課程名稱︰普通化學甲上 課程性質︰化學系必帶 課程教師︰陸駿逸 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2008/11/19 考試時限（分鐘）：10:20~12:30(延長) 是否需發放獎勵金：嗯 試題 : ________________________________________________________________________ 　　　　　 　　General Chemistry I Midterm Exam 2008/11/19 1.(18pts) Write down the Lewis structures and predict the geometries of the following compounds. Do they have the electric dipole moments? (a) SF4 (b) BF3 (c) O3 2.(6pts) Write down the chemical formula of the following compounds. (a) Calcium cyanide (b) Potassium hypochlorite (c) Ammonium dichromate 3.(9pts) Write down the names of the following compounds. (a) Al2O3 (b) Cu2S (c) Mg2SiO4 4.(30pts) Given the time-dependent Schrodinger eqation of a particle in the poteneial well 0≦x≦2 . δ 1 δ^2 i ─ Ψ(x,t) = - ─ ── Ψ(x,t) δt 2 δx^2 where for simplicity we have set h/2π=1 and m=1 (a) Suppose that at t=0,the wave function is Ψ(x,t=0)=sinπx. What is the wave function at the later time Ψ(x,t) which satisfies the Schrodinger eqation？ What is the energy of the particle？ (b) Suppose that at t=0, the wave function is 1 Ψ(x,t=0) = ─ sinπx - √(2/3)sin2πx. What is the wave function √3 at the later time Ψ(x,t) which satisfies the Schrodinger eqation? (c) Followiog the question (b), does the function 1 Ψ(x,t=0) = ─ sinπx - √(2/3)sin2πx satisfies the time- √3 independent Schrodinger equation？ (d) Following the equation (b), what is the averaged energy of the particle at time t=0 5.(20pts) Given the time-independent Schrodinger equation of a particle 1 δ^2 in the finite well 0≦x≦2. - ─ ─── Ψ(x) + V(x)Ψ(x) = EΨ(x) 2 δx^2 where for simplicity we have set h/2π=1 and m=1. The potential is V(x) = 3 for x≧2 or x≦0, V(x) = 0 when 0≦x≦2. (a) Tofind the solution (Ψ(x) together with its E) which is useful for quantum mechanics, what is the suitable boundary condition for the wave function at x → ∞ and x → -∞？ (b) Write down the joining conditions at x = 0 abd x = 2？(You don't need to prove them.) (c) Suppose that we try to find a bound state by guessing (rightly or wrongly) E = 2. Try to find out whether you can get a wave function Ψ(x) satisfies the conditions in (a)(b) above. 6.(15pts) Given two atomic orbitals Ψ1(r,θ,ψ) = R3d(r)Y2,1(θ,ψ) and Ψ2(r,θ,ψ) = R3d(r)Y2,-1(θ,ψ). The radial part is R3d(r) α r^(2)e^(-r/3a0) where a0≒0.5A us Bohr radius. (a) Combine them to obtain the two conventional d orbitals. (b) Indicate the names of the orbitals you obtained(e.g. dx^2,dxy,..) (c) Draw two figures to represent the wave function of these two orbitals. 7.(15pts)Consider the 1D problem where the two electrons are in an infinite potential well 0≦x≦L. (a) Suppose that one electron is in the orbital Ψ1(x) = √(2/L)sin(πx/L), and another one is in the orbital Ψ3(x) = √(2/L)sin(3πx/L).Write down the two states with the correct exchange symmetry where the two electrons have the opposite ms. (b) What are the probability densites for these two states where the two electrons happen to be at the same point x = L/2？ ________________________________________________________________________ --

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