課程名稱︰普通化學一 課程性質︰必修 課程教師︰鄭原忠 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰100年10月19日 考試時限（分鐘）：120分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : General Chemistry (I) Mid-term Exam #1 Date: 10/19/2011 106 points 10 bonus points total 116 points ┌────────────────────┐ │Physical constants: │ │c = 3.0*10^8 m/s │ │mass of an electron = 9.1*10^(-31) kg │ │h = 6.626*10^(-34) Js │ │1 eV = 1.60*10^(-19) J │ │R = -13.6 eV │ └────────────────────┘ 1. (10%) A 60.00 g sample of a dry-cleaning fluid was analyzed and found to contain 10.80 g carbon, 1.36 g hydrogen, and 47.84 g chlorine. Answer the following questions: (a) Determine the empirical formula of the compound using the following atomic masses: C: 12.0, H: 1.0, Cl: 35.5. (b) Suggest a molecular formular for this compound that is stable in air. 2. (10%) Sulfuric acid (H SO ) form in the chemical reaction (unbalanced): SO + O + H O → H SO 2 2 2 2 4 (a) Balance the chemical equation and determine which compound is the limiting reactant. (b) What mass of H SO should be produced, and what masses og the 2 4 other reactants remain? 3. The time-independent Schrödinger equation (TISE) for a particle in two- dimension is: 2 ┌ 2 2 ┐ -h │δ Ψ δ Ψ│ ────│─── + ───│ + V(x,y) Ψ = EΨ 2 │ 2 2 │ 8π m └ δx δx ┘ Consider a particle in a 2-D square box of length L. (a) (3%)Clearly and concisely define the parameters and functions appear in the TISE. (b) (2%)What is the TISE of the 2-D particle-in-a-box system? Clearly identify the boundary conditions for the stationary states. (c) (5%)The stationary wave function are n πx n πy x y Ψ (x,y) = N sin(───) sin(───) n ,n L L x y Insert the expression into the TISE to derive an expression for energy levels in terms of n , n , and L. x y (d) (5%)Contour plots of four stationary wave function are shown on the right. The x and y directions of the box lie along the horizontal and vertical directions, respectively. Identify the quantum numbers n , n for states a-d. x y (e) (5%)Give the degeneracies of the states a-d. Sort the four states from low to high energies. 4. (10%)Consider TISE for the harmonic oscillator model: 2 2 -h δΨ 1 2 ──── ── + ── kx Ψ = EΨ 2 2 2 8π m δx 2 -αx Show that a Gaussian wave function, Ψ(x) = Ne where α is a positive parameter, is a stationary solution. Determine α and argue that the Gaussian is the ground state. What is the zero-point energy? 5. (10%)The 2s radial function for a hydrogen-like atom is 3/2 1 ┌ Z ┐ ┌ Zr ┐ -Zr/2a R (r) = ─────│──│ │1 - ─ │ e 0 2s sqrt(2) └ a ┘ └ 2a ┘ 0 0 Consider an electron in the 2s orbital of a Helium atom. (a) Sketch the radial part of the wave function as a function of r, you should explicitly label the positions of node(s) and maxima. (b) Sketch the radial probability density as a function of r. Again, explicitly label the positions of node(s) and maxima. 6. On the right are figures of four hydrogen atomic orbitals including a contour plot in the x-y plane, the radial function, and the radial distribution function. (a) (12%)Give the principle quantum number and angular quantum number for each of the orbitals. Use the s, p, d, f, ... symbols in your answers. (b) (3%)Sort the orbitals from low energy to high energy. 7. Photoelectron spectroscopy studies of neon atoms excited by x-rays with wavelength 9.890*10^(-10) m show three peaks in which the electron have kinetic energy values 383.4 eV, 1205.2 eV, and 1232.0 eV. (a) (5%)Calculate the ionization energy of the electrons in each peak. (b) (5%)Assign each peak to an orbital of the neon atom, and use the results to draw a energy-level diagram. (c) (Bonus,5%)Clearly state the assumptions that are required in order to use photoelectron spectrum to assign orbital energies. (d) (Bonus,5%)Calculate the effective charge for each orbital and give explanations of the trend. 8. Answer ture or false for the following statements (3 points each): (a) The zero point energy is higher for a He atom in a box than for an electron in the same box. (b) Molecules with a longer π-conjugated system tend to absorb photons with longer wavelengths. (c) An example of vibrational isotope effect: ν / ν is roughly H-Cl D-Cl the square root of 2. (d) Any bound system must have a non-zero zero-point energy. (e) The wave function of a system must always satisfy the time-independent Schrödinger equation. (f) The magnitude of the angular momentum of a hydrogen-like atom is proportional to sqrt[l(l+1)]. (g) An orbital can be used to represent an electronic state of a many- electron atom. --

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