[試題] 陳逸聰 普通化學乙 期中考

[blackpanther (黑蟠桃)]

課程名稱︰普通化學乙
課程性質︰必修
課程教師︰陳逸聰
開課學院：工學院
開課系所︰土木系
考試日期（年月日）︰2007/04/27
考試時限（分鐘）：三小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :

1.Neutron diffraction is used in determining the structures of molecules.

(a)Calculate the de Broglie wavelength of a neutron moving at 1.00% of the

   speed of light. (4%)

(b)Calculate the velocity of a neutron with a wavelength of 75pm. (4%)


2.Using the Heisenberg uncertainty principle, calculate △x for each of the

  following.

(a)An electron with △v = 0.100m/s (3%)

(b)A baseball (mass = 145g) with △v = 0.100m/s (3%)

(c)How does the answer of part (a) compare with the size of a H atom? (2%)

(d)How does the answer of part (b) compare with the size of a baseball? (2%)


3.The Schrodinger equation for a particle (of mass m) in a box, with potential

  V = 0 at 0<x<l and V = ∞ at x≦0 and x≧l, is

    h^2  (d^2)Ψ
  -── ──── = EΨ
    2m   d (x^2)

(a)Derive the quantized energies and corresponding wavefunctions of the

   particle. (10%)

(b)Calculate the average position (<x>) and average linear momentum (<p>) for

   the ground state (n=1). (5%)

  As a rough approximation, conjugated polyenes, such as butadiene, vitamin A,

  and carotene, maybe considered as linear one-dimensional boxes. Vitamin A

  absorbs electromagnetic radiation most strongly at 332nm, where vitamin A is

  excited from n = 1 to n = 2 quantum states.

(c)What wavelengths of electronic radiation would absorbed by butadiene and

   carotene? (Shorter or longer than 332nm?) Explain the reasons as to why you

   think so. (5%)

(d)Estimate the length of the vitamin A "box". (5%)


4.For hydrogen atoms, the wave function for the state n = 3, l = 0, ml = 0 is

               1         1
  Ψ300 = ────── (─)^(1.5) ×[27－18＋2(σ^2))] ×e^(-σ/3)
           81×√(3π)  a0

  where σ = r/a0 and a0 is the Bohr radius (5.29×10^-11 m). Calculate the

  position of the nodes for this wave function. (6%)


5.Write the Schrodinger equation for a helium atom. (You do NOT need to solve

  it. Just write out the equation.) (6%)


6.The observed dipole moment for HCl is 1.11D and the chemical bond length for
             .
  HCl is 1.27A. (1D = 3.336×10^-30 C˙m)

(a)If HCl is fully ionic, calculate the Coulomb potential energy in the HCl

   molecule. (4%)

(b)Calculate the partial charges on H and Cl, respectively. (2%)

(c)Estimate the percent ionic character of HCl. (2%)


7.Use bond energies to estimate △H for the following reaction:

  C6H12O6(s) → 2CO2(g)＋ 2CH3CH2OH(l)

  The structure of glucose (C6H12O6) is

  Bond energy : C－C 246kJ/mol

                C－O 358kJ/mol

                O－H 467kJ/mol

                C－H 413kJ/mol

                C＝O 799kJ/mol (6%)


8.Consider the following bond lengths:
           .
  C－O 1.34A
           .
  C＝O 1.23A
           .
  C≡O 1.09A
                                                                           .
  In the (CO3)2- ion, all the three C－O bonds have identical bonds of 1.36A.

  Why? (5%)


9.Terminology, illustration, and explanation.

(a)Give experimental examples that can demonstrate the dual nature of light.

   (6%)

(b)Describe briefly how fireworks produce their brilliant colors. (4%)

(c)Zero-point energy. (3%)

(d)Bohr's correspondence principle. (3%)

(e)Take the orbitals in hydrogen atom to explain the degeneracy of quantum

   states. (3%)

(f)Effective nuclear charge. (3%)

(g)List the decreasing orders of reducing abilities for Li, Na, and K in gas

   phase and in aqueous  solution. Explain the reasons as to why they are so.

   (5%)


第七題中葡萄糖的結構圖在Zumdahl的Chemical Principles, 5th edition中的習題第36題

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