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
l
on both n and but not ml).
Multi-electron atoms
7s
6s
7p
6p
5p
6d
5d
5s
4s
4p
3d
E 3s
2s
1s
5f
4f
4d
3p
2p
Order: 1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f6d7p
5f 6d 7p
4f 5d 6p
4d 5p
3d 4p
3p
2p
8s
7s
6s
5s
4s
3s
2s
1s
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 1s
1s
2s
Be 1s
2s
2p
B
2s
2p
Li
1s
C
1s
2s
2p
or 1s
2s
2p
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