[試題] 104上林英智無機化學一第一次期中考

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課程名稱︰無機化學一課程性質︰必修課程教師︰林英智開課學院：理學院開課系所︰化學系考試日期（年月日）︰104/10/21 考試時限（分鐘）：120分鐘試題 : 1. In the particle-in- a-box model show that Ψ = A sin rx + B cos sx (A, B, r, and s are constants) is a solution to the wave equation for the one- dimensional box, prove r=s=(2mE)^(1/2)(2π/h). (5 points) 2. In solving the Schordinger equation, Spherical Coordiante System (r,θ,φ) is used replacing the (x, y, z) i.e. x = r sinθcosφ; y = r sinθsinφ; z = r cosθ yielding the following equation and Ψ(x, y, z) = Ψ (r,θ,φ)= R(r)Θ(θ)Φ(φ) http://i.imgur.com/IefcUVL.png

Use the technique of separation of variables to solve the part of φ (Φ(φ)). (10 points) 3. For the electronic configuration of carbon (2s)^2 (2p)^2 Derive the term symbols (spectroscopic terms). Find at least one wave equation for all states (not all microstates). Hint use the orthogonal and normalization relationship. (15 points) 4. Use the "Spin factoring" method to find the spectroscopic terms of d^2 f^1 and d^3. (15 points) 5. (a) Use the Slater's rule to estimate the ionization energy of sodium and potassium. (b) Calculate S (shielding constant) and Z* for 4s and 3d electrons of Sc and Ti, comment these data with that of Ni. (10 points) 6. The size of the transition-metal atoms decreases slghtly from left to right in the periodic table. What factors must be considered in explaining this decrease? In particular, why does the size decrease at all, and why is the decrease so gradual? (5 points) 7. Draw the resonance structures for the isoelctronic ions NSO- and SNO-, and assign formal charges. Which ion is likely to be more stable? (5points) 8. Give Lewis dot structures and sketch the shapes of the following: (a) IO4^- (b) IO(OH)5 (c) ClOF_4^- (d) XeO2F2 (e) TeF4^2-. (10 points) 9. (a) In PF4^+, the F...F and P-F distances are 238pm and 145.7pm, respectively. Use the Ligand Close Packing model to predict the P-F distance in POF3, which has an F-P-F angle of 101.1. (b) The C-F distances (from 131.9 to 132.9 pm) and the F-C-F bond angles (from 101.3 to 109.5) differ considerably in F2C=CF2, F2C=O, CF4 and F3CO-, the F-F distance in all four structures is very nearly the same (215 to 218pm). Explain, using the Ligand Close Packing model. (10 points) 10. (a) Are the CF3 groups in PCl3(CF3)2 more likely axial or equatorial? Explain. (b) Are the axial or equatorial bonds likely to be longer in ScCl5? Explain. (5 points) 11. Give descriptions and explanations of the following graph on the first (middle), second ionization (upper) energy and electron affinity (bottom). http://i.imgur.com/pPCcHjv.jpg