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PROBLEMS1ACARACCELERATESATARACEOF50KMPERHOURPERSECONDEXPRESSTHISACCELERATION2ARENTOF10WAFLOWSINTOACONDENSEROFCAPACITY100IFFOR50SCALCULATETHEPOTENTIALDIFFERENCEBETWEENTHEPLATESOFTHECONDENSER3APATIENTISGIVENANZRAYCAPOSUAOF200RCALCULATETHISEXPOSUREINCKG4AFTERAFULLCOURSEOFTREATMENT,AMMORRECEIVEDADOSEOF4000ADSEXPRESSTHISDOSEINGRAYS,INMCVPERG5ASOURCEOFCOBALT60WITHHALFLIFEOF52YEARSHASANACTIVITYOF1100CIEXPRESSTHISACTIVITYINBECQUEREHESTIMATETHEACTIVITYAFTER55YEARS6HYDROGENINNATUREEXISTSAAMIXTUREOFIHAND,HWITHATOMICMASSESOF1007825AND2014102,RESPECTIVELYTHESEOCCURINRELATIVEABUNDANCE99985AND0015CALCULATETHEATOMICWEIGHTOFHYDROGENCHECKYOURANSWERWITHTABLE137LITHIUMINNATURECONSISTSOFTWOISOTOPESOFATOMICMASSES601513AND701601,WITHPERCENTAGEABUNDANCESOF742AND9258FINDTHEATOMICWEIGHTCHECKYOURANSWERWITHTABLE188INTHECOMPLETEDECAYOF1000ATOMSOFBHOWMANYBETAPARTICLESWILLBERELEASEDANDHOWMUCHENERGYASGAMRAYSSEEFIG139ADEUTERIUMATOMISMADEUPOFAPROTONATOMICMASS1007276,ANELECTRONATOMICMASS0000548,ANDANEUTRONATOMICMASS1008665THEMASSOFTHEDEUTERIUMATOMIS2014102FINDTHEENERGYINMRVREQUIREDTOBRINGABOUTTHEDISINTEGRATIONOFTHEDEUTERIUMINTOHYDROGENPLUSANEUTRON10ACERTAINRADIOACTIVEMATERIALEMITSGAMRAYSWITHENERGYIMVVANOTHERSAMPLEOFRADIOACTIVEMATERIALEMITSGAMTRAYSWITHENERGY10KEVIFBOTHOFTHESEMILTHESAMEAMOUNTOFENERGYPERNUTTIME,COMPARETHEIRACTIVITIES11ARADIOSTATIONTRANSMITSATAFREQUENCYOF900KHZFINDTHEWAVELENGTHOFTHERADIATIONFINDTHEENERGYINELECTRONVOLTSOF1QUANTUMOFSUCHRADIATION12ELECTROMAGNETICWAVESOFLENGTH10CMAREUSEDINRADARINSTALLATIONSCALCULATETHEFREQUENCYOFSUCHRADIATIONANDTHEENERGYOF1QUAMOFSUCHRADIATION13THEEYEISSENSITIVETOYELLOWLIGHTWITHWAVELENGTH550NMFINDTHEFREQUENCYOFSUCHRADIATIONANDTHEENERGYINELECTRONVOLESOF1QUAMOFSUCHRADIATION14ANXRAYMACHINEOPERAWITHAPEAKPOTENTIALOF280,000VOTESFINDTHEMINIMUMWAVELENGTHOFTHERADIATIONEMITTEDBYTHEXRAYTUBE,ANDTHEFREQUENCYOFTHISRADIATION15GAMMARAYSFROMRADIUMHAVEENERGIESUPTO22MEVWHATISTHEWAVELENGTHINPMOF22MEVRADIATIONTHEDISTANCEBETWEENADJACENTATOMSINAROCKSALTCRYSTALIS281PUTCANYOUAWHYTHERADIATION,FROMRADIUMPASSTHROUGHAMATERIALSUCHOCKSALTASIFITWERETRANSPARENT16DETERMINETHEMINIMUMWAVELENGTHOFTHERADIATIONEMITTEDFROMA35MEVLINAC17ARADIOTRANSMITTEROPERATESAT10KWAT300KHZFINDTHENUMBEROFQUANTATIEDPERSECOND18WHATISTHEENERGYANDWAVELENGTHOFTHERADIATIONETNIUEDFROMTUNGSTENWHENANELECTRONFALLSFROMTHEMTOTHEKSHELL19ANANTIPROTONISAPLOTWITHANEGATIVECHARGEWHATENERGYWOULDBEEMITTEDIF,PROTONANNIHILATEDANANTIPROTON20ANELECTRONHASAKINETICENERGYOF1M,VFINDITSTOMENERGYANDHENCECA/M,USEEQUATIONL20TODETERMINEIT,LOCITYRELATIVETOTHEVELOCITYOFLIGHTCHECKYANSWERAGAINSTTABLE1721SHOWTHATWHENVC,EQUATION121REDUCESTOKEM0/222ASOURCEOFGOLD198WITHAHALFLIFEOF269DAYSHASANINITIALACTIVITYOF5CICALCULATETHEACTIVITYAFTER40DAYSEXPRESSTHISACTIVITYINBECQUERELS23THETWOFORMSOFEQUATION123AREIDENTICALPROVETHISBYSHOWINGTHAT2“EINWHEREXISANYNMBER24THEGAMRAYSFROM“GOHAVEAHALFVALUELAYERINLEADOF11CMESTIMATETHETHICKNESSOFLEADREQUIREDTOATTENUATESUCHABEAMBYAFACTOROF10“WHATISTHECANGEOFTHESEPHOTONSINLEAD25CELLSGROWWITHADOUBLINGTIMEOF20HOURSASSUMINGEXPONNTIALGROWTH,CALCULATETHENUMBEROFCELLSPRESENTAFTERTHREEDAYS,STARTINGWITH10CELLSPLOTONSEMILOGPAPER26ATUMORCONTAINING10“CELLSISINACTIVATEDBYRADIATIONWITHAMEANLETHALDOSEOFD“150GYFINDTHENUMBEROFSURVIVORSAFTERADOSEOF45GY27FROMTHEDEFINITIONOFA,THETRANSFORMATIONCONSTANT,ANDTHEUSEOFEQUATION124CALCULATETHEINITIALNUMBEROFDISINTEGRATION,PERSECONDFORTHEGOLDSOURCEDESCRIBEDINFIGURET4EXPRESSTHISINITIALACTIVITYINBEQUERELSANDCURIESPLOTTHEDECAYOFTHISACTIVITYASAFUNCTIONOFTIMEANDSHOWTHATTHETOTALNUMBEROFDISINTEGRATI0N,ISFTS28SHOWBYNUMERICALINTEGRATIONTHATTHEAREAUNDERTHECURVEOFFIGURE14ISAPPROXATELY39X10SATOMDAYSSINCETHEREWERE108ATOMSPRESENTINITIALLYTHISSHOWSTHATTHEMEANLIFEIS39DAYSTHISCHECKSWITH1/A29CALCULATETHEVALUEOFONEDOLLARCOMPOUNDEDMONTHLYAT10PERMAFTER1YEARCOMPARETHISRESULTWITHTHEVALUEOBTAINEDWHENCOMPOUNDINGSCONTINUOUS30WHATINTERESTRATECOMPOUNDEDCONTINUOUSLYISREQUIREDTODOUBLEYOURMONEYVERY10YEARS31ACELLCULTURECONTAINING10CELLSHASADOUBLINGTIMEOF10HOURSFINDTHENUMBEROFCELLS“BORN“PER32THEHALFLIFEOFGOLD198IS269DAYSCALCULATETHETRANSFORMATIONCONSTANTANDTHEANLIFE33WITHYOURCALCULATORDETERMINE2,AND3FOR,FEWVALUESOFZBETWEEN0AND4NOWDETERMINETHESLOPEOFTHESEFUNCTIONSNUMERICALLYFOREXAMPLE,THESLOPEOFATZ4ISABOUT00S/02PLOTTHEFUNCTIONSANDTHESLOPESSAFUNCTIONOFZOBSERVETHATTHESLOPEOFE“ISTHESAMEASEWHILETHESLOPEOF2ISLESSTHAN2“ANDSLOPEOF3ISGREATERTHAN3AISTHEONLYFUNCTIONWHOSEDEDVMTIVEISEGUO/TOTHEION34USINGTHERESULTFROMPROBLEM33,DIFFERENTIATETHEEQUATIONNNEE“WITHRESPECTTOTIMEANDSHOWTHATYOUOBTAINTHEDIFFERENTIALEQUAION125THISSHOWSTHEIMEGRATIONPERFORMEDINTHEFINALPARTOFSECTION117ISCORRECT35OBTAINAPORTABLEGEIGERCOUNTERWITHSPEAKEROUTPUTSOTHATINDIVIDUALPULSESCANBEHEARDPLACETHISOUTSIDETHEROOMORDOWNTHECORRIDORFROMACOBALT60UNITOBVETHECOUNTINGRATEWITHTHEMACHINEOFFTURNONTHECOBALTUNITANDOBSERVETHEQUANTUMNATUREOFRADIATIONBYMVINGTHEDETECTORBEHINDWALLBARRIERS,DEMONSTRATETHEEXTREMEPENETRATINGPOWEROFTHERADIATION,FROMCOBALT36FINDATLEASTTWOOTHEREXAMPLESOFEXPONENTIALBEHAVIORWRITEDOWNTHEDIFFEREN11TIALEQUATIONANDTHEINTEGR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HOTONFLUENCE/RCHECKYOUVALUESWITHTHEANSWERSGIVEINTABLEA214ANIONIZATIONCHAMBERHASWALLSMADEOFALUMINUMANDISUSEDMMEASUREABSORBEDDOSEINAWATERPHANTOMFROMABEAMFROMA10MVLINEARACCELERATORACOBALTEXPOSUACALIBRATIONFACTORISOBTAINEDANDHASAVALUE107THEIONCHAMBERHASANINNERRADIUSOF15MMANDAWALLTHICKNESSOF2MMFORONEUNITONTHELINECONITOR,THEDOSIMETERGIVEREADINGOF143FOLLOWINGAMPLE710,DETERMINETHEABSORBEDDOSEANDDIXUSSTHEASSUMPTIONSTHATAREREQUIREDINORDERTOOBTAINITSVALUEESTIMATETHEACCURACYOFTHEVALUEYOUHAVEOBTAINEDPROBLEMS1APULSEOFRADIATIONPRODUCESEQUALCONCENTRATIONSOFPOSITIVEANDNEGATIITFORWHICHA16X10SCOTSIFTHEINITIALCHARGECENTRATIONQO20NSPC/CM,PLOTTHECHARGECONCENTRATIONAFUNCTIONOFTIMEWHATTIQUIREDFORQOTODROPTOL/2THEORIGINALVALUE1/4THEORIGINALVALUEISTHISEXPONENTIALDECAY2THEPLATESOFANIONCHAMBERARE50CMAPARTAND600VOLTSISAPPLIEDBETWEENTHEMAPULSEOFRADIATIONPRODUCESANINSTANTANEOUSUNIFORMCHARGEDISTRIBUTIONNTHEAIRBETWEENTHEPLATESDETERMINETHETIMEDURINGWHICHRECOMBINATIONRANTAKEPLACE3FINDTHEFRACTIONOFIONSCOLLECTEDINAPARALLELPLATEIONCHAMBEREXPOSEDTORADIATION,WHICHLIBERATES180PC/CMPERPULSETHEPLATESARE18CMAPARTAND360VOLTSISAPPLIEDBETWEENTHEM4APARALLELPLATECHAMBERWITHPLATES15CMAPARTAND300VOLTSBETWEENTHEMISEXPOSEDTOCONTINUOUSRADIATION,WHICHLIBERATES8WC/CMSTOTHEAIRBETWEENTHEPLATESFINDTHEFRACTIONOFIONSCOLLECTED5ACYLINDRICALAIRFILLEDIONCHAMBEROFRADIUS06CMWITHACENTRALELECTRODEOFRADIUS01CMISEXPOSEDTOACOBALT60BEAMATANEXPOSURTAOF200R/MINIFTHECOLLECTINGVOLTAGEIS180VOLTS,DETERMINETHEFRACTIONOFIONSCOLLECTED6THECHAMBEROFPROBLEM5ISEXPOSEDMAPULSEDBEAMWITHANEXPOSUREOF205RPERPULSEFINDTHEFRACTIONOFIONSCOLLECTED7PERFORMTHEINTEGRATIONOFEQUATION98ANDSHOWTHATTHEINTEGRALISGIVENBYEQUATION998PERFORMTHEINTEGRATIONOFQUAON917ATOYIELDEQUATION917B9PERFORMTHECALCULATIONINVOLVEDINPROCEEDINGFROMEQUATION919ATOEQUATION919610THECHAMBERDESCRIBEDINPROBLEM5ISUSEDTOMEASURETHERADIATIONFROMAFULLVEDIAGNOSTICXRAYUNIT,WHICHYIELDSANAVERAGEEXPOSURRATEOF100R/MINDETERMINETHEFRACTIONOFIONSLOSTCORECOMBINATIONASSUMINGFIRSTAUNIFORMEXPOSURERATEANDTHENSQUAREPULSESEACHLAS,ING1/120SEC11AHIGHPOWERHIGHENERGYLINACGIVERAGEDOSERATEOF10GY/MINATFMETERTHISISEQUIVALENTTOABOUT333XIO0PC/CMMWALLEDCAVITYACYLINDRICALCHAMBERWITHARADIUSOF05CMANDANINNERELECVODE005CMRADIUSISUSEDTORETHISRADIATIONWITH400VOLTSACROSSTHECHAMBERANDTHEHNACPRODUCING100PULSES/S,ESTIMATETHEFRACTIONOFIONSCOLLECTEDTHESAMELINACHASAPARALLELPLATEMONITORCHAMBER40CMFROMTHETARGETIFTHEPLATESARE1MMAPARTANDAPOTENTIALOF200VOLT,ISAPPLIEDBETWEENTHEM,ESTIMATETHEFRACTIONOFTHECHARGELOSTTORECOMBINATION12DERIVEEQUATION927FROMEQUATIONS924,925AND92613SHOWTHATFORTHECOFFIGURE97C,VNV,R,/R,RXV,R,/R,WHATRESISTORVALUESWOULDYOUCHOOSETOMAKEVNIOV,V,14ANIONCHAMBERWITHOUTERDIAMETER100CMISUSEDTOMEASURETHEOUTPUTOFANRAYMACHINETHATHASATREATMENTCONEDESIGNEDTOTREATATADISTANCEOF500CMTHECHAMBERISPLACEDINCONTACTWITHTHISTREATMENTCONEWID,ITSCENTER505FROMTHETARGETTHECHAMBERHASACALIBRATIONFACTOROF0315X100ROENTGENSPEROULOMBATATEMPERAAOF200CANDAP,MOF1013KPAFORTHERADIATIONBEIN

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