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Module 1 : Atomic Structure

Lecture 1 : Multi-Electron Atoms

6.8

Electron Distributions in Na

Fig 6.4 shows the radial electron densities for various orbitals of the sodium atom. The ground state electronic configuration is 1s² 2s² 2p⁶ 3s¹. The first shell 1s is held very close to the nucleus (within 0.3 Å). This is closer than the case for Li atom because of the higher nuclear charge of Na. The second shell (2s and 2p) cover the range from 0.3 Å to 1.2 Å and the 3s shell extends from about 1.2 Å to 3 Å. Notice that each shell has a region of peak electron density, which rises sharply initially from a small value and again decays to zero slowly (actually exponentially, as is true for all orbitals). If the outer electron from Na is removed, we get Na⁺.

Figure 6.4 Electron density in Na atom

The experimental radii of Na and Na⁺ are 3.72 Å and 0.97 Å which match reasonably with the sketch. The larger experimental value raises the possibility of 3p and 3d also contributing indirectly to the atomic size. This turns out to be true. While obtaining an average field, “instantaneous” correlations or interactions between electrons were neglected. Inclusion of instantaneous (or simultaneous) correlations can be done by including the contributions of excited “orbitals”. If 3p and 3d of Na are occupied, they would correspond to the excited states of the atom.

Using the methodology of this chapter (and further improvements in it), the charge densities and energy level diagrams of all the atoms in the periodic table can be constructed. When we deal with higher atomic numbers, other interactions such as the spin-orbital interaction (interaction between spin and orbital angular momenta), hyperfine interactions (interaction of electron spin with the nuclear spin) and relativistic effects (when electron velocities approach that of the velocity of light) come into play and these have been studied in detail.