final - PHYSICS 2D FINAL EXAM FALL QUARTER 2009 PROF....

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Unformatted text preview: 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 = 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 " ; 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 c (1 # cos $ ); h m c = 0.0243 A ; Coulomb constant : K 2 = 14.4 V 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 . eNtripetAl fOrCe F c = mv 2 r Bohr atom: E n = " ke 2 Z 2 r n = " Z 2 E n 2 ; E = ke 2 2 a =13.6 eV ; K = m e v 2 2 ; U = " ke 2 Z r hf = E i " E f ; r n = r n 2 ; r = a Z ; a = h 2 m e ke 2 = 0.529 A ; L = m e vr = n h angular momentum de Broglie:...
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This note was uploaded on 04/02/2010 for the course PHYS 2D 2D taught by Professor Sinha during the Spring '10 term at UCSD.

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final - PHYSICS 2D FINAL EXAM FALL QUARTER 2009 PROF....

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