physchemfinal1 - PHYSICAL CHEMISTRY l(CHEM 211 Final...

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Unformatted text preview: PHYSICAL CHEMISTRY l (CHEM 211) Final Exam.(300 ms) Dec. 21, 2005 '"Physical constants, mass of electroni allxlO’31 kg, Eolzmanrl constant: memo-2“ 1K”, Planck constant: 6626x10’3“ Js, speed of light: 3x10B ins". l.(25pts) Explain the iollowmgs briefly. (a) overtones ,V (b) symmetric lop molecule / \ (c) gross selection rule / (cl) principal moments of inertia 2.(35pts) Answer the following questions {or the hydrogen molecule ion (Hz‘). (al Write the Hamiltonian operator in ammic units within the Born-Oppenheimer approximation. (b) Find the wavefunetions and energies of the 'Ioluest" bonding and antihonding LCAO-MO of the molecule by using linear Variation method. m.~es. “n49: (Use the symbol J for Coulomb integral and K for exchange integral.) ”We“ ”Mn. 3.(50pts) Answer the following questions for the homnnuclear diatomic molecule. (3) Write the ground-state and first excited’state electron configurations of H2, and find all the molecular term symbols that can arise from each electron configuration (b) As the atomic number increases from Li to F, the energies of the may and mi». map, orbimls approach mh other and interchange order in going from N2 to 02 Give your reasoning for this behavior. (0) Draw the 11..sz and $2.2m orbitals. (d) Give the ground-state electron configuration of 02. Is the molecule paramagnetic or diamagnetic? (e) Determine the groundrsmte molecular term symbol of 02. (I \ 4(65pts) Answer the following questions for HCI molecule. (a) The energy of the Cl 3]) orbital is slightly lower than that of the H is orbitall Show the molecularrorbilal energy-diagram of the molecule. (b) erbe the waveluncn‘ons for the "lamest" handing and anubondlng molecular orbitals, and sketch the shape of them. (6) Give the groundrstate electron configuration of the molecule, and determine the I bond order. ~— (d) If the light with a wavenumber of about 1100 cm-1 is irradiated on the gaseous X. HCi sample, What kind of spectrum will be observed? Sketch the spectrum, and discuss the physical origin for the variation of peak intensities {:hBlghtS). (e) If the light with a wavenurnber of about l,000*10,000 cm-l is irradiated on the sample, what kind of spectrum Will be observed? Sketch the spectrum, and discuss the molecular infomlation you can obtain {mm it (1') Close examination shows that the lines (=peaksl in the spectrum of (e) are more closely t) a: l 1th lnmllt" ...
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