IPhO 1983 Theoretical Question IV MARKING SCHEME FOR ANSWERS TO THE THEORETICAL QUESTION IV Part MARKING SCHEME - THE THEORETICAL QUESTION IV- COMPTON SCATTERING Tota l Sco res IV. For: the situation before the first scattering of photon the momentum i p and the energy i E of the initial photon ⋅= ⋅ == ii i i i fhE c fh h P λ 0.3p the frequency of initial photon i i c f λ = 0.1p the momentum oe p and the energy oe E of initial, free electron in motion − ⋅ =⋅= − ⋅ =⋅= 2 2 0 2 2 10 1 1 1 β β cm cmE vm vmP oe e eoe 0.3p De Broglie wavelength of the first electron 2 100 1 βλ − ⋅ ⋅ == ee oe vm h p h 0.2p the situation after the scattering of photon 7.0 points MARKING SCHEME COMPTON SCATERING– Page 1 from 4 IPhO 1983 Theoretical Question IV the momentum 0 p and the energy 0 E of the scattered photon ⋅= ⋅ == oo o o o fhE c fh h P λ 0.3p the frequency of scattered photon 0 λ c f o = 0.1p the principles of conservation of moments and energy +=+ =+ eei oei EEEE ppP 100 0 0.3p the conservation of moment on Ox direction θα coscos 0 1 c fh vm c fh e i ⋅ =⋅⋅+ ⋅ 0.3p the conservation of moment on Oy θα sinsin 0 1 c fh vm e ⋅ =⋅⋅ 0.3p ( ) θ cos2 1 0 2 1 2 0 22 1 2 1 22 0 ⋅⋅−+⋅=⋅ − ⋅ ie e ffffhv c v cm 0.4p The conservation of energy 0 2 01 2 fhcmfhcm ⋅+⋅=⋅+⋅ 0.3p or ( ) 10 2 0 2 1 2 0 1 ffhcm c v cm e −⋅+⋅= − ⋅ 0.2p ( ) ( ) 10 2 0 2 10 242 0 2 1 42 0 1 ffchmffhcm c v cm e −⋅⋅⋅+−⋅+⋅= − ⋅ 0.2p ( ) 010 cos1 f c f c cm h −=− ⋅ θ 0.2p cm h ⋅ =Λ 0 0.2p the wavelength of scattered photon ( ) θλλ cos1 0 −⋅Λ−= i 0.3p MARKING SCHEME COMPTON SCATERING– Page 2 from 4 IPhO 1983 Theoretical Question IV > < 0 0 EE i i λλ 0.1p the situation before the second collision the situation after this scattering process The conservation principle for moment in the scattering process =⋅⋅− ⋅⋅+= 0sinsin coscos 2 2 0 βθ λ βθ λλ e f e f vm h vm hh 0.3p ( ) 2 2 0 2 2 0 2 cos 2 e ff vm hhh ⋅= ⋅ ⋅ − + θ λλλλ 0.3p ( ) ( ) −⋅Λ=− −=−⋅ ⋅ θλλ λλθ cos1 cos1 0 0 0 f f cm h 0.5p < > 0 0 EE f f λλ 0.1p MARKING SCHEME COMPTON SCATERING– Page 3 from 4 IPhO 1983 Theoretical Question IV ×=×= ×⋅× × =Λ ×= −− − − − mmm m f 1012 831 34 10 1002,01041,2 103101,9 106,6 1025,1 λ 0.2p the value of wavelength of photon before the second scattering m 10 0 1023,1 − ×= λ 0.1p fi λλ = 0.3p = = ee ee EE pp 21 21 0.2p the moment of final electron ( )( ) ( )( ) θλλ θ θλ λ cos1 cos2 cos1 11 22 2 −Λ−⋅ ⋅ − −Λ− += ff f f e hp 0.4p The de Broglie wavelength of second electron after scattering (and of first electron before scattering) ( )( ) ( )( ) −Λ−⋅ ⋅ − −Λ− +== θλλ θ θλ λ λλ cos1 cos2 cos1 11 1 22 21 ff f f ee 0.3p final result: m ee 10 21 1024,1 − ×== λλ 0.2p Total score theoretical question IV 7.0 poi nts Professor Delia DAVIDESCU, National Department of Evaluation and Examination– Ministry of Education and Research- Bucharest, Romania Professor Adrian S.DAFINEI,PhD, Faculty of Physics University of Bucharest, Romania– MARKING SCHEME COMPTON SCATERING– Page 4 from 4