final - PHYSICS 2D FINAL EXAM SPRING QUARTER 2008 PROF...

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Unformatted text preview: PHYSICS 2D FINAL EXAM SPRING QUARTER 2008 PROF. HIRSCH JUNE 13th, 2008 Formulas : Time dilation; Length contraction: " t = # " t ' $ # % ; 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, 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 Force on charge q in r E and r B fields : r F = q ( r E + r v " r B ) ; centripetal acceleration = v 2 / R Stefan's law : R = " T 4 , R = power/unit area ; " = 5.67 # 10 $ 8 W / m 2 K 4 ; R = cU /4 , U = energy density = u ( % ) d % & ’ Planck's law : u ( " , T ) = n ( " ) # $ ( " , T ) = 8 % " 4 # hc / " e hc / " kT & 1 ; Wien's law : " m T = hc 4.96 k B Photoelectric effect : eV = ( 1 2 mv 2 ) max = hf ¡ # , # ¢ work function Photons: E = hf = pc ; f = c / " ; Quantum oscillator: # n = nhf ; probability P ( # n ) $ e % # n / k B T Compton scattering: ¡ '- ¡ = h m e C (1 ¢ cos £ ) ; Rutherford scattering: b = kq ¤ Q M ¤ v 2 cot £ 2 ; ¥ N = ¡ sin 4 ( £ /2) Electrostatics : F = kq 1 q 2 r 2 (force) ; U = q ¡ (potential energy) ; ¡ = kq r (potential) Hydrogen spectrum: 1 £ = 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 = mk 2 e 4 2 h 2 =13.6 eV ; E n = E kin + E pot , E kin = " E pot /2 = " E n hf = E i " E f ; r n = r n 2 ; r = a Z ; a = h 2 mke 2 = 0.529 A ; L = mvr = n h angular momentum X -ray spectra: f 1/2 = A n ( Z " b ) ; K : b =1, L : b = 7.4 CONSTANTS¡ h = 4.¢36 " ¢£ # ¢5 eV $ s ¤ hc = ¢¥,4££ ¦V § ¤ k B = ¢/¢¢,6££ ¦V/K ¤ ke ¥ = ¢4.4 eV A h c =1973 eV A ; e = 1.6 ¡ 10 ¢ 19 C ; N A = 6.02 ¡ 10 23 ; h = h /2 £ COnveRsiOns¡ ¢eV £¢.¤ " ¢¥-¢9 jOules ¦ ¢A £¢¥-¢¥ m = ¥.¢ nm ¦ ¢ MeV = ¢¥ ¤ eV sin0 ° = cos90 ° = 0, sin30 ° = cos60 ° = 1/2, sin45 ° = cos45 ° = 1/ 2 , sin60 ° = cos30 ° = 3 /2, sin90 ° = cos0 ° = 1 DOUbLE sLiT i¡TERfERE¡CE ¢ d si¡ ¡ = n ¢ (maxima) , d si¡ ¡ = ( n + £¤¥) ¢ (mi¡ima) de Broglie: " = h P ; f = E h...
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final - PHYSICS 2D FINAL EXAM SPRING QUARTER 2008 PROF...

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