Multi-Electron+Atoms

Multi-Electron Atoms

No electron – electron interaction To keep things simple, we use an approximation that the electrons do not interact. One electron remains in the lowest orbital, and effectively shields the other electron from the some of the nuclear charge. This gives rise to the idea of effective nuclear charge Z*. How much of the nuclear charge is felt by the second electron is determined by how much its wave function penetrated the wave function of the lowest electron. Because the p orbitals have a node through the nucleus, and the s orbital does not, this makes the inner electron more efficient at shielding the charge, and changes the energy levels. The electron in the p orbital feels a greater effective charge, so it has a deeper energy well. The d has two nodes through the nucleus, so their energy wells are shallower than the s and p.

If we add in electron – electron interaction, this reduces the effective charge in all cases, but some cases even more. It was also found empirically that there could only be two electrons in any sublevel. This is called the Pauli Exclusion Principle. It was found that the electron has a magnetic moment, called the spin. A highly uniform electron beam was found to split into two when passed through a magnetic field. Thus each suborbital could contain two electrons if they had opposite spins. Next we looked at more complex atoms, their first ionization energies and the energies required to ionize the atoms completely, one electron at a time. Graphing these energies showed certain periodic trends. It was much harder to remove the second to last electron than the third to last. The same for 10th and 11th, and 18th and 19th.

[See the Excell page "PHY540 Ionization energy data analysis" Sheet 2 for graph of the ionization energies.]

This also corresponds to a jump in atomic radii.

[See the Excell page "Atomic Radii".]

As more electrons are added to a specific quantum level, the effective charge z* for those electrons increases. This pulls them closer to the nucleus. The increase in radius for the alkali metals is due to the addition of a higher energy level. It wasn’t given, but the radius of Li+ is smaller than He, Na+ is smaller than Ne, and k+ is smaller than Ar following the trend of greater Z*. There is a finer detail when we look at the first ionization energy. The pattern goes: big drop, two up, little drop, three up, little drop, three up and back to big drop. The big drop corresponds to a jump in atomic radius – a new level is added. The two up is filling the s suborbital, the next three are putting the first electron into each of the three p suborbitals, the next three are the second electron filling up each of the p suborbitals. This explains the structure of the periodic table.

The electron orbitals can be described by three quantum numbers: the principle quantum number (n=1,2,3,…), the ??? quatum number (//l//=0, 1,2, …n-1), and the spin (- ½, ½).