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Module 1 : Atomic Structure

Lecture 6 : Multi-Electron Atoms

6.4

Atomic Structure and the Periodic Table

It would be nice if the problem of atoms containing more than one electron can be solved exactly like the hydrogen atom. Such a solution would give a complete understanding of charge densities and the electronic spectra of many electron atoms. Although such a solution has eluded the chemist all along, a very good (though not exact) description of electronic structure of atoms has been given in terms of atomic orbitals and orbital energies. Let us first outline the description in terms of atomic orbitals.

Next to hydrogen in the periodic table is helium. The second electron is also placed in the 1s orbital, giving the electronic configuration for 1s². The second electron has a spin which is “opposite” to that of the first electron. Although this antiparallel pairing of spins has an energy cost, this is much less than the energy of 1s¹ 2s ¹ where the second electron is in the higher 2s level. When one electron is in 1s and another in 2s, their spins need not be paired. Does this violate the Pauli exclusion principle?

The third atom is Li. The first two electrons are placed in 1s giving the configuration 1s². The third one may be placed in 2s or 2p. The charge densities in 2s and 2p orbitals are distinct. An electron in a 2s orbital has a much greater probability of being found “near” the nucleus as the 2s orbital has a non zero value at the nucleus (see Fig 5.1). A 2p electron has a far smaller probability of being found near the nucleus because of its node in the nuclear plane. Therefore a 2s electron experiences a larger effective nuclear charge than a 2p electron. The energy of a 2s electron is lower than that of a 2p electron and the electronic configuration of Li is 1s² 2s¹ and not 1s² 2p¹ . The latter has a higher energy and corresponds to an excited state. The degeneracy of 2s and 2p which was found in the H-atom is removed in Li. The 2p electron in Li is said to be more screened from the nuclear charge than a 2s electron.

We can continue this “filling” up of orbitals: Be (1s² 2s² ), B (1s² 2s² 2p¹ ), C(1s² 2s² 2p² ) and N (1s² 2s² 2p ³ ). The p electrons in C and N occupy distinct orbitals 2p _x , 2p _y and 2p_z and avoid electon pairing. This is in conformity with the Hund's rule, according to which states of atoms with maximum multiplicity (large value of total spin obtained by avoiding spin pairing) will be favoured. When two spins are paired, the total spin = ½ - ½ = 0. When spins are unpaired, the total spin = n/ 2 where n = number of unpaired electrons.