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PHYSICS 13 HOUR EXAM 2 FALL 2003 NAME___________________________________________ Grades: points/possible points I /50 II /30 III /50 IV /50 V /20Total: /200 This is a closed book, closed notes exam. You may usecalculators.Make sure you show all your work! You will get partial credit.Useful data and equations: 1 dimensional Schrödinger equation: −h´22md2dx2ψ(x) +V(x)ψ(x) =Eψ(x)(η=h/2π) |ψ(x)|2is the Probability per unit length. Kinetic Energy = 1/2 mv2= p2/2m (for a plane wave = η2k2/2m) de Broglie: λ=h/p ; wave number k=2π/λ Photon energy E = hf = hω/2πQuantum mechanical angular momentum |L|= [λ(λ+1)]1/2ηand Lz= mlηTransition and photon selection rule: λ→λ±1Atomic electron spectroscopic notation: principal quantum number n = 0,1,2,...; orbital angular momentum quantum number symbol λ= 0,1,2,...,n-1, with notation λ= 0->s, 1->p, 2->d, 3->f,...; magnetic quantum no. mλ= -l, -l+1, ... , l-1, l . Spin ms= -1/2, +1/2 Electric dipole moment pE1= Q r (Q=charge) Rydberg Constant = 13.6 eV = kEM2e4m/2η2= -E0(= - E1ground state energy of Hydrogen) Atomic electron around nucleus of charge Z, En= -Z2|E0|/n2 Magnetic moment - orbital: µL= [λ(λ+1)]1/2µBspin: µS= gS[s(s+1)]1/2µBMagnetic moment along z-axis µLz= - mλµBand µSz= -gSmsµBwith gS= 2 and µB= 5.79x10-5eV/Tesla Interaction Energy U = -µ •B= -µzBc = 3.00x 108meter/sec electron charge: e=1.60x10-19Coul h = 6.63 x 10-34J sec= 4.14 x 10-15eV sec η= 6.58 x 10-16eV sec kEM= 14πε0= 8.99x109Nm2/Coul2hc = 1.24 x 10-6eV m ηc = 1.97x10-7eVm Rest energy of electron = mec2= 5.11x105eV Rest mass of electron = me= 9.11x10-31Kg
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