課程名稱︰普通化學甲上 課程性質︰外系生/高中預修班普通化學 課程教師︰金必耀 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2008/11/14 考試時限（分鐘）：超過 120 分鐘 (沒有待到最後不知道) 是否需發放獎勵金：否 （如未明確表示，則不予發放） 試題 : https://ceiba.ntu.edu.tw/course/d0f3fa/content/midterm.pdf (希臘符號自動換成拼音以球排版方便) 1.(10%) A chemist in a galaxy far, far away performed the Millikan oil drop experiment and got the following results for the charge on various drops. What is the charge of the electron in zirkombs? 2.56*10^(-12) zirkombs, 7.68*10^(-12) zirkombs 3.84*10^(-12) zirkombs, 6.40*10^(-12) zirkombs 2.(8%) In the Kjeldahl method for analysis of nitrogen in protein, the sample is digested in concentrated sulfuric acid, converting the nitrogen to ammonium sulfate (NH_4)_2SO_4. NaOH is then added, converting (NH_4)_2SO_4 to ammonia gas NH_3 , which is distilled into a standard HCl solution, where the neutralization reaction NH3 + HCl → NH4_Cl occurs. The unneutralized acid is determined by titration. Find the percent nitrogen by mass in a 10.0 g protein sample if the HCl concentration in 500.0 mL of acid solution is reduced from 0.2000 M to 0.0742 M in Kjeldahl analysis. 3.(8%) State, in general terms, under what conditions one may expect the diffraction of matter waves to be important in determining the dynamics of a particle, and under what conditions diffraction is unimportant. 4.(8%) de Broglie suggested that the electrons possess both the particle and wave characters. The wavelength (lamda) of the moving particle can be calculated from the relation wavelength = h/mv. Compute the de Broglie wavelengths of (a) A hydrogen atom with a velocity of 10^3 m/s. (b) An electron with an energy 0.05 eV. 5.(5%) Photons are emitted in the Lyman series as hydrogen atoms undergo transitions from various excited states to the ground state. If ground-state He^(+) ions are present in the gas, can they absorb these photons? Explain. 6.(10%) The equation referred to by Debye in response to Schrodinger’s lecture on de Broglie waves is the classical wave equation. For describing a standing wave psi(x) in one dimension, it is (d^2 psi)/(dx)^2 + (4*pi^2/lambda)*psi = 0 where lambda is the wavelength of the standing wave. (For a fixed lambda, a solution of this equation is the sine wave y = A*sin(2px/l).) Show that this equation becomes a one-dimensional form of Schrodinger's wave equation: (-h^2/8*m*pi^2)*((d^2 psi)/(dx)^2) + Vpsi = Epsi when the generalized form of the de Broglie wavelength lambda for a particle moving in the presence of a potential, V(x), is substituted into the classical equation and some algebraic rearrangement is made. 7.(9%) Give the number of orbitals and their labels for all orbitals with (a) n = 3 (b) n = 5, l = 1 (c) n = 2, l =1, m = ± 1 8.(8%) Sketch radial wave functions R_nl(r) and r^2|R_nl(r)|^2 for 1s, 2s, 3s orbitals. 9.(10%) Sketch signed contour plots or boundary surfaces on appropriate axes of the following orbitals: 2s, 2p_x, 3p_x. 3d_xy, 4d_x^2-y^2. Also write down the numbers of radial and angular nodal planes for the corresponding orbitals. 10.(12%) Write down the electron configurations of following atoms or ions: C, Mg, Kr, Sc, Cr, Ni^(2+). 11. Consider an universe in which the eletrons obey the Pauli exclusion principle, but have an intrinsic spin angular momentum of 5/2 instead of 1/2. Thus the spin orientations in space are 5/2, 3/2, 1/2, -1/2, -3/2, -5/2. Label these states alpha, beta, gamma, delta, epsilon, zeta. In all other ways the universe under consideration is like our own. (a) Consider the helium atom, a two-electron system, in its ground state. What is the degeneracy of this state? (5%) (b) When electron-electron interaction is included, the degeneracy of these states will be removed. Indicate the lowest-energy electron configuration? (Hint: Assume that Hund's rule is still valid in this universe.) (5%) (c) List the charge on the nuclei of the first four inert gas atoms in the universe under consideration. (5%) Useful constants: 1. Planck constant: h = 6.62607*10^(-34) J*s 2. proton mass m_p = 1.672623*10^(-27) kg 3. electron mass me = 9.10938*10^(-31) kg 4. 1 eV= 1.60210*10^(-12) erg -- 當我們在遠方相遇，我必能清楚看見 你已為我開燈點亮整個宇宙的黑暗 --

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