Make multi electron atom look like a one electron atom
Assumes every electron to be on its own experiencing an effective nuclear charge, Zeff
Then the orbitals for the electrons take the form of those in hydrogen but their energies and sizes are modified by simply using an effective nuclear charge
One electron atom
The Concept of Electron Spin
The solution of the Schrödinger equation above accounts very well for the structure of the H-atom spectrum and, as we will see, for other atoms too.
However under very high resolution “fine structure” is observed in the transitions which is not explained using this approach.
Dirac extended wave mechanics to include Special relativity and an extra coordinate - time.
Solution of the Dirac equation yields a new intrinsic angular momentum -
The Electron Spin
An electron has
The projection of this spin is also quantized (by analogy with orbital angular momentum; l and ml) such that the spin projection quantum number, ms=½, (spin up or a) and ms=-½, (spin down or b)
This is the final theoretical plank behind the structure of the periodic table.
Pauli Exclusion Principle
(as all electrons necessarily have the same s=1/2)
Hence, no individual orbital may be occupied by more than 2 electrons
Electrons occupying the same orbital must be “paired up”.
no two electrons in the same atom can have the same 4 quantum numbers n, l, ml, ms
The Pauli Principle and Symmetry
The Pauli Exclusion Principle applies to any
pair of identical (spin quantum
number s = half integer) – protons, electrons,
neutrons have s = ½ and are fermions.
BUT, any number of (s = integer)
can occupy the same orbital - 12C (s = 0) and
the photon (s = 1)are bosons
Now, as we proceed from H to other atoms, we need to consider
The Pauli Exclusion Principle
2. The coulombic repulsions between the electrons
B) Atoms with one outer electron
Easiest: alkali metals Li, Na, K, Rb but also Be+, Mg+, Ag (4d105s1) as only one outer electron.
But still, the situation is no longer as simple as the H-atom due to the inner electrons - the “core”;