課程名稱︰普通化學甲〈上〉
課程性質︰物理系大一必帶
課程教師︰陸駿逸
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰98/11/11
考試時限（分鐘）：130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.(24pts)Write down the Lewis structures, assign the formal charge, and
predict the geometries of the following ions. Do they have the electric
dipole moments?
(a) (S2O3)^2-
(b) (NO3)^-
(c) (BrO2)^-
(d) H2CSO
2.(8pts)Write down the chemical formula of the following compounds.
(a) Ammonium carbonate
(b) Magnesium chromate
(c) Potassium permanganate
(d) Sodium peroxide
3.(9pts)Write down the names of the following compounds.
(a) Ca(CN)2
(b) NaHCO3
(c) Hg2SO4
4.(20pts)Given the time-dependent Schrodinger equation of a particle in the
potential well 0≦x≦2π
∂ -1 ∂^2
i---Ψ(x,t) = --- ----- Ψ(x,t)
∂t 2 ∂x^2
where for simplicity we have set h/2π =1 and m=1. Outside the well, the
potential is very high (infinite).
(a) At t=0, the wave function is known as Ψ(x,t=0)=N(sin(x/2)-sinx) where
N=(2π)^-0.5. Plot the wave function.
(b) Calculate the averaged energy at t=0.
(c) Obtain and plot the wave function at the later time t=8π,t=16π and
t=24π.
5.(20pts)Explain the relation between the two Schrodinger equations. When
will you use the time independent Schrodinger equation?
6.(20pts)Consider the 2D problem where the electron is in an in finite
potential well. The potential is zero within the region 0≦x≦Lx and
0≦y≦Ly, where Lx=(2/3)Ly. Find the five solutions of the time-independent
Schrodinger equation which have the lowest energies.
7.(20pts)Draw the suitable pictures to illustrate the following atomic
orbitals. a0≒0.5Åis a constant.
(a) φ~(r-2a0)e^(-r/2a0)
(b) φ~xe^(-r/2a0)
(c) φ~(3y^2-r^2)e^(-r/3a0)
(d) φ~(x^2-z^2)e^(-r/3a0)
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