2 d2p415106 19410192141013sr1 aA d2a415106 53310190781013sr2Itspossibletowritethisintermsofapercentchangechangein p a p a 22214078 214078093933Problem2Di ID: 184182
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2 perihelionandaphelion: p=A d2p=4:15106 1:941019=2:1410�13sr(1) a=A d2a=4:15106 5:331019=0:7810�13sr(2)It'spossibletowritethisintermsofapercentchange:%changein = p� a p+ a 2=2(2:14�0:78) 2:14+0:78=0:93=93%:(3)Problem2Di erentialSolidAngleAbeamofchargedparticles(e.g., particles)isdirectedtowardatargetfoil.Theincomingparticlesarescatteredatvariousangles,,relativetotheinitialdirectionofthebeam.(a)Whatisthedi erentialsolidangleforparticlesscatteredatameanangle=5overanangularrangeofd=1?Thedi erentialsolidangleisdenedasd =2sind.Firstwemustconvertdtoradians:d=1=180=0:017rad.Wealsohavesin5=0:087,sod =2(0:087)(0:017)=0:009sr.(b)Whatisthedi erentialsolidangleforparticlesscatteredatameanangle=85overanangularrangeofd=1?Nowwehavesin85=0:996,sod =2(0:996)(0:017)=0:106sr.(c)Basedongeometricargumentsalone,wouldyouexpectmoreparticlestobescatteredat5orat85?Thisisabitofasubtlequestion.Ifwehadnoknowledgeofthephysicalinter-actionbetweentheincomingparticlesandthenucleiwithinthetarget,wemightassumethattheparticlesscatterequallyinalldirections.Ifthiswerethecase,thenwewouldexpectmoreparticleswouldbescatteredintothedi erentialsolidanglecenteredat85sinceitrepresentsamuchlargerfractionofthetotal4solidangle,orequivalently,itconstitutesamuchlargerfractionoftheentiresurfaceareaofaspherecenteredatthescatteringcenter(anucleuswithinthetarget).WhenwediscussRutherfordscatteringinthenextlecture,wewillndthatinfactitisrelativelyrareforanincoming particletobescatteredatalargeanglebecauseitrequiresthattheincomingparticlepassveryclosetoanucleus.Thisisveryimprobablesincenucleiaresosmallrelativetothesizeofatoms. coursenamePS#