课程名称︰普通化学甲上 课程性质︰物理系必带 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）︰2018/11/16 考试时限（分钟）：130分钟 是否需发放奖励金：是 （如未明确标示，则不予发放） 试题 : 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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