Prelim1_2008_AnswerKey - Chem 216: Please do not open this...

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Unformatted text preview: Chem 216: Please do not open this exam until told to do so by a TA. Please check there are 6 questions to your exam. The TA’s have been told not to answer questions during the exam. If you finish at least 15 minutes early you may turn your exam in. OthenNise please wait at your desk for a TA to pick up your exam. No calculators may be used on this test. One 5x8 index card of notes are allowed. name: thuu day of the week your lab meets: Professor John Kirkwood was a distinguished member of the chemistry question 1 department at Cornell. I His research on the question 2 liquid state and other _ issues in statistical question 3 . . mechanics remains question 4 'mportant' question 5 question 6 Total 1. (10 pts) Identify the following two atomic orbitals in the boxes provided. Answers should be of the form: 3dx2-y2, 5pz etc... 1/2 —1/2 0 0 2. (18 pts) DL and H are represented by respectively the matrices, and . Consider the —1/2 1/2 0 1 experiment described below. In this experiment there is initially a photon of vertical polarized light. There is furthermore a detector which measures the passing of a photon (but strangely enough not its postion). Vertical polarized light is 1 represented by the vector, . What percent of the time does a photon emerge from this experiment? What effect 0 does the detector have on this answer? If a photon does emerge is it polarized? Please place your answers in the provided boxes. experiment \7‘ —-—-—> ———> ———> % of time photon ector (it'illibti C ((99 0‘ > Lite} 1 (34’) What effect does detector have: M It a photon emerges _ is it polarized: ‘ 3. (20 pts) In the boxes provided, draw as contour maps the 4dxy and 4dx2—y2 orbitals for a circular drum. Now consider the distortion on the drum shown below. Draw in the boxes provided, as contour maps, the new "4dxy" and "4dx2_y2" orbitals.- State in the provided boxes whether the energy has increased or decreased for each of these two orbitals. Has energy increased or decreased?: Ildxyll Ildx2_y2Il 4. (20 pts) The energy measurement of an electron in a certain molecule can be represented by the 4x4 matrix given below. (The on in the matrix expression cerresponds to a real number, -12 eV). The eigenvectors of this matrix are also given ‘ 0 1H? below. An electron is initially in the w state, represented by the vector, . What are the possible measured 4/112 0 energies for an electron in the 1;! state? What are the respective probabilites for these various energies? Please place your answers in the provided boxes. After the measurement what state or states can the system be in? a 1 o 1 '5 ‘5': 1/2 1/2 1/2 1/2 I L 1 or 1 o {— '1 1/2 —1/2 1/2 -1/2 '- ‘* . o 1 or 1 ‘- ' 1/2 1/2 —1/2 —1/2 1 o 1 a L " 1/2 —1/2 —1/2 1/2 14‘ d “L possmle measured eneries: -14, ’2? t '. 1 L g ,2 state or states the electron is in after measurement: 5. (20 pts) In class we derived diatomic MO diagrams where we started with two sets of A03. In this problem, we will use the same procedure for deriving an M0 diagram, but where one of the starting set of orbitals is an M0 rather than AOs. HH ll C l HH M05 as shown in the figure on the right. An H- ion approaches this molecule from the right, as shown below. H is more electropositive than C. Place the H” A0 at a The molecule on the left has two carbon based H H a possible correct location on the far right of the boxed figure. Then, in the center of C._ the box, draw an M0 of the a combined system. For full ‘; H- credit, place the correct ,x number of electrons in the i‘ final MO. HH 6. (20 points) A violet photon is placed in a 2pz orbital (violet lights corresponds to wavenumber , k, and wavelength, l). The violet light passes either through a double slitted or a single slitted screen before arriving at final positions A and B. The - intensity of light at positions A and B are respectively IA and IB. Calculate the ratio of lA/IB. 60° B 1|12pz = C r e-f/2 cos B ...
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Prelim1_2008_AnswerKey - Chem 216: Please do not open this...

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