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Unformatted text preview: Name: Chem 5314 test #1 solutions, out of 60 marks I want complete, detailed answers to the questions. Show all your work to get full credit. Data: The classical wave equation in one dimension is ∂ 2 u ( x,t ) ∂x 2 = 1 v 2 ∂ 2 u ( x,t ) ∂t 2 (1) The Schr¨ odinger time dependent equation in one dimension is i ~ ∂ψ ( x,t ) ∂t = ~ 2 2 m ∂ 2 ψ ( x,t ) ∂x 2 + V ( x ) ψ ( x,t ) (2) The Schr¨ odinger time independent equation in one dimension is ~ 2 2 m d 2 ψ n ( x ) dx 2 + V ( x ) ψ n ( x ) = E n ψ n ( x ) (3) The particle in a one dimensional box (of size L ) energy levels are E n = n 2 π 2 ~ 2 2 mL 2 n = 1 , 2 , 3 ,... (4) The particle in a threedimensional box (of side lengths a , b , c ) energy levels are E = π 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 ,... (5) energy levels of the particle on a ring: E n = n 2 ~ 2 2 mR 2 n = 0 , 1 , 2 ,... (6) 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 Avogadro’s constant = N A = 6.022 × 10 23 mol 1 Planck constants: h = 6.6262 × 10 34 Js and ~ = 1.05459 × 10 34 Js π = 3.14159 1 eV = 1.6022 × 10 19 J (electron volt to joule conversion) Relationship between the wavelength of a photon and its energy: λ = hc/E 1 Problem 1 – 16 marks Figure 1 has 4 parts corresponding to questions a), b), c), and d) respectively. TheFigure 1 has 4 parts corresponding to questions a), b), c), and d) respectively....
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This note was uploaded on 02/08/2012 for the course CHEM 5314 taught by Professor Nielsen during the Fall '11 term at University of Texas at Dallas, Richardson.
 Fall '11
 Nielsen
 Physical chemistry, pH

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