Effective Nuclear Charge in Atoms

Study Notes

In a many-electron atom, the attractive force between an electron and the nucleus increases as the nuclear charge increases and decreases as the electron moves farther from the nucleus.
Each electron in a many-electron atom experiences the repulsion due to other electrons and is screened from the nucleus by the other electrons.
The partially screened nuclear charge is called the effective nuclear charge (Zeff).
The amount of screening of the actual nuclear charge (Z) is defined by using a screening constant (S), a positive number.

The effective nuclear charge increases from left to right across any period of the periodic table.
The effective nuclear charge increases slightly as we go down a column because the more diffuse core electron cloud is less able to screen the valence electrons from the nuclear charge.

According to the quantum-mechanical model, atoms do not have sharply defined boundaries at which the electron distribution becomes zero.
The radius of an atom is called the nonbonding atomic radius or the van der Waals radius.
The bonding atomic radius (also known as the covalent radius) for any atom in a molecule is equal to half of the bond distance.
Within each group, bonding atomic radius tends to increase from top to bottom, primarily due to the increase in the principal quantum number (n) of the outer electrons.
Within each period, bonding atomic radius tends to decrease from left to right, primarily due to the increase in effective nuclear charge (Zeff) across a period.

An isoelectronic series is a group of ions all containing the same number of electrons.
In any isoelectronic series, ionic radius decreases with increasing nuclear charge as the electrons are more strongly attracted to the nucleus.

The ionization energy of an atom or ion is the minimum energy required to remove an electron from the ground state of the isolated gaseous atom or ion.
The first ionization energy (I1) is the energy needed to remove the first electron from a neutral atom.
The second ionization energy (I2) is the energy needed to remove the second electron.
The ionization energies for a given element increase as successive electrons are removed: I1 < I2 < I3, and so forth.

I1 generally increases as we move left to right across a period.
I1 generally decreases as we move down any column in the periodic table.
The s- and p-block elements show a larger range of I1 values than do the transition-metal elements.
Generally, the ionization energies of the transition metals increase slowly from left to right in a period.

When electrons are removed from an atom to form a cation, they are always removed first from the occupied orbitals having the largest principal quantum number, n.
Thus, in forming ions, transition metals lose the valence-shells electrons first, then as many d electrons as required to reach the charge of the ion.
If there is more than one occupied subshell for a given value of n, the electrons are first removed from the orbital with the highest value of l.
Electrons added to an atom to form an anion are added to the empty or partially filled orbital having the lowest value of n.

All ionization energies for atoms are positive: Energy must be absorbed to remove an electron.
The energy change that occurs when an electron is added to a gaseous atom is called the electron affinity because it measures the attraction, or affinity, of the atom for the added electron.
For most atoms, energy is released when an electron is added.
The greater the attraction between an atom and an added electron, the more negative the atom’s electron affinity.