課程名稱︰物理化學下
課程性質︰農化系必修
課程教師︰張大釗
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2013.3.21
考試時限（分鐘）：50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. Selectone example in the lecture and follow scientific mithod (observation,
hypothesis, experiments and conclusion) to describe it.(15)
2. Calculate de Broglie wavelength for a baseball(0.14kg) traveling at 40m/s
and an electron traveling at 1.0X10^7 m/s. What is the significance of
this finding?(15)
2 2
3. Consider the operators d/dx and d /dx . Is φ(x)=Ae^ikx+Be^(-ikx) an
eigenfunction of these operators? If so, what are the eigenvalues?(10)
..
4. Using Schtodiber equation, HΨ=EΨ, to derive the energy E=n^2 h^2/8ma^2
for a free particle in a box, where H=-(h/2π)^2/2m(d^2/〖dx〗^2 ) and
Ψ=α sinx.(15)
5. Assuming hexatriene (CH2=CH-CH=CH2-CH=CH2) with bond length 8.67 A and
butadiene (CH2=CH-CH=CH2) with bond length 5.87A are linear molecules,
calculate the wavelength for their lowest electronic energy transitions.
What do you learn from this finding?(15)
6. The following data were observed in an experiment of the photoelectric
effect on a surface of K between incidnet wavelength and evitted
electrons of the voltage.
λ(nm) 250 300 350 400 450
V(volts) 2.81 1.93 1.18 0.84 0.44
What is the importance of this study?(20)
7. Using HΨ=EΨ to calculate resonance energy and electron density of two
delocalized π-electrons of O3 molecule (O =O -O ←→ O -O =O ). Assuming
A B C A B C
O3 is a linear molecule. ΣHi and Ψ=ПΦi , where Φi=Σ(Cij)(ΨCij)
and <Ψij |Hi| Ψij'> = α for J=J',=β for J=J'±1 and =0 otherwise. Using
variation method, we can obtain secular equation as
/ \ / \
│ α-E B 0 │ │C1A│
│ B α-E B │ │C1B│ = 0
│ 0 B α-E│ │C1C│
\ / \ /
(a) Calculate the resonance energy.
(b) Derive the wave functions.
(c) Are these wave functions normalized and orthogonal with each other?
(d) Draw energy diagram.
(e) Calculate electron density of the ground state and first excited state
of O and O atoms in O3 molecule.(40)
A B
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