课程名称︰普通化学一 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）︰2013/11/20 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. (15pts) What are the chemical formulas of the following compounds? (a) Sodium peroxide (b) Potassium dichromate (c) Calcium sulfate (d) Ammonium cyanide (e) Magnesium bromide 2. (18pts) Draw the Lewis structures of the folowing compounds. Lable the oxidation numbers and the formal charges. (a) NaClO3 (b) SCN- (c) H3NBF3 3. (15pts) Use the VSEPR theory to predict the geometries of the following compounds. (a) (BrO3)- (b) SO2Cl2 (S is the center atom) (c) NNO 4. (20pts) Write a paragraph to describe how does Pauling difine the electronegativity scale. 5. (20pts) Consider the matter wave inside a potential well within 0≦x≦3. Suppose the wave funcion at an instance is ψ(x)=cx(3-x) where c is a constant. (a) Remember that the wave function is related to the probability. What is a suitable value for c? (b) Use the averaged kinetic energy formula ＜E＞ 2 2 2 3 1 ┌ h ┐ d 1 ┌ h ┐ =∫dxψ*(x)｛-─│— │ ──ψ(x)｝=—│— │ε to calculate the 0 2m└2π┘ 2 2m└2π┘ dx constantε. (c) Expand ψ(x) as the sum of the sinusoidal wave ψ(x) π 2π 3π =a sin(—x)+a sin(—x)+a sin(—x)+.... 1 3 2 3 3 3 Calculate a and a . 1 2 nπ (d) Write down the kinetic energy E of the wave sin(—x). n 3 ∞ 2 (e) Use the first two terms of Σ E │a │ to calculate the (approximate) n=1 n n averaged kinetic energy ＜E＞. 3 π 3 2 π You may need the following integrals: ∫xsin(—x)dx=9/π,∫x sin(—x)dx= 0 3 0 3 3 3 2 π 3 2 2π 27/π-108/π ,∫x sin(—x)dx=-9/(2π),∫x sin(—x)dx=-27/(2π) 0 3 0 3 2 ∂ ∂ 6. (20pts) Given the wave equation i──Ψ(x,t)=-——Ψ(x,t). ∂t 2 ∂x (a) The equation has two solutions Ψ (x,t)=sin(x)f (t) and Ψ (x,t)= 1 1 2 cos(3x)f (t). Suppose that at t=0, f (0)=f (0)=1. 2 1 2 Find f (t) and f (t). 1 2 (b) Suppose that Ψ (x,t)=2Ψ (x,t)-iΨ (x,t). Substitute Ψ (x,t) 3 1 2 3 into the wave equation to show that it is also a solution. (c) Draw the real part of Ψ (x,t) for t =0, t =π/2, t =π. 3 0 1 2 7. (20pts) Draw the following atomic orbitals, and write down the quantum numbers n and l. In your drawing, remember to label the x, y, z axises. -r/(2a0) (a) ψ(x,y,z)～ye -r/(3a0) (b) ψ(x,y,z)～xze 2 2 -r/(3a0) (c) ψ(x,y,z)～(x -z )e -r/(2a0) (d) ψ(r,θ,φ)～cos(φ+π/4)sinθe 2 2 2 -r/(3a0) (e) ψ(x,y,z)～(2y -x -z )e 2 2 2 Where r=√(x +y +z ), and a0≒0.5Å. --

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