課程名稱︰普通化學甲上
課程性質︰物理系必帶
課程教師︰陸駿逸
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2018/11/16
考試時限（分鐘）：130分鐘
是否需發放獎勵金：是
（如未明確標示，則不予發放）
試題 :
Genral Chemistry
(1)(10pts)Write the chemical formulas for the following compounds:
(a)Potassium sulfate
(b)Ammonium chromate
(c)Lithium hydride
(d)Calcium cyanide
(e)Hydrazine
(2)(8pts)What is the definition of the Mulliken's electronegativity scale?
(3)(10pts)Draw Lewis electron dot diagrams for the following species: (a)
perchlorate ion (b)sulfer hexafluoride.
(4)(12pts)For each of the following molecules or ions, give the steric number
and sketch and name the approximate molecular geometry. In each case, the
central atoms is written first and the other atoms are bonded to it
directly.
(a)PF3
(b)ClF
3
(c)SO F
2 2
(5)(10pts)Assign oxidation numbers to the atoms in each of the following
species:
4- 2-
NH NO , Fe(CN) , Cr O
4 3 6 2 7
(6)(30pts)A particle is confined in a 1D infinite potential well. The particle
wave function obeys the time-dependent Schrodinger equation.
h ∂ h^2 ∂^2
i------Ψ(x,t)= - ---- ------Ψ(x,t)
2π∂t 2m ∂x^2
within 0≦x≦L
(a)Suppose that at time t=0, the wave function is given as
Ψ(x,0)=N(2sin(πx/L)-sin(2πx/L))
where N is a normalization constant. What is the wave function at the
later time Ψ(x,t)?
(b)Does Ψ(x,t) obeys the time-independent Schrodinger equation?
(c)Calculate the averaged energy <E> at t=0
(d)Calculate the averaged energy <E> at an arbitrary later time t.
(7)(15pts)The five 3d orbitals of the heavy atom Kr are occupied by ten
electrons. Knowing the orbital wave functions
φ (x,y,z)=C(2z^2-x^2-y^2)e^(-r/3a0)
3d_(z^2)
φ (x,y,z)=(√3)C(x^2-y^2)e^(-r/3a0)
3d_(x^2-y^2)
φ (x,y,z)=(2√3)Cxye^(-r/3a0)
3d_(xy)
φ (x,y,z)=(2√3)Cyze^(-r/3a0)
3d_(yz)
φ (x,y,z)=(2√3)Cxze^(-r/3a0)
3d_(xz)
where a0 is the Bohr radius, and C is a normalization constant. Show that
the sum of the electron density from these ten electrons becomes spherical
symmetric.
(8)(15pts)Given the hydrogen 1s orbital φ (x,y,z)=Ce^(-r/a0) where C is a
1s
constant, and a0=ε0h^2/(πme^2) is the Bohr radius. Show that φ obeys
1s
the Schrodinger equation
h^2 e^2
(- --------▽^2- ---------) φ(x,y,z)=E φ(x,y,z)
8π^2m 4πε0r
where ▽^2=∂^2/∂x^2+∂^2/∂y^2+∂^2/∂z^2. Obtain the expression for the
energy E for this orbital.
∂r ∂(x^2+y^2+z^2)^(1/2)
Hint: --- =-----------------------
∂x ∂x
(9)(20pts)Given the 2px orbital φ (x,y,z)=Cxe^(-r/2ao) where r=
2px
(x^2+y^2+z^2)^(1/2), C is a constant, and a0 is the Bohr radius.
(a)Is φ the eigenfunction of h ∂ h ∂? If so, what is its
2px L =i--z---- - i--y----
x 2π∂y 2π ∂z
eigenvalue? What is <Lx>?
(b)Is φ the eigenfunction of h ∂ h ∂? If so, what is its
2px L =i--y---- - i--x----
z 2π∂x 2π ∂y
eigenvalue? What is <Lz>?
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