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Unformatted text preview: 1 PHYSICS 13 FINAL EXAM FALL 2003 NAME___________________________________________ Useful data and equations : Schrdinger equation: ( =h/2 ) h 2 2m d 2 dx 2 (x) + V(x) (x) = E (x) For two interacting bodies, the m is replaced by reduced mass and x is the separation. Quantum mechanical angular momentum | L |= [ l(l +1)] 1/2 and L z = m l Note the h-bar or more generally | J | = [j(j+1)] 1/2 and J z = m j with m j = j, j-1, ..., -j Addition of orbital ( l ) and spin (1/2) angular momenta yields j= l-1/2, l +1/2. Addition of J 1 and J 2 yields sum J with quantum number j = |j 1-j 2 |, |j 1-j 2 |+1, ..., j 1 +j 2-1, j 1 +j 2 Atomic electron spectroscopic notation: n l 1 or 2 or , where n is principal quantum number, l is orbital angular momentum quantum number, l =0,1,2,...,n-1, with notation l =0->s, 1->p, 2->d, 3->f,... Avogadro's Number: N A = 6.0 x 10 23 number of atoms, molecules or nuclei in a MOLE (or gram molecular wt) Non-relativistic Kinetic Energy =mv 2 /2 Magnetic dipole interaction energy = Z B Z Lorentz Transformation frame S moves in the +x direction with V as seen in S: x= (x+Vt), y=y, z=z, t= (t+Vx/c 2 ) where =1 / (1-v 2 /c 2 ) Doppler effect = (1+ v/c ) / (1 v/c ) Time dilation t = t Relativistic Energy E= m 0 c 2 / (1-v 2 /c 2 ) ; Rest energy = m c 2 ; Relativistic Kinetic Energy = E - m c 2 Photon: E=hf ; c= f ; k=2 / ; =2 f Electric dipole moment p E1 = Q r (Q=charge, r=separation) Average Thermal Energy at Temperature T(Kelvin) = k(Boltzmann)T/2 per degree of freedom Decay N(t) = N(0)exp(- t), =1/(mean lifetime) = ln2/T 1/2 where T 1/2 is the half-life Nuclear Binding Energy E b = (Zm(p) + Nm(n) - M A ) c 2 Coulomb Potential k EM Q 1 Q 2 /r Newton Law of Gravitation : potential energy = Gm 1 m 2 /r Constants : Velocity of light: c = 3.00x 10 8 meter/sec electron charge: e=1.60x10-19 Coul Newton gravitational constant G = 6.67x10-11 J*m/Kg 2 k(Boltzmann) = 1.38x10-23 J/K = 8.62x10-5 eV/K Plancks constant: h = 6.63 x 10-34 J sec= 4.14 x 10-15 eV sec = h/2 = 1.05 x 10-34 J sec = 6.58 x 10-16 eV sec k EM = 1/4 = 8.99x10 9 Nm 2 /Coul 2 hc = 1.24 x 10-6 eV m Rest energy of electron = m e c 2 = 511 keV = 0.511 MeV m e =9.1x10-31 Kg Unified mass units 1 u = 1.66x10-27 Kg (1u)c 2 = 931.5 MeV Units: Energy: 1 J(oule) = 1 Kg m 2 /sec 2 ; 1 eV(electron Volt) = 1.6x10-19 J CHOOSE 2 OUT OF LAST 3 PROBLEMS (V, VI, VII) i.e drop one **EXTRA CREDIT Prob.VIII 2 PHYSICS 13 FINAL EXAM FALL 2003 NAME___________________________________________ This is a closed book, closed notes exam. You may use calculators. Make sure you show all your work! You will get partial credit for correct intermediate steps....
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