20 43,163 300,163 I 0 30 3 :1,5I,20,"":ID1,5,21," .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0"q1,6,23,"ENERGY OF BETA PARTICLE IN MEV"1,18,8,"DISTRIBUTION OF ENERGY"1,18,9,"AMONG BETA PARTICLES"ޘ1,18,10,"EMITTED IN BETA DECAY"1,18,11,"OF RADIUM E, A = 210"( J 0 18 2 :1,4,2J,"-": J1,2,2,"18":1,2,4,"16":1,2,6,"14":1,2,8,"12":1,2,10,"10":1,2,12,"8":1,2,14,"6":1,2,16,"4":1,2,18,"2":1,2,20,"0"Ù1,320,50,200,110,185,260ߙ1,82,120,48,100,314,601,35,17,"T "1,35,18," MAX"'1,315,160,3,2:1,315,160,10 20@ 0:(147)$6)"WE CAN WRITE THE EQUATION FOR THE RADIOACTIVE DISINTEGRATION OF RADIUM E AS FOLLOWS".8)" 210 210 -"88)" BI --> PO + E + Q"B8)"83 84"wL"WHERE Q IS THE DISINTEGRATION ENERGY ANDIS EQUAL TO THE DIFFERENCE IN MASSES OF THE INITIAL AND FINAL PARTICLES."V6)"WE MIGHT THINK THAT ALL THE BETA PARTICLES EMITTED BY THE BI-210 NUCLEI WOULD HAVE THE SAME VELOCITY AS MEASURED"``"BY A BETA-RAY SPECTROMETER. LET US PAUSEHERE TO SHOW THE PRINCIPLE OF THIS USEFUL INSTRUMENT.":wj(147): 1,1:1,2t1,6,1,"A BETA-RAY SPECTROMETER"~1,164,140,80,64,270,90:1,164,140,120,96,270,90:1,1:1,164,140,100,80,265,90O1,44,140 60,140 60,146 44,146 44,140:1,68,140 84,140 84,146 68,146 68,1401,44,150 60,150 60,156 44,156 44,150:1, 68,150 84,150 84,156 68,156 68,150䝜1,46,152,1:1,70,152,1:1,46,142,1:1,70,142,11,2:1,64,165,3,2:1,64,165,191,1:1,9,21,"BETA EMITTER":1,11,18,"SLITS":1,264,145,4,3:1,266,145,1:1,244,140 260,140:1,268,140 284,1401,28,19,"DETECTOR"1,0,23,"VARIABLE MAGNETIC FIELD B OUT OF SCREEN":1,0,22," "01,2:1,163,140 163,70:1,20,8,"^":1,21,12,"R": 20L 0:(147):""ȟ6)"IF R IS THE RADIUS OF THE INSTRUMENT THE MOMENTUM P OF ANY BETA PARTICLE THAT CAN TRAVERSE THE ""INSTRUMENT IS GIVEN BY":12)"P = EBR":U "WHERE E IS THE ELECTRONIC CHARGE AND B IS THE MAGNETIC FLUX DENSITY.":m(147):""4)" THE DILEMMA OF BETA-RAY EMISSION "::(147):""1(6)"AS SHOWN ON THE GRAPH OF THE DISTRIBUTUION OF ENERGY AMONG ELECTRONS EMITTED IN THE DECAY OF RADIUM E ONE CAN"2"SEE THAT THE ELECTRON ENERGIES VARY CONTINUOUSLY FROM 0 TO A MAXIMUM VALUE ":<18)"T "F18)" MAX":P"WHICH HAS A CHARACTERISTIC VALUE FOR A PARTICULAR NUCLIDE. FOR RADIUM E THE VALUE IS":*Z18)"T = 1.17 MEV" P + E + ANTINEUTRINO":6)"NOTE THAT THE SPIN OF EACH OF THE PARTICLES INVOLVED IN THIS PROCESS IS 1/2 AND THEREFORE SPIN (AND ANGULAR ""MOMENTUM IS CONSERVED. WITHOUT THE NEUTRINO ANGULAR MOMENTUM WOULD NOT NE CONSERVED." : (147)""6)"IT IS FURTHER SUPPOSED THAT THE NEUTRINO CARRIES WITH IT A MOMENTUM EXACTLY BALANCING THE MOMENTA OF THE "Ѭ"ELECTRON AND THE RECOILING DAUGHTER NUCLEUS." :(147):""10)" POSITRON EMISSION ":(147))&""06)"POSITIVE ELECTRONS, USUALLY CALLEDPOSITRONS, WERE DISCOVERED IN 1932 IN COSMIC RAY STUDIES. IN 1934 POSITRONS"!:"WERE FOUND TO BE EMITTED SPONTANEOUSLY BY CERTAIN NUCLEI. POSITRONS HAVE PROPERTIES IDENTICAL WITH THOSE OF THE"D"ELECTRON EXCEPT THEY CARRY A CHARGE OF +E INSTEAD OF -E. POSITRON EMISSION CORRESPONDS TO THE CONVERSION OF A"N"NUCLEAR PROTON INTO A NEUTRON, A POSITRON, AND A NEUTRINO"X10)" +"!b10)"P --> N + E + NEUTRINO":9l(147):""v6)"IT SHOULD BE NOTED HERE THAT WHILEA FREE NEUTRON CAN UNDERGO BETA DECAY INTO A PROTON, THE LIGHTER PROTON CANNOT""BE TRANSFORMED INTO A NEUTRON EXCEPT WITHIN A NUCLEUS.": (147):(147)6)"POSITRON EMISSION LEADS TO A DAUGHTER NUCLEUS OF LOWER ATOMIC NUMBER WHILE THE MASS NUMBER IS NOT CHANGED. "ϰ"THE FOLLOWING EQUATIONS ILLUSTRATE THE TWO TYPES OF DECAY.":밨6)" A A -"6)" X -> X + E + ANTINEUTRINO"-6)"Z Z+1":I6)" A A +"p6)" X -> X + E + NEUTRINO"6)"Z Z-1":(147):""6)"THE SHAPE OF THE POSITRON ENERGY SPECTRUM DIFFERS FROM THE SHAPE OF THE BETA PARTICLE SPECTRUM IN THAT THERE ARE""VERY FEW LOW ENERGY POSITRONS EMITTED COMPARED TO THE NUMBER OF LOW ENERGY ELECTRONS EMITTED.":"THE NEXT FIGURE SHOWS THE SPECTRA OF A POSITRON EMITTER AND A BETA EMITTER FOR COMPARISON.": (147): 1,11,0,1,"# OF PARTICLES"; 1,43,20 43,163 300,163b* I 0 30 3 :1,5I,20,"":I41,5,21," .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0">1,6,23,"ENERGY OF PARTICLE IN MEV"ӳH1,22,4,"SOLID LINE:"R1,18,5,"DISTRIBUTION OF ENERGY"\1,18,6,"AMONG BETA PARTICLES"?f1,18,7,"EMITTED IN BETA DECAY"Yp1,18,8,"OF RADIUM E"qz1,24,10,"CIRCLES:"1,20,11,"NUMBER OF POSITRONS"1,20,12,"EMITTED IN DECAY OF"д1,20,13,"COPPER-64"1,180,82,3,2:1,180,82,1 J 0 18 2 :1,4,2J,"-": J21,320,50,200,110,185,260N1,82,120,48,100,314,60b1,35,17,"T "v1,35,18," MAX"1,55,155,3,2:1,65,120,3,2:1,75,100,3,2:1,85,95,3,2:1,200,161,3,2:1,95,100,3,2:1,110,115,3,2:1,130,127,3,21,150,139,3,2:1,170,151,3,21,55,155,1:1,65,120,1:1,75,100,1:1,85,95,1:1,200,161,1:1,95,100,1:1,110,115,1:1,130,127,1:1,150,139,11,170,151,1 20:(147): 0""޶10)" INVERSE BETA DECAY ":$(147)p.6)"IT IS POSSIBLE FOR A NUCLEUS TO ABSORB AN ELECTRON. SUCH 'ELECTRON CAPTURE' IS EQUIVALENT TO POSITRON EMISSION."86)"IT IS ALSO POSSIBLE FOR A NUCLEUS TO ABSORB AN ANTINEUTRINO. THIS PROCESS IS EQUIVALENT TO NEUTRINO EMISSION.":: B6)"THUS THE REACTION":0L10)" +"WV10)"P + ANTINEUTRINO -> N + E":`6)"INVOLVES THE SAME PROCESS AS THE DECAY OF A PROTON WITHIN A NUCLEUS":j10)" +"t10)"P -> N + E + NEUTRINO":'~6)"THIS LATER REACTION IS CALLED 'INVERSE BETA DECAY'.":3(147)6)"INVERSE BETA DECAY IS THE SOLE KNOWN MEANS WHEREBY NEUTRINOS (AND ANTINEUTRINOS) INTERACT WITH MATTER.""THIS RESULTS IN THE ABILITY OF NEUTRINOS TO TRAVERSE VAST AMOUNTS OF MATTER.":p6)"THE PROCESS OF INVERSE BETA DECAY PROVIDES A METHOD FOR ESTABLISHING THE EXISTENCE OF NEUTRINOS.":溰6)"IN 1953 REINES, COWAN AND OTHERS DEVISED AN EXPERIMENT TO DETECT THE NEUTRINOS IN THE IMMENSE FLUX OF "a"NEUTRINOS IN THE BEAM OF RADIATION FROM A NUCLEAR REACTOR. IN THIS EXPERIMENT A TANK OF WATER CONTAINING CADMIUM IN""SOLUTION WAS PLACED NEAR THE SAVANNAH RIVER REACTOR. THIS SOLUTION PROVIDED PROTONS TO REACT WITH THE NEUTRINOS THAT"C"THAT EXISTED IN GREAT ABUNDANCE FROM THEMANY BETA DECAYS THAT OCCURRED IN THE REACTOR.":O(147)̼6)"THEY SURROUNDED THE TANK WITH GAMMA RAY DETECTORS IN THE EXPECTATION THAT A PROTON WOULD ABSORB A NEUTRINO TO"L"YIELD A POSITRON AND A NEUTRON. THEY THOUGHT THAT THE POSITRON WOULD BE ANNIHILATED WHEN IT MET AN ELECTRON, AND"ɽ"THAT THE RESULTING PAIR OF 0.51 MEV PHOTONS WOULD BE RECORDED IN THE COUNTERS. THEY ALSO SURMISED THAT THE"F"NEUTRON PRODUCED IN THE REACTION WOULD BE CAPTURED IN A FEW MICROSECONDS BY A CADMIUM NUCLEUS AND THAT THE 8 MEV OF"ľ "RELEASED ENERGY WOULD BE DIVIDED AMONG THREE OR FOUR PHOTONS WHICH COULD BE PICKED UP BY THE GAMMA-RAY DETECTORS. "C"WHEN THE EXPERIMENT WAS CAREFULLY DONE THE EXPECTED VARIATION IN THE FREQUENCY OF NEUTRINO-CAPTURE EVENTS WAS OBSERVED"~"THUS ESTABLISHING THE EXISTENCE OF THE NEUTRINO.":((147):""26)"THE FOLLOWING FIGURE ILLUSTRATES THE REACTIONS OCCURRING IN THE EXPERIMENT.":<(147):1,1:1,2"F1,40,100,12,10UP1,0,0,"A NEUTRINO FROM REACTOR REACTS WITH A"lZ1,0,10,"NEUTRINO"d1,8,12,"------------>"n1,180,100,12,10:1,22,12,"P":1,0,1,"PROTON IN WATER PRODUCING A NEUTRON AND A POSITRON. THE POSITRON AND AN ELECTRON"`x1,0,3,"ANNIHILATE EACH OTHER PRODUCING TWO GAMMA RAYS. THE NEUTRON IS ABSORBED BY"1,0,5,"A CADMIUM NUCLEUS WHICH EMITS 3 OR 4 GAMMA RAYS. THE DETECTION OF THESE GAMMA RAYS IN THE EXPECTED VARIATION "Œ1,0,8,"PROVES THE EXISTENCE OF THE NEUTRINO."F–1,240,120,18,15:1,29,15,"E":1,29,14," +"t 1,178,100 220,113:1,178,100 122,130ª1,1:1,240,170,18,15:1,29,21,"E":1,29,20," -"´1,2:1,120,130,12,10:1,15,16,"N":1,1Sþ1,24,24,"ANNIHILATION":1,270,147 210,147:1,25,18,"<":1,34,18,">":1,240,147,3,2:1,22,17,".5 MEV":1,32,17,".5 MEV"1,90,130,15,12:1,10,16,"CD":1,10,15,"*"1,2,18,"NEUTRON CAPTURE":1,2,19,"IN A FEW MICROSECONDS":1,2,20,"FOLLOWED BY EMISSION":1,2,21,"OF 3-4 GAMMA RAYS" 20: 0:(147) ""?12)" GAMMA DECAY ":K(147)6)"NUCLEI CAN EXIST IN STATES OF DEFINITE ENERGIES, JUST AS ATOMS CAN. MANY NUCLEI, AFTER UNDERGOING ALPHA OR "G"BETA DECAY, ARE LEFT IN AN EXCITED STATEAND RELEASE THEIR EXCESS ENERGY AS ELECTROMAGNETIC RADIATION, ALSO CALLED ""GAMMA RAYS. AN EXCITED NUCLEUS IS OFTEN DENOTED BY AN ASTERISK AFTER ITS USUAL SYMBOL.":"(147)0,"NUCLEI RETURN TO THEIR GROUND STATES BY EMITTING PHOTONS WHOSE ENERGIES CORRESPOND TO THE ENERGY DIFFERENCES"6"BETWEEN THEIR INITIAL AND FINAL STATES. MOST EXCITED NUCLEI HAVE VERY SHORT HALFLIVES AGAINST GAMMA DECAY, BUT SOME"7@"CAN REMAIN EXCITED FOR SEVERAL HOURS. A LONG-LIVED EXCITED NUCLEUS IS CALLED AN 'ISOMER' OF THE SAME NUCLEUS IN ITS GROUND STATE"^J" 87*"T"THUS THE EXCITED NUCLEUS SR HAS A HALF"^" 38"h"LIFE OF 2.8 HOURS AND IS ACCORDINGLY AN"r" 87"|"ISOMER OF SR ."&Ȇ" 38":>Ȑ(147):""eȚ10)" INTERNAL CONVERSION ":qȤ(147)Ȯ6)"AN EXCITED NUCLEUS CAN DECAY TO ITS GROUND STATE BY GAMMA RAY EMISSION OR IT CAN RETURN TO THE GROUND STATE BY "hɸ"GIVING UP ITS EXCITATION ENERGY TO ONE OF THE ELECTRONS ORBITING AROUND IT. THIS PROCESS IS KNOWN AS 'INTERNAL""CONVERSION'. IN THIS PROCESS THE EMITTEDELECTRON HAS A KINETIC ENERGY EQUAL TO THE LOST NUCLEAR EXCITATION ENERGY MINUS"g"THE BINDING OF THE ELECTRON IN THE ATOM.IN ADDITION TO INTERNAL CONVERSION THE NUCLEUS MAY CAPTURE AN ATOMIC ELECTRON,""ANNIHILATE IT, AND EMIT A PHOTON.":(147):""10)" MULTIPLE PROCESSES ":(147):""d6)"WHEN IN A PARTICULAR ENERGY LEVEL,A NUCLEUS MAY SOMETIMES BE ABLE TO MAKE TWO OR THREE ALTERNATE TRANSITIONS. SEE" "THE ACTINIUM SERIES CHART FOR AN EXAMPLE": 6)"THE FOLLOWING ENERGY LEVEL DIAGRAMILLUSTRATES A COMMON PHENOMENUM IN RADIOACTIVITY-BETA DECAY FOLLOWED BY"Q "GAMMA RAY EMISSION FROM THE RESULTANT EXCITED NUCLEUS.":]& (147)g0 1,1: 1,2,1,"ENERGY STATES IN BETA AND GAMMA DECAY"D 1,60,40 140,40:1,110,40 225,100N 1,33,12," X":1,33,13,"Z-1":1,33,11," A*"X 1,6,4,"X":1,7,3,"A*":1,5,5,"Z"bb 1,200,100 260,100:1,200,105 260,105:1,200,110 260,110~l 1,23,8,"BETA EMISSION"v 1,10,16,"GAMMA EMISSION"̀ 1,230,100 230,105:1,235,105 235,110:1,240,100 240,110"Ί 1,210,100 210,170:1,215,105 215,170:1,220,110 220,170;Δ 1,200,170 260,170kΞ 1,33,21," X":1,33,22,"Z-1":1,37,20,"A"Ψ 1,12,21,"GROUND STATE":1,10,12,"EXCITED STATES"β 20: 0:(147)