The core electrons will
tend to the outer
electron from the full
Shielding and Penetration
If an electron is always outside the core it experiences only a net charge of nucleus and core.
If, however, the electron spends much of its time close to the nucleus (within the core) it will experience a larger nuclear attraction and have a lower energy (more tightly bound).
Hence the energy of the outer electron depends on how much it the core region.
This in turn depends on the type (s, p, d, f etc.) of orbital it is in.
Recall the radial distribution functions .
An e- in the 3s orbital spends more time close to the nucleus than an electron in 3p and is thus more tightly bound (lower energy).
The energy of a given quantum state is now no longer simply a function of its principal quantum number but also of its penetration into the core region which depends on the orbital shape (and thus l).
In general the energies of sub-shells of the same principal quantum number n lie in the order
Zeff – the effective nuclear charge
To account for the effects of penetration and shielding we use
an effective nuclear charge Zeff such that
where s is the shielding parameter and Z is the charge of the nucleus.
Zeff is a function of n and l as electrons in different shells and subshells approach nucleus to different extents
Trends in Zeff
The Grotrian diagram for Na
Different l levels have different energy.
The H-atom levels are marked on the RHS
Note more rapid stabilisation of 4s with respect to 3d due to
Radial Distribution Function 3d vs 4s
The Aufbau Principle and the Structure of the Periodic Table
To obtain a ground state configuration for an atom we apply the Pauli exclusion and the Aufbau principle which states that electrons are added to orbitals in increasing order of energy.