[試題] 102上 陸駿逸 普通化學一 期中考

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課程名稱︰普通化學一
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）︰2013/11/20
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :

1. (15pts) What are the chemical formulas of the following compounds?
    (a) Sodium peroxide
    (b) Potassium dichromate
    (c) Calcium sulfate
    (d) Ammonium cyanide
    (e) Magnesium bromide
2. (18pts) Draw the Lewis structures of the folowing compounds.
           Lable the oxidation numbers and the formal charges.
    (a) NaClO3
    (b) SCN-
    (c) H3NBF3
3. (15pts) Use the VSEPR theory to predict the geometries of the
           following compounds.
    (a) (BrO3)-
    (b) SO2Cl2 (S is the center atom)
    (c) NNO
4. (20pts) Write a paragraph to describe how does Pauling difine
           the electronegativity scale.
5. (20pts) Consider the matter wave inside a potential well within 0≦x≦3.
           Suppose the wave funcion at an instance is ψ(x)=cx(3-x)
           where c is a constant.
    (a) Remember that the wave function is related to the probability.
        What is a suitable value for c?
    (b) Use the averaged kinetic energy formula ＜E＞
                              2   2                 2
          3           1 ┌ h ┐  d          1 ┌ h ┐
        =∫dxψ*(x)｛-─│— │ ──ψ(x)｝=—│— │ε to calculate the
          0           2m└2π┘    2        2m└2π┘
                                 dx
        constantε.

    (c) Expand ψ(x) as the sum of the sinusoidal wave ψ(x)

               π         2π        3π
        =a sin(—x)+a sin(—x)+a sin(—x)+....
          1    3     2    3     3    3

        Calculate a  and a .
                   1      2
                                                         nπ
    (d) Write down the kinetic energy E  of the wave sin(—x).
                                       n                 3


                                   ∞        2
    (e) Use the first two terms of Σ E │a │ to calculate the (approximate)
                                   n=1 n   n

        averaged kinetic energy ＜E＞.

                                           3     π           3 2    π
    You may need the following integrals: ∫xsin(—x)dx=9/π,∫x sin(—x)dx=
                                           0     3            0      3

                3  3 2    π               3 2    2π
    27/π-108/π ,∫x sin(—x)dx=-9/(2π),∫x sin(—x)dx=-27/(2π)
                   0      3                0      3

                                                   2
                                     ∂           ∂
6. (20pts) Given the wave equation i──Ψ(x,t)=-——Ψ(x,t).
                                    ∂t             2
                                                 ∂x

    (a) The equation has two solutions Ψ (x,t)=sin(x)f (t) and Ψ (x,t)=
                                         1             1          2

        cos(3x)f (t). Suppose that at t=0, f (0)=f (0)=1.
                2                           1     2

        Find f (t) and f (t).
              1         2

    (b) Suppose that Ψ (x,t)=2Ψ (x,t)-iΨ (x,t). Substitute Ψ (x,t)
                       3         1         2                    3

        into the wave equation to show that it is also a solution.

    (c) Draw the real part of Ψ (x,t) for t =0, t =π/2, t =π.
                                3           0     1        2

7. (20pts) Draw the following atomic orbitals, and write down the quantum
           numbers n and l. In your drawing, remember to label the
           x, y, z axises.

                     -r/(2a0)
    (a) ψ(x,y,z)～ye

                      -r/(3a0)
    (b) ψ(x,y,z)～xze

                     2  2  -r/(3a0)
    (c) ψ(x,y,z)～(x -z )e

                                       -r/(2a0)
    (d) ψ(r,θ,φ)～cos(φ+π/4)sinθe

                      2  2  2  -r/(3a0)
    (e) ψ(x,y,z)～(2y -x -z )e

                2  2  2
    Where r=√(x +y +z ), and a0≒0.5Å.


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