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

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PHYSICS 2D FINAL EXAM WINTER QUARTER 2011 PROF. HIRSCH MARCH 14th, 2011 Formulas: Time dilation; Length contraction: Δ t = γ Δ t ' Δ 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: ( Δ s ) 2 =( c Δ t ) 2 -[ Δ x 2 + Δ y 2 + Δ z 2 ] v 2 / c 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 + v / c 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 = σ T 4 , e tot = power/unit area ; = 5.67 × 10 8 W / m 2 K 4 e tot = cU /4 , U = energy density = u ( λ , 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 π 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 φ work function; Bragg equation: n =2 d sin ϑ Compton scattering: '- = h m e c cos θ ); h m e c = 0.0243 A Coulomb constant : ke 2 = 14.4 eV A Coulomb force: F = kq 1 q 2 r 2 Coulomb potential: V = kq r ; Coulomb energy: U = kq 1 q 2 r Force in electric and magnetic fields (Lorentz force): r F = q r E + q r v × r B Rutherford scattering: Δ n = C Z 2 K α 2 1 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 = E 0 Z 2 n 2 E 0 = ke 2 2 a 0 = m e ( ke 2 ) 2 h 2 = 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 ω = 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 ) Δ k Δ x ~1 ; Δ Δ t ~1 group and phase velocity : v g = d dk v p = k Heisenberg: Δ x Δ p ~ h Δ t Δ E ~ h Schrodinger equation: - h 2 2m 2 Ψ x 2 +U(x) Ψ (x,t) =i h Ψ t Ψ (x,t) = ψ (x)e -i E h t
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