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 ml).

E

1s

2s2p

3s 3p

3d4s4p

4d6s 5p

5d 4f5f

Multi-electron atoms

5s

6p7s 6d7p

Order: 1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f6d7p

8s7s6s5s4s3s2s1s

7p6p5p4p3p2p

6d5d4d3d

5f4f

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

1s 2s

2p1s 2s

2p1s 2s

C

2p1s 2s 2p1s 2sor

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-ArK, Ca, Sc, Cr, Mn, Cu, Zn-KrCs, Ba, La, Ce-Lu, Hf

Atomic radii, Å