All 20 Chapters Covered
o o o
SOLUTION MANUAL
o
, Chaptero 1o Solutions
Radiationo Sources
■ Problemo1.1.o RadiationoEnergyoSpectra:oLineovs.oContinuous
Lineo(orodiscreteoenergy):oa,oc,od,oe,of,oandoi.oContinuo
usoenergy:ob,og,oandoh.
■ Problemo1.2.o Conversionoelectronoenergiesocompared.
Sinceotheoelectronsoinoouteroshellsoareo boundolessotightlyothanothoseoinocloseroshells,oconversionoelectronsofromoouteroshellsowillo ha
veogreateroemergingoenergies.o Thus,otheoMoshelloelectronowilloemergeowithogreateroenergyothanoaoKooroLoshelloelectron.
■ Problemo1.3.o Nuclearodecayoandopredictedoenergies.
Weowriteotheoconservationoofoenergyoandomomentumoequationsoandosolveothemoforotheoenergyoofotheoalphaoparticle.o Momentumois
ogiven otheosymbolo"p",o andoenergyois o"E".o Forotheosubscripts,o"al"ostandsoforoalpha,owhileo"b"odenotesotheodaughteronucleus.
pal2 pb2
paloo pbooo0 E
o al oEb Ealoo Ebo oQ and Qoo5.5oMeV
2omal 2omb
Solvingoourosystemoofoequationsoforo Eal,o Eb,o pal,o pb,o weogetotheosolutionsoshownobelow.o Noteothatoweohaveotwoopossibleosetsoofosolutio
nso(thisodoesonotoeffectotheofinaloresult).
mal 5.5omalo
Ebo o5.5o 1o Ealo
maloomb maloomb
3.31662 mal mb 3.31662 mal mb
paloo pboo
maloomb maloomb
Weoareointerestedoinofindingotheoenergyoofotheoalphaoparticleoinothisoproblem,oandosinceoweoknowotheomassoofotheoalphaoparticleoan
dotheo daughtero nucleus,o theo resulto iso easilyo found.o Byosubstitutingoouro knownovalueso ofo maloo4o ando mboo206o intoo ouro derivedoEa
lequationoweoget:
Ealoo5.395oMeV
Noteo:oWeocanoobtainosolutionsoforoallotheovariablesobyosubstitutingomboo206oandomaloo4ointootheoderivedoequationsoaboveo:
Ealoo5.395oMeV Eboo0.105oMeV palooo6.570 amuoMeV pbo oo6.570 amuoMeV
■ Problemo1.4.o Calculationoofo WavelengthofromoEnergy.
Sinceoanox-rayomustoessentiallyobeocreatedobyotheode-excitationoofoaosingleoelectron,otheomaximumoenergyoofoanox-
rayoemittedoinoaotubeooperatingoatoaopotentialoofo195okVomustobeo195okeV.o Therefore,o weocanouseotheoequationoE=h,owhichoisoalso
oE=hc/Λ,ooroΛ=hc/E.o Pluggingoinoouromaximumoenergyovalueointoothisoequationogivesotheominimumox-rayowavelength.
hooc
Λo whereoweosubstituteohoo 6.626oo1034oJoos,o coo299o792o458omoosoandoEoo195okeV
E
1
, Chaptero 1o Solutions
1.01869oJ–m
Λo o 0.0636oAngstroms
KeV
■ Problemo 1.5.o o 235oUFissiono EnergyoRelease.
235 117
Usingotheo reactiono o Uo o o o Snoo118oSn,o andomassovalues,oweocalculateo theomassodefecto of:
Mo235oUoo o Mo117oSnooMo118oSnoo M
oandoan oexpectedoenerg
yoreleaseoofoMc2.
931.5oMeV
oo oo oo o223o MeV
AMU
Thiso iso oneoofotheo mostoexothermicoreactionso availableo toous.o Thiso iso oneoreasono why,oofocourse,o nuclearo powerofromouraniumofis
sionoisosooattractive.
■ Problemo1.6.o SpecificoActivityoofo Tritium.
Here,oweouseotheotextoequationoSpecificoActivityo=o(ln(2)*Av)/oT12*M),owhereoAvoisoAvogadro'sonumber,oT12oisotheohalf-
lifeoofotheoisotope,oandoMoisotheomolecularoweightoofotheosample.
ln2oAvogadroo'osoConstant
SpecificoActivityo
T12oM
3ograms
WeosubstituteoT12oo12.26oyearsoandoM= toogetotheospecificoactivityoinodisintegrations/(gram–year).
mole
1.13492oo1022
SpecificoActivityo
gramo–year
TheosameoresultoexpressedoinotermsoofokCi/goisoshownobelow
9.73okCi
SpecificoActivityo
gram
■ Problemo1.7.o Acceleratedoparticleoenergy.
Theo energyoofoao particleo withochargeo qofallingothroughoao potentialoVo isoqV.o Sinceo V=o 3oMVo isoouromaximumopotentialodifference,o theo
maximumoenergyoofo ano alphao particleo hereo iso q*(3o MV),o whereo qo iso theo chargeo ofo theo alphao particleo (+2).o Theomaximumoalphaoparticl
eoenergyoexpressedoinoMeVoisothus:
Energyoo3oMegaoVoltsoo2oElectronoChargeso o6.o MeV
2
, Chaptero 1o Solutions
■ Problemo1.8.o Photofissionoofo deuterium. 1oDo o Γo
2 1
0ono
1
1opo+o Qo (-2.226oMeV)
Theo reactionoofointerestoiso o 2oDo o o 0oΓo o 1onoo o 1o p+oQo(-2.226oMeV).o Thus,otheoΓomustobringoanoenergyoofoatoleasto2.226oMeV
1 0 0 1
inoorderoforothisoendothermicoreactionotooproceed.o Interestingly,otheooppositeoreactionowillobeoexothermic,oandooneocanoexpectotoofi
ndo2.226oMeVogammaoraysoinotheoenvironmentofromostrayoneutronsobeingoabsorbedobyohydrogenonuclei.
■ Problemo1.9.o NeutronoenergyofromoD-Toreactionobyo150okeVodeuterons.
Weowriteodownotheoconservationoofoenergyoandomomentumoequations,oandosolveothemoforotheodesiredoenergiesobyoeliminatingotheo
momenta.o Inothisosolution,o"a"orepresentsotheoalphaoparticle,o"n"orepresentsotheoneutron,oando"d"orepresentsotheodeuterono(and,oasob
efore,o"p"orepresentsomomentum,o"E"orepresentsoenergy,oando"Q"orepresentsotheoQ-valueoofotheoreaction).
pa2 pn2 pdo2
paoo pnoo pd E
o a E
o n Ed
o EaooEnooEdo oQ
2oma 2omn 2omd
Nexto weo wanto too solveotheo aboveo equationso foro theo unknownoenergieso byoeliminatingotheo momenta.o (Noteo :o Usingo computeros
oftwareosuchoasoMathematicaoisohelpfuloforopainlesslyosolvingotheseoequations).
Weo evaluateo theo solutionobyopluggingoino theo valuesoforo particleo masseso(weo useo approximateovaluesoofo "ma,"o "mn,"ando "md"o ino
AMU,owhichoisookayobecauseoweoareointerestedoinoobtainingoanoenergyovalueoatotheoend).o WeodefineoalloenergiesoinounitsoofoMeV,on
amelyotheo Q-value,oandotheo givenoenergyoofotheodeuterono(bothoenergyovaluesoareo inoMeV).o o Sooweosubstituteomao =o4,omno =o1,omd
=o2,oQo=o17.6,oEdo =o0.15ointooouromomentaoindependentoequations.o Thisoyieldsotwoopossibleosetsoofosolutionsoforotheoenergieso(ino
MeV).oOneocorrespondsotootheoneutronomovingoinotheoforwardodirection,owhichoisoofointerest.
Enoo 13.340o MeV Eaoo 4.410o MeV
Enoo 14.988o MeV Eaoo 2.762o MeV
Nextoweosolveoforotheomomentaobyoeliminatingotheoenergies.oWhenoweosubstituteomao =o4,omno =o1,omdo =o2,oQo=o17.6,oEdo =o0.15ointo
otheseoequationsoweogetotheofollowingoresults.
pd 1 1
pno o 2 3opdo2o o352 pao 8opdo o2 2 3opdo2o o352
5 5 10
Weodooknowotheoinitialomomentumoofotheodeuteron,ohowever,osinceoweoknowoitsoenergy.oWeocano furthero evaluateo ourosolutionsofor
pnoando paobyosubstituting:
pdo
Theoparticleo momentao(oinounitsoof amuMeV )oforoeachosetoofosolutionsoisothus:
pnoo 5.165 paoo 5.940
pnoo 5.475 paoo 4.700
Theo largestoneutronomomentumooccursoinotheoforwardo(+)odirection,osootheohighestoneutronoenergyoofo14.98oMeVocorrespondso
toothisodirection.
3
o o o
SOLUTION MANUAL
o
, Chaptero 1o Solutions
Radiationo Sources
■ Problemo1.1.o RadiationoEnergyoSpectra:oLineovs.oContinuous
Lineo(orodiscreteoenergy):oa,oc,od,oe,of,oandoi.oContinuo
usoenergy:ob,og,oandoh.
■ Problemo1.2.o Conversionoelectronoenergiesocompared.
Sinceotheoelectronsoinoouteroshellsoareo boundolessotightlyothanothoseoinocloseroshells,oconversionoelectronsofromoouteroshellsowillo ha
veogreateroemergingoenergies.o Thus,otheoMoshelloelectronowilloemergeowithogreateroenergyothanoaoKooroLoshelloelectron.
■ Problemo1.3.o Nuclearodecayoandopredictedoenergies.
Weowriteotheoconservationoofoenergyoandomomentumoequationsoandosolveothemoforotheoenergyoofotheoalphaoparticle.o Momentumois
ogiven otheosymbolo"p",o andoenergyois o"E".o Forotheosubscripts,o"al"ostandsoforoalpha,owhileo"b"odenotesotheodaughteronucleus.
pal2 pb2
paloo pbooo0 E
o al oEb Ealoo Ebo oQ and Qoo5.5oMeV
2omal 2omb
Solvingoourosystemoofoequationsoforo Eal,o Eb,o pal,o pb,o weogetotheosolutionsoshownobelow.o Noteothatoweohaveotwoopossibleosetsoofosolutio
nso(thisodoesonotoeffectotheofinaloresult).
mal 5.5omalo
Ebo o5.5o 1o Ealo
maloomb maloomb
3.31662 mal mb 3.31662 mal mb
paloo pboo
maloomb maloomb
Weoareointerestedoinofindingotheoenergyoofotheoalphaoparticleoinothisoproblem,oandosinceoweoknowotheomassoofotheoalphaoparticleoan
dotheo daughtero nucleus,o theo resulto iso easilyo found.o Byosubstitutingoouro knownovalueso ofo maloo4o ando mboo206o intoo ouro derivedoEa
lequationoweoget:
Ealoo5.395oMeV
Noteo:oWeocanoobtainosolutionsoforoallotheovariablesobyosubstitutingomboo206oandomaloo4ointootheoderivedoequationsoaboveo:
Ealoo5.395oMeV Eboo0.105oMeV palooo6.570 amuoMeV pbo oo6.570 amuoMeV
■ Problemo1.4.o Calculationoofo WavelengthofromoEnergy.
Sinceoanox-rayomustoessentiallyobeocreatedobyotheode-excitationoofoaosingleoelectron,otheomaximumoenergyoofoanox-
rayoemittedoinoaotubeooperatingoatoaopotentialoofo195okVomustobeo195okeV.o Therefore,o weocanouseotheoequationoE=h,owhichoisoalso
oE=hc/Λ,ooroΛ=hc/E.o Pluggingoinoouromaximumoenergyovalueointoothisoequationogivesotheominimumox-rayowavelength.
hooc
Λo whereoweosubstituteohoo 6.626oo1034oJoos,o coo299o792o458omoosoandoEoo195okeV
E
1
, Chaptero 1o Solutions
1.01869oJ–m
Λo o 0.0636oAngstroms
KeV
■ Problemo 1.5.o o 235oUFissiono EnergyoRelease.
235 117
Usingotheo reactiono o Uo o o o Snoo118oSn,o andomassovalues,oweocalculateo theomassodefecto of:
Mo235oUoo o Mo117oSnooMo118oSnoo M
oandoan oexpectedoenerg
yoreleaseoofoMc2.
931.5oMeV
oo oo oo o223o MeV
AMU
Thiso iso oneoofotheo mostoexothermicoreactionso availableo toous.o Thiso iso oneoreasono why,oofocourse,o nuclearo powerofromouraniumofis
sionoisosooattractive.
■ Problemo1.6.o SpecificoActivityoofo Tritium.
Here,oweouseotheotextoequationoSpecificoActivityo=o(ln(2)*Av)/oT12*M),owhereoAvoisoAvogadro'sonumber,oT12oisotheohalf-
lifeoofotheoisotope,oandoMoisotheomolecularoweightoofotheosample.
ln2oAvogadroo'osoConstant
SpecificoActivityo
T12oM
3ograms
WeosubstituteoT12oo12.26oyearsoandoM= toogetotheospecificoactivityoinodisintegrations/(gram–year).
mole
1.13492oo1022
SpecificoActivityo
gramo–year
TheosameoresultoexpressedoinotermsoofokCi/goisoshownobelow
9.73okCi
SpecificoActivityo
gram
■ Problemo1.7.o Acceleratedoparticleoenergy.
Theo energyoofoao particleo withochargeo qofallingothroughoao potentialoVo isoqV.o Sinceo V=o 3oMVo isoouromaximumopotentialodifference,o theo
maximumoenergyoofo ano alphao particleo hereo iso q*(3o MV),o whereo qo iso theo chargeo ofo theo alphao particleo (+2).o Theomaximumoalphaoparticl
eoenergyoexpressedoinoMeVoisothus:
Energyoo3oMegaoVoltsoo2oElectronoChargeso o6.o MeV
2
, Chaptero 1o Solutions
■ Problemo1.8.o Photofissionoofo deuterium. 1oDo o Γo
2 1
0ono
1
1opo+o Qo (-2.226oMeV)
Theo reactionoofointerestoiso o 2oDo o o 0oΓo o 1onoo o 1o p+oQo(-2.226oMeV).o Thus,otheoΓomustobringoanoenergyoofoatoleasto2.226oMeV
1 0 0 1
inoorderoforothisoendothermicoreactionotooproceed.o Interestingly,otheooppositeoreactionowillobeoexothermic,oandooneocanoexpectotoofi
ndo2.226oMeVogammaoraysoinotheoenvironmentofromostrayoneutronsobeingoabsorbedobyohydrogenonuclei.
■ Problemo1.9.o NeutronoenergyofromoD-Toreactionobyo150okeVodeuterons.
Weowriteodownotheoconservationoofoenergyoandomomentumoequations,oandosolveothemoforotheodesiredoenergiesobyoeliminatingotheo
momenta.o Inothisosolution,o"a"orepresentsotheoalphaoparticle,o"n"orepresentsotheoneutron,oando"d"orepresentsotheodeuterono(and,oasob
efore,o"p"orepresentsomomentum,o"E"orepresentsoenergy,oando"Q"orepresentsotheoQ-valueoofotheoreaction).
pa2 pn2 pdo2
paoo pnoo pd E
o a E
o n Ed
o EaooEnooEdo oQ
2oma 2omn 2omd
Nexto weo wanto too solveotheo aboveo equationso foro theo unknownoenergieso byoeliminatingotheo momenta.o (Noteo :o Usingo computeros
oftwareosuchoasoMathematicaoisohelpfuloforopainlesslyosolvingotheseoequations).
Weo evaluateo theo solutionobyopluggingoino theo valuesoforo particleo masseso(weo useo approximateovaluesoofo "ma,"o "mn,"ando "md"o ino
AMU,owhichoisookayobecauseoweoareointerestedoinoobtainingoanoenergyovalueoatotheoend).o WeodefineoalloenergiesoinounitsoofoMeV,on
amelyotheo Q-value,oandotheo givenoenergyoofotheodeuterono(bothoenergyovaluesoareo inoMeV).o o Sooweosubstituteomao =o4,omno =o1,omd
=o2,oQo=o17.6,oEdo =o0.15ointooouromomentaoindependentoequations.o Thisoyieldsotwoopossibleosetsoofosolutionsoforotheoenergieso(ino
MeV).oOneocorrespondsotootheoneutronomovingoinotheoforwardodirection,owhichoisoofointerest.
Enoo 13.340o MeV Eaoo 4.410o MeV
Enoo 14.988o MeV Eaoo 2.762o MeV
Nextoweosolveoforotheomomentaobyoeliminatingotheoenergies.oWhenoweosubstituteomao =o4,omno =o1,omdo =o2,oQo=o17.6,oEdo =o0.15ointo
otheseoequationsoweogetotheofollowingoresults.
pd 1 1
pno o 2 3opdo2o o352 pao 8opdo o2 2 3opdo2o o352
5 5 10
Weodooknowotheoinitialomomentumoofotheodeuteron,ohowever,osinceoweoknowoitsoenergy.oWeocano furthero evaluateo ourosolutionsofor
pnoando paobyosubstituting:
pdo
Theoparticleo momentao(oinounitsoof amuMeV )oforoeachosetoofosolutionsoisothus:
pnoo 5.165 paoo 5.940
pnoo 5.475 paoo 4.700
Theo largestoneutronomomentumooccursoinotheoforwardo(+)odirection,osootheohighestoneutronoenergyoofo14.98oMeVocorrespondso
toothisodirection.
3
