# final - PHYSICS 2D FINAL EXAM WINTER QUARTER 2009 PROF....

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Unformatted text preview: PHYSICS 2D FINAL EXAM WINTER QUARTER 2009 PROF. HIRSCH MARCH 20, 2009 Formulas : Time dilation; Length contraction: " t = # " t ' \$ # " t p ; L = L p / # ; c = 3 % 10 8 m / s 1 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, energy (total, kinetic, rest): p " = # mu " ; E = # mC 2 ; K = ( # \$ 1) mC 2 ; 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 Planck : E n = nhf ; probability P ( E n ) " e # E n / k B T ; E ( \$ , T ) = E n n % P ( E n )/ P ( E n ) n % Planck's law : u ( " , T ) = N ( " ) # E ( " , T ) = 8 \$ " 4 # hc / " e hc / " k B T % 1 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 Compton scattering: " '- " = h m e c (1 ¤ cos £ ); h m e c = 0.0243 A ; Coulomb constant : ke 2 = 14.4 eV A EL¡CtRostAtICs¢ F = kq 1 q £ r £ (foRC¡) ; U = kq 1 q £ r (Pot¡NtIAL ¡N¡Rgy) 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 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 = ke 2 Z 2 r ; 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: ¥ = 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...
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## This note was uploaded on 12/07/2009 for the course PHYS phys 2d taught by Professor Hirsch during the Winter '08 term at UCSD.

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

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