final - PHYSICS 2D PROF HIRSCH FINAL EXAM(8 problems FALL...

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PHYSICS 2D FINAL EXAM FALL QUARTER 2009 PROF. HIRSCH (8 problems) DECEMBER 8th, 2009 Formulas : Time dilation; Length contraction: " t = # " t ' $ # " t p ; L = L p / # ; c = 3 % 10 8 m / s Lorentz transformation: x ' = " ( x # vt ) ; y '= y ; z '= z ; t ' = " ( t # vx / c 2 ) ; inverse : v $ - v Spacetime interval: ( " s ) 2 = ( c " t ) 2 -[ " x 2 + " y 2 + " z 2 ] Velocity transformation: u x ' = u x " v 1 " u x v / c 2 ; u y ' = u y # (1 " u x v / c 2 ) ; inverse : v $ - v Relativistic Doppler shift : f obs = f source 1 + v / c / 1 " v / c (approaching) Momentum: r p = " m r u ; Energy : E = " mc 2 ; Kinetic energy: K = ( " # 1) mc 2 Rest energy : E 0 = mc 2 ; E = p 2 c 2 + m 2 c 4 Electron : m e = 0.511 MeV / c 2 Proton : m p = 938.26 MeV / c 2 Neutron : m n = 939.55 MeV / c 2 Atomic mass unit : 1 u = 931.5 MeV / c 2 ; electron volt : 1eV =1.6 " 10 -19 J Stefan's law : e tot = " T 4 , e tot = power/unit area ; " = 5.67 # 10 $ 8 W / m 2 K 4 e tot = cU /4 , U = energy density = u ( " , T ) d " 0 # $ ; Wien's law : " m T = hc 4.96 k B Boltzmann distribution: P ( E ) = Ce - E /( k B T ) Planck's law : u " ( " , T ) = N " ( " ) # E ( " , T ) = 8 $ " 4 # hc / " e hc / " k B T % 1 ; N ( f ) = 8 $ f 2 c 3 Photons: E = hf = pc ; f = c / " ; hc =12,400 eV A ; k B = (1/11,600) eV / K Photoelectric effect : eV s = K max = hf " # , # $ work function; Bragg equation : n % = 2 d sin & Compton scattering : " '- " = h m e c (1 # cos $ ); h m e c = 0.0243 A ; Coulomb constant : ke 2 = 14.4 eV A Force in electric and magnetic fields (Lorentz force): r F = q r E + q r v " r B ; Drag force : D = 6 # a $ v Rutherford scattering: " n = C sin 4 ( # /2) ; h c = 1,973 eV A Hydrogen spectrum: 1 " mn = R ( 1 m 2 # 1 n 2 ) ; R = 1.097 $ 10 7 m # 1 = 1 911.3 A Electrostatic force, energy : F = kq 1 q 2 r 2 ; U = kq 1 q 2 r . Centripetal force : F c = mv 2 r Bohr atom: E n = " ke 2 Z 2 r n = " Z 2 E 0 n 2 ; E 0 = ke 2 2 a 0 =13.6 eV ; K = m e v 2 2 ; U = " ke 2 Z r hf = E i " E f ; r n = r 0 n 2 ; r 0 = a 0 Z ; a 0 = h 2 m e ke 2 = 0.529 A ; L = m e vr = n h angular momentum de Broglie : " = h p ; f = E h ; # = 2 $ f ; k = 2 $ " ; E = h # ; p = h k ; E = p 2 2 m Wave packets: y ( x , t ) = a j cos( k j x " # j t ), or j $ y ( x , t ) = dk a ( k ) e i ( kx - # ( k ) t ) % ; & k & x ~ 1 ; & # & t ~ 1 group and phase velocity : v g = d " dk ; v p = " k ; Heisenberg : # x # p ~ h ; # t # E ~ h Schrodinger equation: - h 2 2m " 2 # " x 2 +U(x) # (x,t) = i h " # " t ; # (x,t) = $ (x)e -i E h t
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