課程名稱︰物理化學下 課程性質︰必修 課程教師︰陳逸聰 開課學院：理學院 開課系所︰農業化學系(化學系開課) 考試日期（年月日）︰2009年06月16日 考試時限（分鐘）：170分鐘 是否需發放獎勵金：Yes!! （如未明確表示，則不予發放） 試題 : 1. A particle in an one-dimensional box is subject to a potential well of ╭ ∞, x≦0 and x≧a V(x) = ｛ ╰ 0, 0≦x≦a (a) Write out the corresponding Schrodinger equation. (2%) n^2 h^2 (b) Calculate the eigenvalues of this systen to be E＝ ───── (5%) 8 m a^2 (c) Find the wave functions of this system. (5%) (d) A crude treatment of the π electron of a conjugated molecule 　　 regards these electrons as moving in the particle-in-a-box potential. The Pauli exclusion principle allows no more than two electrons (with opposite spins) to occupy each box level. For the molecule Ｃ═Ｃ─Ｃ═Ｃ─Ｃ═Ｃ, take the box length as 10Α and use this model to estimate the wavelength of light absorbed when a π electron is excited from the highest-occupied to the lowest-vacant box level. (4%) 2.(a) Calculate the fundamental vibration frequency of carbon monoxide, CO, considering it to behave like to harmonic oscillator with a force constant 1902.5 N/m. (4%) (b) By how much will this frequency change if the molecule contains the isotope C-13 instead of the more abundant C-12? (4%) 3. The equilibrium bond length of HF is 0.92Α. From the rotational energy J(J+1) (h/2π)^2 E(rot)＝───────── (J＝0,1,2,3,4...) 2 μ r^2 Where J is the rotational quantum number, μ is the reduced mass, r is the bond length. (a) Calculate the reduced mass of HF. (3%) (b) Calculate the radiation wavelength needed to make the rotational transition of HF from J＝0 to J＝1. (5%) 4. The ionization potential of an electron in an atom or molecule is the energy required to remove the electron. Calculate the ionization potential for a 1s electron in He+. Give your answer in unit of eV and kJ/mol. (5%) 5. Construst the delocalized orbital energy level diagrams of (a) 1,3-butadiene (b) cyclobutadiene (c) benzene (14%) 6. The dipole moment of the bonds C─F and C─O are 1.4 D and 1.2 D, respectively. The bond lengths are 141 pm and 143 pm, respectively. Estimate the percentage ionic character of the bonds. (8%) 7. A 2.5-mm cell was filled with a solution of dye. The concentration of the dye was 15.5 mmol/L and the wavelength of the radiation was 256 nm (where there is a maximum in the absorption). (a) Calculate the molar absorption coefficient of dye at this wavelength given that the transmission was 32 percent. (4%) (b) What will the transmittance be in a 4.50-mm cell at the same wavelength? (4%) 8. The longest-wavelength absorption band of chlorophyll a peaks in vivo at a wavelength of about 680 nm. (a) For photons with a wavelength of 680 nm, calculate the energy in J/photon, in electron volts, and in kJ/einstein. (3%) (b) CO2 fixation in photosynthesis can be represented by the reaction is ΔH ＝ +485 kJ/mol of CO2 fixed. What is the minimum number of einsteins of radiation that need to be absorbed to provide the energy needed to fix 1 mol CO2 via photosynthesis? (3%) (c) Experimentally, many values have been determined for the number of photons required to fix one CO2 molecule. The presently accepted "best values" lie between 8 and 9 photons per CO2 molecule. What is the photochemical quantum yield, based on your answer to part (b), for this process. (3%) 9. Write the distance dependences for (a) Coulomb interaction (b) Dipole-dipole interaction (c) London attraction (d) Van der Waal repulsion (8%) 10. Explain the absorption, spontaneous emmision, stimulated emmision, and transition dipole moment in spectroscopy. (8%) 11. Give examples to explain homogeneous broadening and inhomogeneous broadening in spectroscopy. (8%) --

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