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Unformatted text preview: Name: Chem 5314 test #3 solutions, out of 37 marks I want complete, detailed answers to the questions. Show all your work to get full credit. Data: Z  e x 2 = (1) Z  x 2 e x 2 = 2 3 / 2 (2) The Schr odinger time dependent equation in one dimension is i ~ ( x,t ) t = ~ 2 2 m 2 ( x,t ) x 2 + V ( x ) ( x,t ) (3) The Schr odinger time independent equation in one dimension is ~ 2 2 m d 2 n ( x ) dx 2 + V ( x ) n ( x ) = E n n ( x ) (4) The particle in a one dimensional box (of size L ) energy levels are E n = n 2 2 ~ 2 2 mL 2 n = 1 , 2 , 3 ,... (5) The particle in a threedimensional box (of side lengths a , b , c ) energy levels are E = 2 ~ 2 2 m n 2 x a 2 + n 2 y b 2 + n 2 z c 2 n x , n y , n z = 1 , 2 , 3 ,... (6) energy levels of the particle on a ring: E n = n 2 ~ 2 2 mR 2 n = 0 , 1 , 2 ,... (7) potential energy of the harmonic oscillator: V ( x ) = 1 2 kx 2 = 1 2 2 x 2 ground state wavefunction of the harmonic oscillator: ( x ) = 2 1 / 4 e x 2 (8) with = 2 ~ and = ( k/ ) 1 / 2 (9) 1 where k is the force constant and is the reduced mass. reduced mass formula: = m 1 m 2 / ( m 1 + m 2 ) energy levels of the harmonic oscillator: E n = ( n + 1 / 2) ~ , n = 0, 1, 2, ... potential energy of the Morse oscillator: V ( r ) = D e [1 e ( r r ) ] 2 (10) energy levels of the Morse oscillator: E n = ( n + 1 / 2) ~  ( n + 1 / 2) 2 ( ~ ) 2 4 D e (11) energy levels of the rigid rotor: E = ( + 1) ~ 2 2 r 2 (12) Speed of light = c = 3.0 10 8 m/s electron mass = 9.11 10 31 kg mass conversion from amu to kg: 1.66 10 27 kg/amu Avogadros constant = N A = 6.022 10 23 mol 1 Planck constants: h = 6.6262 10 34 Js and ~ = 1.05459 10 34 Js = 3.14159 1 eV = 1.6022 10 19 J (electron volt to joule conversion) Relationship between the wavelength of a photon and its energy:...
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 Fall '11
 Nielsen
 Physical chemistry, pH

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