课程名称︰化学键 课程性质︰化学系选修 课程教师︰金必耀老师 开课学院：理学院 开课系所︰化学系 考试日期（年月日）︰2013/4/19 考试时限（分钟）：110mins 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Chemical bonding Midterm Spring,2013 1.(16%)Bohr model of atoms (a)Apply the Bohr-de Broglie approach and variational principle to find out the quantized energies for the stationary states of a hydrogen-like atom. (b)Then apply the same technique to the ground state energy of a Helium atom. 2.(10%)Hydrogen atomic orbitals (a)Use sketches of 2s and 2p orbitals to distinguish between (a) the radial wavefunction and (b) the radial distribution function. (b)Draw picture of the two d orbitals in the xy-plane as flat projection in the plane of paper. Label each drawing with the appropriate mathematical function, and include a labelled pair of Cartesian coordinate axes. Label the orbital lobes correctly with + and - signs. 3.(16%)Vanadium atem Consider the vanadium atom with the ground-state electron -ic configuration [Ar]3d^34s^2. Use the following interelectronic repulsion terms J and one-electron ionization energy terms W: J(3d,3d) = 17.36eV J(3d,4s) = 11.16eV J(4s,4s) = 8.68eV W(3d) = 65.21eV W(4s) = 46.86eV (a)Calculate the excitation energy: V(3d^3 4s^2) ---> V(3d^5) (b)Calculate the ionization energy for removal of a 3d electron: V(3d^3 4s^2) ---> V+(3d^2 4s^2) + e- (c)Calculate the ionization for removal of a 4s election: V(3d^3 4s^s) ---> V+(3d^3 4s^1) + e- (d)From your results in parts (b) and (c), which electron, 3d or 4s has the lower ionzation energy? 4.(12%)VSEPR and Valence sphere model In class, I mentioned that the Gillespie-Nyholm-Sidgwick-Powell theory,ie,. VSEPR, of chemical bonding, which, according to Prof. Henry Bent, get the right answer (sometimes) for the wrong reason. Why is that? Use methane as an example to interpret it. (Hint: The total energy of a methane molecule consists of the following contributions Etot = Ekin + Eee + Een where Ekin, Eee and Een are the kinetic energy of electron pair, electron- electron replusion, and electron-nuclear energy attraction, respectively. The simplest way to take care of the Pauli exclusion principle is to assume that valence electron pairs are represented by four non-overlapping charge spheres with charges -2e. The radii of these four sphere are in principle related to the kinetic energies or de Broglie wavelengths of electron pairs. Eee and Een can be determined through the arrangement of charged spheres classically.) 意思就是不用大算特算 只要定性解释就好了 5.(12%)VSEPR What shapes would you expect for the species (a)SO3, (b)SO3 2-, (c)IF5, (d)ICl4- ? 6.(12%)Valence bond model Draw hybrid-orbital representations including π bonds for NO3-, NCO- and CNO-. 7.(14%)Hybrid orbitals consider the following two hybrid orbitals: ψa = N(2pz + γ2s) ψb = N(2pz - γ2s) where 2p and 2s are atomic orbitals on one atom. (a)Determine the normalization constant N, expressed in terms of the constant γ. (b)Show that ψa and ψb are orthogonal. (c)Sketch the shape of the hybrid orbitals for γ=0.2. (d)Repeat part (c) for γ=1.0. 8.(12%) Hybrid orbitals Predict the hybridization of orbitals required in (a)BCl3, (b)NH4+, (c)SF4, (d)XeF4 这题分数很多 最好顺便写出主量子数 不用大算特算真是可喜可贺 ˊˇˋ --

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