Question

Effective Nuclear Charge and Periodic Trends

Coulombs Law describes the interaction between two charges and varies by the magnitude of these charges and inversely with the distance between them. ? ∝ ?1?2/? For atoms, we’ll label the charges as the nuclear charge and electron charge. ? ∝ ?????????/?

As you go up in atomic number (Z), the number of protons in the nucleus increases, making the charge on the nucleus increase, so that in general. ???? = ? ∙ (+1)
However if we think only of the electrons in the outermost shells (valence electrons), they do not see the full strength of the nuclear charge because it is partially shielded (or canceled out if you prefer) by the core electrons. So we define something called effective charge.
????????? ?ℎ???? = # ?? ??????? − # ?? ???? ????????? ???? = ? − ????
In general, Zeff increases as you go across in the periodic table.
1. Fill out the following table to verify that effective charge increases as you go across a row.

Element	Na	Mg	Al	Si	P	S	Cl	Ar
Protons	11
Core e-	10
Zeff	+1

2. For which element in the above table will the coulomb interaction between nucleus and valence electrons be the strongest? The weakest?

The second trend we need to consider with Coulomb’s Law is the distance between the charges. This is an inverse relationship (? ∝ 1 ? ) so the interaction gets weaker as you get further away.

3. In general, as you go down a column in the periodic table, will the interaction between the nucleus and valence electrons get stronger or weaker? Explain.

While you can simply memorize all the different periodic trends, many can be understood in terms of the two competing factors in Coulombs law ( ???? ??. ????????, r). Atomic radius – average distance between the nucleus and the outermost (valence) electrons.

4a. Going across rows in the periodic table, do you expect atomic radius to increase or decrease?

b. Going down columns in the periodic table, do you expect atomic radius to increase or decrease?

c. Put the following atoms in order from smallest to largest: Be, F, C, O

d. Put the following atoms in order from smallest to largest: Mg, Ba, Ca, B

Ionic radius – To understand ionic radii we must also consider the effect of electron-electron repulsion.

a. Cations have less electron-electron repulsion and are smaller than the corresponding neutral atom.

b. Anions have more electron-electron repulsion and are larger than the corresponding neutral atom.

5. When determining trends in ionic radius, we need to compare similar species. Similarities are:

a. Same number of electrons, different numbers of protons Which will be smaller, a species with 12 electrons and 10 protons, or one with 12 electrons and 12 protons?

b. Same number of protons, different number of electrons. Which will be smaller, a species with 12 electrons and 12 protons, or one with 10 electrons and 12 protons?

c. Same group of the periodic table, same ionic charge. State an example of this situation and specify which ion is larger.

Answer 1

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