Problem 6 Atomic and molecular orbitals - PianetaChimica.it

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