Multi-electron atoms and the Periodic Table We cannot solve Schrödinger’s equation for multielectron atoms. Bummer. Nevertheless, we extend our understanding of the H atom wavefunctions to multielectron atoms in an approximate fashion.

What’s the same? Same quantum numbers apply and have the same meaning. Same rules apply to the possible values of quantum numbers. Same orbital types and nodal properties. What’s different? Atomic number impacts on orbital energies. Electron-electron interactions are present: electron shielding. Orbital energy degeneracies for given n are lost (energy depends on both n and l but not m l ).

E 1s 2s 2p 3s 3p 3d 4s 4p 4d 6s 5p 5d 4f 5f Multi-electron atoms 5s 6p 7s 6d 7p Order: 1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f6d7p

8s 7s 6s 5s 4s 3s 2s 1s 7p 6p 5p 4p 3p 2p 6d 5d 4d 3d 5f 4f

For atoms in the ground state, electrons will occupy the lowest energy orbital possible. For the H atom, this is the 1s orbital. We describe the manner in which the electrons are organized around a nucleus as its electron configuration. There are several ways of expressing electron configurations: Spectral notation: Box diagrams:

On to He. The Pauli Exclusion Principle: no two electrons can have the same set of four quantum numbers. No orbital can house more than two electrons. He Li Be B 1s 2s 2p1s2s 2p1s2s

C 2p1s2s2p1s2sor Hund’s rule: when electrons occupy orbitals of the same energy, the most stable arrangement is that with the maximun number of parallel spins. Paramagnetic: Diamagnetic:

Na-Ar K, Ca, Sc, Cr, Mn, Cu, Zn-Kr Cs, Ba, La, Ce-Lu, Hf

Atomic radii, Å