課程名稱︰化學鍵 課程性質︰化學系選修 課程教師︰金必耀老師 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2013/4/19 考試時限（分鐘）：110mins 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 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 只要定性解釋就好了 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 這題分數很多 最好順便寫出主量子數 不用大算特算真是可喜可賀 ˊˇˋ --

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