Periodic Properties of the Elements

Sizes of Atoms

From the quantum mechanical model of atoms we can conclude that an atom does not have a sharply defined boundary. This leads to a conceptual problem - just what exactly is the "size" of an atom?

It is possible to estimate the atomic radius of an atom by assuming that atoms are spherical objects that touch each other when they are bonded together in molecules

• The Br-Br distance in Br₂ is 2.28 Å, thus the radius of the Br atom is 1.14 Å
• The C-C bond distance is 1.54 Å, thus the radius of Carbon is 0.77 Å

What about a C-Br bond distance?

• To have useful predictive values, the determined atomic radii should hold true (i.e. be additive) when considering other possible compounds
• Predict C-Br bond distance to be equal to 1.14 + 0.77 = 1.91 Å
• In many different compounds with C-Br bonds, the distance is approximately this length

What are the general characteristics of atomic bond lengths as determined from bond-bond distances (small molecule crystallography, NMR, other methods)

• Within the columns of the periodic table, the atomic radii increase as you go down the column
• Within the rows of the periodic table, the atomic radii decrease as you move to the right

What is the basis for these observations?

Two general factors affect the size of the outermost orbital:

• The principle quantum number
• The effective nuclear charge

Proceeding across a row:

• The number of core (shielding) electrons remains constant (only the valence electrons are increasing)
• The number of protons is increasing
• If the number of protons is increasing, but the core shielding electrons remain constant then the effective nuclear charge (Z_eff) on the valence electrons is increasing, and they will be pulled tighter towards the nucleus, thus the atomic radii will decrease

For elements where we are filling the 3p subshell

• 12 shielding electrons (1s²2s²2p⁶3s²) in each case

Proceeding down a column:

• The valence electrons are remaining constant
• The principle quantum number is increasing
• The shielding electrons are increasing, but so is the nuclear charge - the end result is that essentially the effective nuclear charge on the valence electrons is relatively constant
• Since the major effect is that the principle quantum number increases as you go down a column, the atomic radius increases

For example, the group 1A elements (valence e' are in blue, shielding [core electrons in this case] e' for the valence e' are in red)