Shielding and Penetration

Why is shielding and penetrating important in determining ion size? Electrons interact with each other within an atom, affecting each others affective nuclear charge (Z_eff). Penetration describes how close an electron gets to the nucleus, whereas, shielding(or screening) describes how an inner electron shields an outer electron from the full attractive force of the nucleus. Differences in orbitals will dictate differences in shielding and penetration.  Within the same energy level (quantum n), due to their relative proximity to the nucleus, the s-orbital electrons both penetrate and shield more than p-orbitals electrons, and p electrons penetrate and shield more than d-orbital electrons. Shielding and penetration, along with the affective nuclear charge of an atom determine the size of an ion.  An overly simplistic, but useful method of conceptualizing affective nuclear charge can be given by the following equation:

Z_eff = Z - S

where Z is the number of protons in the nucleus of an atom (the atomic number) and S is the number of core electrons 

Figure 1

Cations and Anions

Neutral atoms who have lost an electron exhibit a positive charge and are called cations - all metals share this characteristic.  These cations are smaller in size than their respective atoms - Why? A lost electron means there is less electron-electron repulsion (shielding) and the protons are able to more tightly pull its electrons closer towards the nucleus (increased Z_eff). A second loss electron will further reduce the size of the atom (now ion).  For instance, the ionic radius of Fe²⁺ is 76 pm, while that of Fe³⁺ is 65 pm.  If creation of an ion involves completely emptying an outer shell, then the decrease in radius is especially great.

Neutral Atoms who have gained an electron are called anions - all non-metals except for the noble gaseous share this trait.  These anions are much larger than their respective atoms - Why? As an extra electron enters an outer orbital, there is increased electron-electron repulsions (shielding) which spread the electrons further apart.  With electrons outnumbering protons, the protons can not pull in the extra electrons as tightly toward the nucleus ( decreased Z_eff).

An isoelectric series of atoms and ions that have the same number of electrons (and thus the same degree of electron-electron repulsion and shielding) but different number of protons (and thus different nuclear attraction). It is useful in visualizing the effects of lost and gained electrons on the size of neutral atoms.                

Figure 2

The Periodic Trend

Because of each atom’s unique ability to lose or gain an electron, periodic trends in ionic radii are not as ubiquitous as trends in atomic radii across the periodic table.  Therefore, trends must be isolated to certain groups and isolated to either cations or anions.  

Let’s first discuss the ionic radii of metals.  The alkali and alkali earth metals (groups 1 and 2) form larger cations as you go down each group.  This shows the positive correlation between atomic radii and cation radii which accounts for the similarity between the ionic and atomic radii periodic trends.  Beginning in the d-block of the periodic table, as you go from to left to right the ionic radii of the cations do not significantly change.  However, the ionic radii do slightly decrease until group 12– after which the trend continues (Shannon 1976).  It is important to note that metals, not including groups 1 and 2, can have different ionic states, or oxidation states, (i.e. Fe can be Fe²⁺ or Fe³⁺) so be cautious when making generalizations of ionic radii trends across the periodic table.

Like groups 1 and 2, all non-metals (except for the noble gasses which do not form ions) form anions which become larger as you go down a group.  For non-metals, cross a period a settle trend of decreasing ionic radii is found (Shannon 1976).  An important generalization between the relationships of cation and anion size is that anions are almost always larger than cations, although there are some exceptions (i.e. fluorides of the some of the alkali metals).

Figure 3

Measurement and Factors Affecting Ionic Radii

The ionic radii of an atom is measured by finding its proportion in an ionic bond with another ion within a crystal lattice.  However, it was hard to consistently and accurately determine the proportions of the ionic bonds. So, after comparing many compounds, chemist Linus Pauling decided to assign a radius of 140 pm to O^2- and use this as a reference point to determine the sizes of other ionic radii (Jenson 2010).  For more information about measuring ionic radii you can visit the Chemwiki module Ionic Radii.

The ionic radius is not a permanent trait of an ion, but can change depending on coordination number, spin state, and other variables (Shannon 1976).  For the same ion, the ionic radii increases with increasing coordination number and will be larger if in a high-spin state than in a low-spin state. 

In Group Theory, the idea of ionic radii as a measurement of spherical shapes only applies with ions in high-symmetry crystal lattices like Na and Cl.  The point symmetry group of a lattice helps determine whether or not the ionic radii in that lattice can be accurately measured (Johnson 1973). For instance, lattices with O6 and Td symmetries are considered to have high symmetry; thus the electron densities display a more spherical shape and ionic radii can be more accurately measured.  However, for less symmetrical and more polar lattices such as the ones with Cn, Cnh, and Cnv symmetries, there are significant changes in the electron density that occur and causes a loss of spherical shape. 

References

1. Housecroft, Catherine E. & Alan G. Sharpe. Inorganic Chemistry. 3^rd ed. England: Pearson Education Limited, 2008.    
2. Shannon R.D.  Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides.  Acta Crystallographica 1976;32(5): 751-767.
3. Jensen B., William.  The Origin of the Ionic-Radius Ratio Rules.  Journal of Chemical Education 2010;86(6):587-8.
4. Oliver, Johnson. Ionic Radii for Spherical Potential Ions. Inorganic Chemistry 1973;12(4):780-85.
5. Birkholz, Mario. Crystal-field induced dipoles in heteropolar crystals II: Physical significance.  Z. Phys.  1995;96:333-40.

Outside Links

• Figure 1 is an original illustration.
• Figure 2 and 3 used with permission from http://www.chem1.com/acad/webtext/atoms/atpt-6.html. Retrieved November 11, 2010.
• http://en.wikipedia.org/wiki/Ionic_radius

Problems

1) Why are cations larger and anions smaller than their respective atoms?

A) Cations are larger than their respective atoms because of increased electron-electron repulsion

B) Anions are smaller than their respective atoms because of increased effective nuclear charge

C) Cations are larger than their respective atoms because of decreased electron-electron repulsion

D) Anions are smaller than their respective atoms because of decreased effective nuclear charge

2) Which of the following are isoelectronic: F^-, Cl^-, Ca²⁺, Ar  

3) List the ions from smallest to largest: Se^2- ,Zr⁴⁺, Na⁺,Mg, Rb⁺, Br^-, K⁺

4) How are ionic radii measured?

5) What are some of the problems with generalizing ionic trends?

Answers

1) Why are cations larger and anions smaller than their respective atoms?

A) Cations are larger than their respective atoms because of increased electron-electron repulsion

B) Anions are smaller than their respective atoms because of increased effective nuclear charge

C) Cations are larger than their respective atoms because of decreased electron-electron repulsion

D) Anions are smaller than their respective atoms because of decreased effective nuclear charge  

A: C & D

Cations are formed when an electron is lost.  When this occurs there are less electron-electron repulsions and there is a greater net nuclear attraction per electron. So, the newly formed ion becomes a more condensed version of its neutral atom.  

Anions are formed when an electron is gained.  When this occurs there are more electron-electron repulsions and there is a lower net nuclear attraction per electron.  This will cause the electrons push each other away and spread out, causing the atom to become larger.  

2) Which of the following are isoelectronic: F^-, Cl^-, Ca²⁺, Ar

A: Cl^-, Ca²⁺, Ar all have 18 electrons; therefore, they are isoelectronic (F^- has 10 electrons). An isoelectronic series is useful in understanding the effects of gained or loss electrons on atom size.  

3) List the ions from smallest to largest: Se^2- ,Zr⁴⁺, Na⁺,Mg, Rb⁺, Br^-, K⁺

A: Zr⁴⁺<K⁺<Rb⁺<Mg<Br^-<Se^2-

^{Ionic radii shorten with increasing positive charge and lengthen with increasing negative charge, and thus, anions are almost always larger than cations.}

4) How are ionic radii measured?

A: Ionic radii are measured by proportioning ionic bond lengths between two ions within a crystal lattice.  After studying many compounds, Linus Pauling found that the approximate ionic radii of O^2- was 140pm.  With this reference point, Pauling was able to calculate the ionic radii of other ions.  

5) What are some of the problems with generalizing ionic trends?

A: Ionic radii are not fixed properties of ions.  For the same ion, the radii can differ in different crystal lattices due certain variables such as coordination number and electron spin.  Group Theory suggests that only ions in high-symmetric non-polar crystal lattices can accurately be measured for their radii.  

Contributors

• Michael H. Nguyen. University of California, Davis

This page viewed 35712 times
The ChemWiki has 9488 Modules.

   UC Davis ChemWiki by University of California, Davis is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.  Tweet

Permissions beyond the scope of this license may be available at copyright@ucdavis.edu. Terms of Use

Powered by Mindtouch Core 2010