8.2
Atomic Radii and Effective Nuclear Charge
The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same nu…
An atom’s size is dictated by the electrons or their orbitals. However, orbitals do not describe a confined space, but rather the statistical probability of where an electron can be found. So how is the atomic size defined, and what influences it?
An atomic radius can be described in two ways. Nonbonding atomic radius, or van der Waals radius of an atom, is one-half of the distance between adjacent nuclei in the atomic solid.
Conversely, a bonding atomic radius, or covalent radius, distinguishes between metals and nonmetals. In metals, the radius is described for atoms in their crystal structure as one-half of the distance between the centers of two neighboring atoms.
In nonmetal, diatomic molecules, the radius is described as one-half of the distance between the centers of bonded atoms.
The periodic table depicts variations in covalent radii that are often called atomic radii, which are influenced by two factors; the number of principal energy levels of valence electrons, and the effective nuclear charge.
The trend in atomic radii for main group elements down the columns is depicted here.
Moving down a group, the principal quantum number, n, increases by one for each element. Thus, as outer electrons get farther from the nucleus, the atomic radius increases down the group.
For example, moving down group 1, the atomic radius increases from lithium to cesium. This trend is demonstrated by the entire periodic table.
Further, the plot reveals that the atomic radius is maximum for each alkali metal and falls to a minimum with each noble gas across the period. The decreasing atomic radii across a period can be explained by the effective nuclear charge.
Recall the concept of an effective nuclear charge. In any multi-electron atom, the inner shell electrons partially shield the outer shell electrons from the pull of the nucleus. Thus, the effective nuclear charge, the charge felt by an outer electron is lesser than the actual nuclear charge.
Electrons in the same valence shell do not shield one another very effectively. Across the period, the nuclear charge increases while the number of inner shell electrons remains constant.
Thus, as the effective nuclear charge increases steadily, the shielding of outer electrons becomes less, and this leads to a decrease in atomic radii.
The radii of most transition elements, however, stay roughly constant across each row. This is because the number of electrons in the outermost principal energy level is nearly constant.
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Q1: What is the difference between van der Waals radius and covalent radius?
Van der Waals radius, or nonbonding atomic radius, is one-half the distance between adjacent nuclei in atomic solids. Covalent radius, or bonding atomic radius, differs for metals and nonmetals. In metals, it's one-half the distance between neighboring atom centers in crystal structures. In nonmetal diatomic molecules, it's one-half the distance between bonded atom centers.
Q2: Why does atomic radius increase when moving down a group in the periodic table?
As you move down a group, the principal quantum number increases by one for each element, placing outer electrons farther from the nucleus. Although nuclear charge increases, the additional inner shell electrons shield outer electrons more effectively. This greater distance outweighs the increased nuclear charge, causing atomic radius to increase down the group.
Q3: How does effective nuclear charge explain the decrease in atomic radius across a period?
Across a period, nuclear charge increases while the number of inner shell electrons remains constant. Outer electrons in the same valence shell do not shield each other effectively. As effective nuclear charge increases, the nucleus pulls outer electrons closer, decreasing atomic radius. This stronger pull creates the periodic trend of decreasing size from left to right.
Q4: What role does electron shielding play in determining atomic size?
Inner shell electrons partially shield outer shell electrons from the nucleus's pull, reducing the effective nuclear charge felt by valence electrons. Core electrons shield efficiently, but outermost electrons do not shield one another effectively. The greater the effective nuclear charge after accounting for shielding, the stronger the nucleus holds outer electrons, resulting in a smaller atomic radius.
Q5: Why do transition elements have relatively constant atomic radii across a row?
Transition elements maintain roughly constant atomic radii across each row because the number of electrons in the outermost principal energy level remains nearly constant. Although nuclear charge increases, the additional electrons enter inner d orbitals, not the valence shell. This results in a roughly constant effective nuclear charge experienced by outer electrons.
Q6: How do alkali metals compare in size within their group?
Alkali metals show maximum atomic radius at the beginning of each period. Moving down group 1 from lithium to cesium, atomic radius increases significantly. This trend reflects the increasing principal quantum number for valence electrons, placing them progressively farther from the nucleus despite increasing nuclear charge.
Q7: What determines whether an atom's size is defined by bonding or nonbonding radius?
Bonding radius applies when atoms form covalent bonds, measured as one-half the distance between bonded atom centers in molecules or crystal structures. Nonbonding radius applies to isolated atoms in solids, measured as one-half the distance between adjacent nuclei. The choice depends on whether atoms are chemically bonded or simply in contact within a solid structure.