[試題] 97上 陸駿逸 普通化學上 期中考

[tienfirst (燕子)]

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 :

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　　　　　        　　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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