PSE_1_Chem113A_W08

PSE_1_Chem113A_W08 - 1 Practice Self Evaluation #1...

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1 Practice Self Evaluation #1 (Chem113A W’08, 02/05/08 6:15-8:15pm+20mins, 100+5, max=100) Name: __________ By writing down my name, I confirm that I strictly obey the academic ethic code when taking this exam. (i) To reduce your workload in the midterm exam week, 2 questions will be graded and counted toward PS#3. Please choose two questions from [3]-[5]. Dear TAs: please grade the following 2 questions ____________. (ii) Five questions. Please budget your time in the real SE#1. You may want to start with the parts you are more familiar with. There will be one extra credit question in real SE#1, but the total score is capped by 100 points. (iii) Formula sheets can be found at VOH. It’s important to show calculation or algebraic details. (iv) Coverage is shown below. Please refer to Lecture Note #1314 for tips on preparing for SE#1 (shown below). (v) Academic ethics need to be strictly obeyed. No exceptions and no kidding. Theme of PSE#1. This flowchart may summarize how quantum mechanics works in modern science. The theme of PSE#1 is to put this flowchart into practice. Step #1, “Spectroscopic Phenomena” Æ “Physical Model”, asks for a high level of experience, insight, creativity, and original thinking (that’s exactly why we integrate “research frontiers” and “advanced topics” into this course) and may be better left for problem set exercises. In the following, we will practice the other 3 steps. Note: 50% of questions in SE#1 will be exactly the same or similar to those in previews, problem sets, and selected textbook exercises and problems. These selected textbook exercises and problems will be listed in lecture note.
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2 [1] Big Picture: with CM, Who Needs QM? [1](a) Success of CM: Bohr’s Correspondence Principle Bohr’s “Correspondence Principle” says, “In the classical limit, quantum results approach classical results”. It implies: in the classical limit, we do not need QM! Please use the spectral distribution ρ ( ν ,T) for blackbody radiation to demonstrate Bohr’s correspondence principle. That is, please prove by algebra that as T Æ (classical limit), ρ ( ν ,T) = (Planck’ s distribution, from QM) approaches (Rayleigh- Jeans law, from CM). Please show algebraic details. [1](b) Success of CM: Bohr’s model on H-like atoms Using a combination of CM ( , no need to prove this) and QM (quantization of angular momentum l = mvr = n ħ , no need to derive this) theories, Bohr successfully explained the discrete spectrum of H-like atoms (Nobel prize in Physics, 1922). Please derive the de Broglie matter wave relation λ =h/p (where linear momentum p=mv) based on the quantization of angular momentum l = mvr = n ħ and the assumption that the quantum wave of the H-like-atom’s electron forms a circular standing wave. Please show algebraic details.
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3 [1](c) Downfall of CM: photoelectric effect
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PSE_1_Chem113A_W08 - 1 Practice Self Evaluation #1...

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