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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