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1 Practice Self Evaluation #2 (Chem113A W’07, Fri. 03/02/07 5:00-7:30pm, 100+5pts, max=100pts) Name: ____ By writing down my name, I confirm that I strictly obey the academic ethic code when taking this exam. Tips: (i) This practice SE#2 is to communicate with you accurately the format and expectation of the real SE#2 and to highlight the important topics in the SE#2s coverage. The questions in the real SE#2, of course, will be different. (ii) Four questions. Please budget your time in real SE#2. Start with the parts you are more familiar with. (iii) In the real Self Evaluation #2, there will be one extra credit question, but the total score is capped by 100 points. (iv) Formula sheets can be found at VOH. It’s important to show calculation or algebraic details. (v) Coverage: shown below (stars mean weighting). Questions [3]+[4] will be graded and are parts of PS #7. (vi) Besides the TA OHs (MWF 12noon) and study session (MTWRF 10am), extra resources for you: 1) Review section by TA Jon, TBA; 2) Review section by Prof. Lin: 03/02/07 Fri. in class 3) Special OHs by Prof. Lin: 2/24 (Sat.) 1-5pm and 2/25 (Sun.) 1-5pm. Happy to serve as your private tutor. 4) Still need more help? Please e-mail Jon, Ava, and myself (e-mail addresses listed in Syllabus). (vii) The end-of-chapter exercises and in-chapter examples from Engel’s will weigh 30-35 points in SE#2. (viii) Academic ethics need to be strictly obeyed. No exceptions and no kidding. [1] Particle in a box and on a ring Chemistry is about molecuales. In this question, we will use very simple quantum model to understand the structure and energy of 3 molecules: anthracene, 1,3-butadiene, and benzene. [1](a) Anthracene. Warm up. There are 2 delocalized π -electrons in anthracene (length 0.6nm). Please estimate the wavelength (nm) of the photon needed to induce the HOMO Æ LUMO transition. (Hint: experimental result ~400nm)
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2 [1](b) 1,3-butadiene . Please estimate the energy (Joule) of a single delocalized π electron in the following state. The length of 1,3-butadiene is estimated to be 0.867nm. [1](c) Benzene. Six of the electrons from benzene C 6 H 6 form a delocalized conjugated π -bond. We will model it as “particle on a ring” with ring radius a and particle (electron) mass m . After obtaining the energy diagram, we will then fill in these 6 electrons. This problem can be best solved in the spherical coordinate system, where the time- independent Schrodinger equation becomes (no need to derive this): where I = ma 2 is called “moment of inertia” and the angle θ describes the position of the particle (electron) around the ring. The general solution to the above time-independent Schrodinger equation is Ψ ( )=A*exp(i n ). Please prove by algebra that n =(2 IE ) 1/2 / ħ (Hint: plug A*exp(i n ) into the equation) [1](d) Boundary condition(s). Please write down the boundary condition(s) for the wavefunction Ψ ( ). What’s its origin (i.e., which of the 7 Born conditions)?
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This note was uploaded on 10/12/2009 for the course CHEM 113A taught by Professor Lin during the Winter '07 term at UCLA.

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