Trends and Effective Nuclear charge

Effective Nuclear Charge


As we have noted, elements in a column (
group) on the periodic table tend to have similar chemistry. We posited earlier in the year that this has to do with similarities in how their electrons are arranged. We derived this just by thinking about the fact that chemistry happens at the level of electrons interacting or trading places, always to find a lower potential energy (PE).
Now, we are starting to use quantum to define the energies of these electrons. We have also learned (or, at least are beginning to learn) that there is periodicity in the pattern of the outermost electrons…all fits together.
So, we will be talking about "
Valence" electrons, which are the ones on the outermost shell that is occupied (corresponds to the period on the table), and "inner" electrons, which we will call "shielding" electrons. They are in between the nucleus and the valence electrons, shielding the attraction between the valence electrons and the nucleus. In each group, the atoms have similar valence structure

Most "trends" across a period can be explained easily by invoking the concept of "effective nuclear charge."


This idea seems harder than it is. It is a simple bookkeeping step to determine how much the outermost electrons of an element are attracted to that atom's nucleus: more nuclear charge, more attraction. Nuclear charge (z) is the same as the atomic number: the number of protons. However, the attraction will be reduced (shielded) by the presence of inner (non-valence) electrons. To restate, a
valence electron is any electron in the outermost shell, or principle quantum number. By the process of elimination, a non-valence electron is one that is in one of the inner shells (has a principle quantum number less than that of the valence. So, take any element in period 3: any electron in either the S orbital or the P orbitals of level 3 is valence. For all period 3 elements, there are 10 non-valence, or shielding electrons. These are the electrons in the 1S, 2S, and 2P orbitals and are in the same configuration as Neon's ten electrons.
The equation for effective nuclear charge is:
z
eff=z-core electrons
Core electrons are those of the previous noble gas plus any d and f electrons added since that noble gas. More on that later.
These are also called “shielding electrons” or the “shielding constant” because they interpose between the valence electrons and the nucleus, effectively shielding the attraction.
For sodium, there are 11 protons, but 10 shielding electrons. So, Zeff is 11-10 or 1. For potassium it is 19-18 or 1. For all elements in group 1, the effective nuclear charge will be 1.
For Mg, Z
eff is 12 (its atomic number) minus 10, the shielding constant for all elements in period 3. So, for period 3, the number of core electrons does not change, but the number of protons increases, the effective nuclear charge increases. That must mean that the valence electrons are more attracted to the nucleus as you move across the period, and thus many properties of the atoms will follow a trend due to that increasing effect. Below are several important properties of atoms and ions and how they are affected by zeff.
  1. Atomic Radius: outermost electrons are mores strongly attracted the more the zeff. radius gets smaller moving left to right. Note also that a smaller radius gives rise to still greater attraction (the closer the electron is to the protons, the more attracted it is).
  2. 1st ionization energy (the energy required to remove an electron to make the atom a 1+ ion): electrons more strongly attracted harder to remove as you move left to right.
  3. Electron affinity (how easy it is to add an electron to make the atom a 1- atom): more attraction easier to add another electron as you move left to right
  4. Electronegativity (how tightly they horde electrons when in a bond with another atom): more attraction as you proceed left to right more likely to steal or hog electrons in bond.

Transition elements


These follow the rule. However, electrons are being added to inner levels and thus the shielding constant is increasing at the same rate as the number of protons. Thus, Zeff is essentially the same for all the transition metals (Z
eff=2).

For trends down a column (group) invoke the atomic radius.


As noted, the closer two charges are, the more they are attracted. As you move down a group Z
eff is unchanged, but the principle quantum number (n) for the valence electrons goes up by 1 each step. "n" is related to the average distance from the nucleus. So, with each step down a group, the valence electrons are farther out, and less attracted:
  1. Atomic radius goes up as n goes up.
  2. 1st ionization energy: larger radius, less attraction, easier to remove loer 1st ionization energy
  3. Electron affinity: less attraction harder to add another electron
  4. Electronegativity: less attraction less likely to steal or hog electrons.


Exceptions:


These require you to consider the exact electron under consideration. For this, we will look in more detail at the quantum description.