課程名稱︰物理化學二
課程性質︰必帶
課程教師︰陳振中
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰98/01/10
考試時限（分鐘）：120
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1.A popular three-parameter approximation for intermolecular potetial is the
Morse potential:
V(R) = De{1-exp[-a(R-Re)]}^2
(a) What is the theoretical "defect" of the Morse potential and why this
"defect" is of no significance in chemistry?
(b) What is the physical meaning of De?
(c) Determine the parameter a in terms of De and the force constant at
equilibrium (k).
2. Apply the Taylor expansion to the potential energy given by the Morse
potential V(R) = De{1-exp[-a(R-Re)]}^2 to show that the force constant k is
given by k = 2*De*(a^2)
3. Calculate the relative population of the first five rotational levels of the
~
ground state vibrational state of H35Cl at 300K. (Bv=10.4398cm^-1 forν=0)
4. Calculate the Huckel molecular orbital energies of allyl radical, which is a
planar radical, in terms of the Coulomb integrals (α) and resonance
integrals (β).
5. By differentiation of the expression for the Lennard-Jones potential, show
dV
that the distance Rm at the minimum where ─ =0 is Rm = (2^(1/6))*σ.
dR
Substituting this relationship into the original equation, show that the
Lennard-Jones potential may also conventionally be given by
Rm Rm
V = ε[(─)^12 -2*(─)^6]
R R
6. Consider a linear triatomic molecule, ABC
(a) Find the center of mass (which by symmetry lies on the molecular axis)
(b) Show that the moment of inertia is given by
1
I = ─[((RAB)^2)*mA*mB + ((RBC)^2)*mB*mC + ((RAB + RBC)^2)*mA*mC]
M
where RAB is the AB bond distance, RBC is the BC bond distance, mi are the
masses of the atoms, and M = mA + mB + mC.
(c) Show that if RAB = RBC and mA = mC, then I = 2*mA*(RAB)^2.
7.
(a) For a particle in a square box of length L with origin at x=0 and y=0,
write down the wave functions and energy levels.
(b) If the system of (a) is perturbed by H'=b for 0.5L＜x＜0.75L and
0.5L＜y＜0.75L , where b is a constant, and H'=0 elsewhere, find E(1) for
the ground state.
P.S.後來助教又多出了兩題，不過我沒把題目抄下來orz
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