# final - PHYSICS 2D FINAL EXAM FALL QUARTER 2008 PROF HIRSCH...

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Unformatted text preview: PHYSICS 2D FINAL EXAM FALL QUARTER 2008 PROF. HIRSCH DECEMBER 8, 2008 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, 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 ¡cATTeRiNg¢ £ '- £ £ h m e c (¤ ¥ cO¡ \$ )¥ h m e c = ¦§¦¨©3 A ¥ COUlOmb cON¡TANT ¢ ke ¨ = ¤©§© eV A El¡CTrosTATiCs : F = ¡q 1 q 2 r 2 (forC¡) ; U = q v (poT¡NTiAl ¡N¡rgy) ; v = ¡q r (poT¡NTiAl) FoRCE in ELECtRiC and magnEtiC fiELds (¡oREntz foRCE)¢ r F = q r E + q r v ¡ r B ; DRag foRCE¢ D = £ ¥ a ¦ v Rutherford scattering: " n = C sin 4 ( # /2) ; reduced mass μ = M 1 M 2 M 1 + M 2 ; h ¡ = 1,973 Ev A 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 =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 ; ¢ = E H ; # = 2 ¢ ¢ ; ¡ = 2 ¢ ¡ ; E = h # ; P = h ¡ ; 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 ¢£d Ph¢¤E VELO¥I¦Y § v g = d ¡ dk ¨ v p = ¡ k ¨ HEI¤E£bERG§ ¢ x ¢ p ~ h ¨ ¢ t ¢ E ~ h PHYSICS 2D FINAL EXAM FALL QUARTER 2008 PROF. HIRSCH DECEMBER 8, 2008 Schrodinger equation: - h 2 2m " 2 # " x 2 +U(x) # (x,t) =i h " # " t ; # (x,t) = \$ (x)e-i E h t Time " independent Schrodinger equation: - h 2 2m # 2 \$ # x 2 +U(x) \$ (x) =E \$ (x) ; dx- % % & \$ * \$ = 1 " square well:...
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final - PHYSICS 2D FINAL EXAM FALL QUARTER 2008 PROF HIRSCH...

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