課程名稱︰普通化學
課程性質︰系上必修
課程教師︰張大釗(音同招，不可以念成川)
開課學院：理學院
開課系所︰藥學系和醫技系
考試日期（年月日）︰2007.10.19
考試時限（分鐘）：大約一節半
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.What is the Avogadro's hypothesis? Under what assumptions,
this hypothesis is valid.
2.Using Scientfic Method to briefly describe the scientific
progress from Dalton's "Atomic model", via Thompson's model,
Rutherford's model, Bohr's model to the modern model.
(Obdervation, model, problem, experiment)
3.Cal the de Broglie wavelength for a ball(0.14KG)traveling
at 40 m/s &an electron(9.11*10^-31KG)traveling at 1.0*10^7
m/s. Whatexperimental evidence was conducted to support
de Broglie equation? What do u learn from these calculation?
4.A simple model of "a particle in a box"was applied to
demonstrate the existence of quantized electronic energy
levels.
Using Schrodinger equation to cal the energy of a particle
in a box. The Hamiltonian operator is given as
H=T+V=-h2/2m(d2/dx2)+V(x)
Assuming V(x)=∞, otherwise.
Thewave function is given as Ψ=αsin(kx).
(a) Please derive the equation for energy.
(b) Give the reason why u could obtain E=n^2h^2/8ma^2?
(c) Give the reason why u could obtain α=(2/a)^1/2?
(d) What is the probability of finding a particle in a one-dimensional
box in energy level n=3 between x=a/2 and x=2a/3?
(e) Assuming butadiene is a linear molecule, the effective
chain length for the movement of π-electron is 5.78m^-9
cal the wavelength of lowest energy transition.
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