Exam 2 2003

# Exam 2 2003 - PHYSICS 13 HOUR EXAM 2 FALL 2003 NAME Grades...

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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 /20 Total: /200 This is a closed book, closed notes exam. You may use calculators. Make sure you show all your work! You will get partial credit. Useful data and equations : 1 dimensional Schrödinger equation: h ´ 2 2m d 2 dx 2 ψ (x) + V(x) ψ (x) = E ψ (x) ( η =h/2 π ) | ψ (x)| 2 is the Probability per unit length. Kinetic Energy = 1/2 mv 2 = p 2 /2m (for a plane wave = η 2 k 2 /2m) de Broglie: λ =h/p ; wave number k=2 π / λ Photon energy E = hf = h ω/2π Quantum mechanical angular momentum | L |= [ λ ( λ +1)] 1/2 η and L z = m l η Transition and photon selection rule: λ λ ± 1 Atomic 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. m λ = -l, -l+1, ... , l-1, l . Spin m s = -1/2, +1/2 Electric dipole moment p E1 = Q r (Q=charge) Rydberg Constant = 13.6 eV = k EM 2 e 4 m/2 η 2 = -E 0 (= - E 1 ground state energy of Hydrogen) Atomic electron around nucleus of charge Z, E n = -Z 2 |E 0 |/n 2 Magnetic moment - orbital: µ L = [ λ ( λ +1)] 1/2 µ B spin : µ S = g S [s(s+1)] 1/2 µ B Magnetic moment along z-axis µ L z = - m λ µ B and µ Sz = - g S m s µ B with g S = 2 and µ B = 5.79x10 -5 eV/Tesla Interaction Energy U = - µ • B = - µ z B c = 3.00x 10 8 meter/sec electron charge: e=1.60x10 -19 Coul h = 6.63 x 10 -34 J sec= 4.14 x 10 -15 eV sec η = 6.58 x 10 -16 eV sec k EM = 1 4 πε 0 = 8.99x10 9 Nm 2 /Coul 2 hc = 1.24 x 10 -6 eV m η c = 1.97x10 -7 eVm Rest energy of electron = m e c 2 = 5.11x10 5 eV Rest mass of electron = m e = 9.11x10 -31 Kg

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