7.1 Overview of Trends and Atomic Radius

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Video Transcript
In this lesson you will learn:

-The Periodic Trend for Atomic Radius

-The definition of Effective Nuclear Charge (Zeff)

-How Effective Nuclear Charge affects Atomic Radius


atomic radius trend

Atomic Radius Increases Down a Group

Atomic radius increases down a group on the periodic table.  This is fairly intuitive as this increase in radius is explained by an increase in the number of shells of electrons as one moves down a group on the periodic table.

Atomic Radius Increases Right to Left Across a Period

Atomic radius increases right to left across a period on the periodic table.  Initially this seems counter-intuitive as this increase in radius is accompanied by a general decrease in atomic mass.  But if we keep in mind that the atomic mass is concentrated in the nucleus whereas the atomic radius is related more to the size of the 'electron cloud' it can be understood that these trends do not need to align.

 

This trend in atomic radius is best understood in terms of the effective nuclear charge experienced by the valence electrons.  The effective nuclear charge (abbreviated Zeff) is measure of the strength of the attraction of a valence electron to the nucleus.  It accounts for both the attraction to the protons in the nucleus and the repulsion from the other electrons in the atom.

 

The effective nuclear charge can be approximated by the following simplified formula:

Zeff = Z - S

where Z is the number of protons and gives the charge of the nucleus and S represents the number of 'shielding' or 'screening' electrons.  For a valence electron the number of shielding electrons is simply equal to the number of core electrons.  This methodology says that valence electrons don't experience repulsion from each other.  This is not technically true but a decent approximation for our purposes as the repulsion from another valence electron should be considerable less than from a core electron.  It turns out that not all core electrons will contribute the same repulsion either as described in Slater's Rules, but the rough approximation being used here will be sufficient to explain the trend in atomic radius.

 

Sodium and magnesium are a good comparison to demonstrate the trend.  Sodium has 11 protons (Z = 11) and 10 core electrons (S = 10) and its effective nuclear charge is

Zeff = Z - S = 11 - 10 = +1

 

Magnesium has 12 protons (Z = 12) and 10 core electrons (S = 10) and its effective nuclear charge is

Zeff = Z - S = 12 - 10 = +2

 

Magnesium's valence electrons experience a higher effective nuclear charge which indicates a greater attraction to the nucleus explaining why it would have a smaller atomic radius (130pm for magnesium vs 154pm from sodium).

 

Overall, as one proceeds from left to right across a period there is an increase in the number of protons in the nucleus while the number of shielding electrons remains constant leading to an increasing effective nuclear charge.  We've now established that effective nuclear charge increases left to right across a period and see how it explains the corresponding decrease in atomic radius.  The atomic radii and effectively nuclear charges for the 2nd period elements is show below.

effective nuclear charge trend third period