Problem 6 Atomic and molecular orbitals - PianetaChimica.it

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33 rd International Chemistry Olympiad ∗ Preparatory ProblemsIt is fun using this formula for a neutral helium atom, but we must exercisesome care. In a helium atom, each electron ‘sees’ the nucleus screened bythe other electron. That is, the effective charge of the nucleus ‘seen’ by eachelectron decreases from its bare value Z=2 to some other value, say, Z eff . Theionization energy for a helium atom in its ground state is knownexperimentally to be 24.46 eV. Estimate Z eff .B. Molecular orbitalsMolecular orbitals of a hydrogen molecule ion (H + 2 ) can be approximately written aslinear combinations of atomic orbitals centered around the two nuclei of themolecule. Consider the (unnormalized) molecular orbitals constructed in this mannerfrom the 1s and 2s orbitals of two hydrogen atoms, say, A and B:% % %% ~A B1 = 1s + 1sA B1 = %1s − %1sA B%2 = %2s + %2sA B% ~ 2 = % 2s − % 2sTaking the z-axis along the line joining the two nuclei, the orbital contours of1are shown schematically below :% 1and% ~ 2ZY+−Similar orbital contours (curves on which the value of ψ is constant) can be drawn for% 2and % ~ .The energies of these wave functions as a function of internuclear distance areshown below schematically:1212Mumbai, India, July 2001
33 rd International Chemistry Olympiad ∗ Preparatory Problems−3.4 2~2E/eV 1~ 1−13.6−15.61.32R/10 −10a. Identify the bonding and antibonding orbitals. State qualitatively whatmakes one orbital bonding and another antibonding.b. Determine the values of the equilibrium internuclear distance R e and thedissociation energy D of the ground state of H + 2 .c. If the molecular ion H + 2 is excited to the state ψ2, to what atomic states will itdissociate?In the following questions, assume that the energy versus internuclear distancegraphs for the orbitals of H 2 and He 2 are similar to the one shown for H + 2 .d. Explain why the ground state total electron spin of the neutral H 2 molecule iszero.e. Write down the electronic configuration of the first excited state of H 2molecule. Predict if it will stay bound or dissociate.f. It is difficult to obtain He 2 in its ground state, but it has been observed in itsexcited states. Explain how this is possible.Problem 7 Fissiona. Consider the following fission reactions of 235 U by thermal neutrons :23594140U + n → Sr + Xe + (.....)9238(...)23592U+ n →Mumbai, India, July14156Ba+(....)+3n13 13
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Problem 6 Atomic and molecular orbitals - PianetaChimica.it

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