Page 255 - Instant notes

Many-electron atoms 241

momentum quantum number, S, and total angular momentum
quantum number, L, the term symbol is wirtten as 2S+1 {L}, where
{L} is the letter S, P, D, F…for L=0, 1, 2, 3…, respectively. The
quantity 2S+1 is called the multiplicity.
Related topics The structure of the hydrogen Molecular orbital theory of
atom (G5) diatomic molecules I (H3)
Chemical and structural effects Molecular orbital theory of
of quantization (G7) diatomic molecules II (H4)
Valence bond theory (H2)

Electron spin

Every electron possesses an intrinsic ½ unit of angular momentum. This is a fundamental
property of the electron, like its mass and charge, that cannot be altered. The spin angular
momentum may be clockwise or anticlockwise corresponding to two quantum states with
electron spin quantum number, m s=+½ and −½. The two spin states of an electron are
often represented by the symbols and ↓, respectively. When electron spins are paired
( ) there is zero net spin angular momentum because the spin angular momentum of one
electron is cancelled by the opposite spin angular momentum of the other electron.

Orbital approximation

In principle, wavefunctions for a many-electron atom (atoms containing two or more
electrons) describe the behavior of all the electrons simultaneously. However, the
Schrödinger equation for such atoms cannot be solved exactly because each electron
interacts with every other electron as well as with the nucleus. In the orbital
approximation, the many-electron wavefunction is described as the product of the
wavefunctions of the individual atomic orbitals occupied by each electron in the atom,
ψ=ψ(1)ψ(2)…
Each individual orbital can be considered like a hydrogenic atomic orbital with the
potential energy modified by the effect of the other electrons in the atom.

Penetration and shielding

An electron in a many-electron atom experiences Coulombic repulsion from all the other
electrons present. The extent of repulsion can be represented as a negative charge at the
nucleus which cancels out a proportion of the Z units of positive charge from the protons
in the nucleus (Z is the atomic number of the atom). The cancelling out reduces the
charge of the nucleus from Ze to Z effe, called the effective nuclear charge. The other
electrons are described as shielding the nuclear charge. The effective nuclear charge is a
convenient way of expressing the net effect of the attraction of the electron to the nucleus