作者tienfirst (燕子)
看板NTU-Exam
标题[试题] 97上 陆骏逸 普通化学上 期中考
时间Fri Nov 21 09:26:13 2008
课程名称︰普通化学甲上
课程性质︰化学系必带
课程教师︰陆骏逸
开课学院:理学院
开课系所︰化学系
考试日期(年月日)︰2008/11/19
考试时限(分钟):10:20~12:30(延长)
是否需发放奖励金:嗯
试题 :
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General Chemistry I Midterm Exam
2008/11/19
1.(18pts) Write down the Lewis structures and predict the geometries of
the following compounds. Do they have the electric dipole moments?
(a) SF4
(b) BF3
(c) O3
2.(6pts) Write down the chemical formula of the following compounds.
(a) Calcium cyanide
(b) Potassium hypochlorite
(c) Ammonium dichromate
3.(9pts) Write down the names of the following compounds.
(a) Al2O3
(b) Cu2S
(c) Mg2SiO4
4.(30pts) Given the time-dependent Schrodinger eqation of a particle in
the poteneial well 0≦x≦2 .
δ 1 δ^2
i ─ Ψ(x,t) = - ─ ── Ψ(x,t)
δt 2 δx^2
where for simplicity we have set h/2π=1 and m=1
(a) Suppose that at t=0,the wave function is Ψ(x,t=0)=sinπx. What
is the wave function at the later time Ψ(x,t) which satisfies
the Schrodinger eqation? What is the energy of the particle?
(b) Suppose that at t=0, the wave function is
1
Ψ(x,t=0) = ─ sinπx - √(2/3)sin2πx. What is the wave function
√3
at the later time Ψ(x,t) which satisfies the Schrodinger eqation?
(c) Followiog the question (b), does the function
1
Ψ(x,t=0) = ─ sinπx - √(2/3)sin2πx satisfies the time-
√3
independent Schrodinger equation?
(d) Following the equation (b), what is the averaged energy of the
particle at time t=0
5.(20pts) Given the time-independent Schrodinger equation of a particle
1 δ^2
in the finite well 0≦x≦2. - ─ ─── Ψ(x) + V(x)Ψ(x) = EΨ(x)
2 δx^2
where for simplicity we have set h/2π=1 and m=1. The potential is
V(x) = 3 for x≧2 or x≦0, V(x) = 0 when 0≦x≦2.
(a) Tofind the solution (Ψ(x) together with its E) which is useful
for quantum mechanics, what is the suitable boundary condition
for the wave function at x → ∞ and x → -∞?
(b) Write down the joining conditions at x = 0 abd x = 2?(You don't
need to prove them.)
(c) Suppose that we try to find a bound state by guessing (rightly or
wrongly) E = 2. Try to find out whether you can get a wave
function Ψ(x) satisfies the conditions in (a)(b) above.
6.(15pts) Given two atomic orbitals Ψ1(r,θ,ψ) = R3d(r)Y2,1(θ,ψ) and
Ψ2(r,θ,ψ) = R3d(r)Y2,-1(θ,ψ). The radial part is R3d(r) α
r^(2)e^(-r/3a0) where a0≒0.5A us Bohr radius.
(a) Combine them to obtain the two conventional d orbitals.
(b) Indicate the names of the orbitals you obtained(e.g. dx^2,dxy,..)
(c) Draw two figures to represent the wave function of these two
orbitals.
7.(15pts)Consider the 1D problem where the two electrons are in an
infinite potential well 0≦x≦L.
(a) Suppose that one electron is in the orbital
Ψ1(x) = √(2/L)sin(πx/L), and another one is in the orbital
Ψ3(x) = √(2/L)sin(3πx/L).Write down the two states with the
correct exchange symmetry where the two electrons have the
opposite ms.
(b) What are the probability densites for these two states where the
two electrons happen to be at the same point x = L/2?
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◆ From: 140.112.199.211
1F:推 kedvirlins :请各位相信这是化学课! 11/21 15:49
2F:推 wartmh :对!这是包着普化外衣的... 11/21 16:04
3F:→ thomas2451 :小心 教授就在你身後 11/21 18:24
4F:→ tienfirst :哈哈~大家怎麽推这麽快~~XDDDDDDDDD 11/21 20:33
5F:推 kedvirlins :应该是我想问怎麽你PO那麽快XD 11/21 23:19
6F:推 cranfis :我打到一半被你PO走............ 11/23 16:34
7F:→ kedvirlins :这份题目颇热门的嘛...(误)XD 11/23 17:55
8F:推 lancer1668 :太精美了....对这真的是化学课.... 11/25 18:08
※ m781115:转录至看板 CHSH_97_320 04/11 23:47