Lecture05 - Lecture5 Jan.20 Rela1vityII

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Unformatted text preview: Lecture5 Jan.20 Rela1vityII h7p://aniketjha.blogspot.com/2010/07/emc2.html iclickerQuiz(Jan.18) Anelectronandpositronwithequaland oppositemomentacollideheadonand annihilateinto2photons,eachmeasured with1.022MeVenergy.Whatisthe invariantmassoftheinterac1on? A) 0 B) me C) 2me D) 4me me=0.511MeV/c2 Howmuchenergywouldberequiredtoaccelerateapar1cleof massmfromresttoaspeedof0.5c?Expresstheanswerasa mul1pleoftherestenergy. E = E f - Ei = ( - 1) mc 2 Ei = mc E f = mc 2 2 = 1.155 E = 0.155mc 2 3 Atwhatvalueofu/cdoesthemeasuredmassofapar1cle exceeditsrestmassby11%? = 1.11 = 1 1- 2 1 1- = = 0.9009 1.11 2 2 = 1 - ( 0.9009 ) 2 2 = 1 - ( 0.9009 ) = 0.434 4 Howmuchworkmustbedoneonaprotontoincreaseits speedfrom0.1cto0.2c?(Therestenergyofaprotonis938.3 MeV.) E1 = 1mc 2 E2 = 2 mc 2 E = ( 2 - 1 ) mc 2 = mc 2 = 0.0156mc 2 1 = 1.0050 2 = 1.0206 E = 14.7eV 5 Aprotonwithrestenergyof938MeVhasatotalenergyof 1000MeV. (a)Whatisthevalueofu/c? (b)Whatistheproton'smomentum?Expressyouranswerin unitsofMeV/c E = mc 2 = 1000MeV = 2 1000MeV = 1.0661 938MeV 2 = 1 - 1 / 2 = 0.3466 E = ( pc ) + mc ( 2 2 ) ( pc ) 2 = E - mc 2 ( 2 2 2 2 ) = (1000MeV ) - ( 938MeV ) pc = 347MeV p = 347MeV / c 6 Findtheenergythatisneededtoremoveoneprotonfroma 4Heatom,leavinga3Hatomplusa1Hatom.(Assumeatomic massof3H=3.016amu,atomicmassof4He=4.0026amu,rest energyofproton=938.272MeV,atomicmassof1H=1.00794 amu.) E = m ( H )c 3 2 + m 1 H c2 - m ( ) ( 4 He c 2 ) = ( 3.016 + 1.00794 - 4.0026 ) ( 931.5MeV ) = 19.9MeV 7 Theenergyreleasedinthefissionofa235Unucleusisabout200 MeV.Howmuchrestmass(inkg)isconvertedtoenergyinthe fissionof1000kgof235U? N = N A 1000kg / ( 235g / M ) = 2.8x10 27 E = N 200MeV = 5.6 10 35 eV E = 5.6 10 35 eV 1.6 10 -19 J / eV = 9 1016 J ( ) m = E / c 2 = 1kg 8 iclickerQuiz(Jan.20) Anelectronhasamomentumequalto1 MeV/c.Whatisitstotalenergy? A) 0.56MeV B) 1.12MeV C) 2.24MeV me=0.511MeV/c2 ...
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This note was uploaded on 02/05/2012 for the course PHYS 342 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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