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Chemistry LibreTexts

2.2: Trends in Size

  • Page ID
    235744
  • Skills to Develop

    • Describe and explain the observed trends in atomic size of the elements

    The elements in groups (vertical columns) of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells. However, there are also other patterns in chemical properties on the periodic table. For example, as we move down a group, the metallic character of the atoms increases. Oxygen, at the top of Group 16 (6A), is a colorless gas; in the middle of the group, selenium is a semiconducting solid; and, toward the bottom, polonium is a silver-grey solid that conducts electricity.

    As we go across a period from left to right, we add a proton to the nucleus and an electron to the valence shell with each successive element. As we go down the elements in a group, the number of electrons in the valence shell remains constant, but the principal quantum number increases by one each time. An understanding of the electronic structure of the elements allows us to examine some of the properties that govern their chemical behavior. These properties vary periodically as the electronic structure of the elements changes. They are (1) size (radius) of atoms and ions, (2) ionization energies, and (3) electron affinities.

    Visualizing periodic trends

    Explore visualizations of the periodic trends discussed in this section (and many more trends). With just a few clicks, you can create three-dimensional versions of the periodic table showing atomic size or graphs of ionization energies from all measured elements.

    Variation in Covalent Radius

    The quantum mechanical picture makes it difficult to establish a definite size of an atom. However, there are several practical ways to define the radius of atoms and, thus, to determine their relative sizes that give roughly similar values. We will use the covalent radius (Figure \(\PageIndex{1}\)), which is defined as one-half the distance between the nuclei of two identical atoms when they are joined by a covalent bond (this measurement is possible because atoms within molecules still retain much of their atomic identity).

    figure 3,2,1.jpeg

    Figure \(\PageIndex{1}\): (a) The radius of an atom is defined as one-half the distance between the nuclei in a molecule consisting of two identical atoms joined by a covalent bond. The atomic radius for the halogens increases down the group as n increases. (b) Covalent radii of the elements are shown to scale. The general trend is that radii increase down a group and decrease across a period.

    We know that as we scan down a group, the principal quantum number, n, increases by one for each element. Thus, the electrons are being added to a region of space that is increasingly distant from the nucleus. Consequently, the size of the atom (and its covalent radius) must increase as we increase the distance of the outermost electrons from the nucleus. This trend is illustrated for the covalent radii of the halogens in Table \(\PageIndex{1}\) and Figure \(\PageIndex{1}\). The trends for the entire periodic table can be seen in Figure \(\PageIndex{2}\).

    Table \(\PageIndex{1}\): Covalent Radii of the Halogen Group Elements
    Atom Covalent radius (pm) Nuclear charge
    F 64 +9
    Cl 99 +17
    Br 114 +35
    I 133 +53
    At 148 +85

    As shown in Figure \(\PageIndex{2}\), as we move across a period from left to right, we generally find that each element has a smaller covalent radius than the element preceding it. This might seem counterintuitive because it implies that atoms with more electrons have a smaller atomic radius. This can be explained with the concept of effective nuclear charge, \(Z_{eff}\). This is the pull exerted on a specific electron by the nucleus, taking into account any electron–electron repulsions. For hydrogen, there is only one electron and so the nuclear charge (Z) and the effective nuclear charge (Zeff) are equal. For all other atoms, the inner electrons partially shield the outer electrons from the pull of the nucleus, and thus:

    \[Z_\ce{eff}=Z−shielding\]

    Shielding is determined by the probability of another electron being between the electron of interest and the nucleus, as well as by the electron–electron repulsions the electron of interest encounters. Core electrons are adept at shielding, while electrons in the same valence shell do not block the nuclear attraction experienced by each other as efficiently. Thus, each time we move from one element to the next across a period, Z increases by one, but the shielding increases only slightly. Thus, Zeff increases as we move from left to right across a period. The stronger pull (higher effective nuclear charge) experienced by electrons on the right side of the periodic table draws them closer to the nucleus, making the covalent radii smaller.

    This graph entitled, “Atomic Radii,” is labeled, “Atomic Number,” on the horizontal axis and, “Radius (p m),” on the vertical axis. Markings are provided every 10 units up to 60 on the horizontal axis beginning at zero. Vertical lines extend from the horizontal axis upward at each of these markings. The vertical axis begins at 0 and increases by 50’s up to 300. Horizontal lines are drawn across the graph at multiples of 50. A black jagged line connects the radii values for elements with atomic numbers 1 through 60 on the graph. Peaks are evident at the locations of the alkali metals: L i, N a, K, R b, and C s, at which points on the graph purple dots are placed and elements are labeled in purple. Similarly, minima exist at the locations of noble or inert gases: H e, N e, A r, K r, X e, and R n, at which points blue dots are placed and element symbols are provided in blue. The locations of period 4 and period 5 transition elements are provided with green dots. These points are clustered together in two locations on the graph which are circled in red and labeled accordingly. The green dots for the transition elements along with the line that connects them form a U shape on the graph within each of the red circles drawn. The atomic radii for the alkali metals in picometers are: L i 167, N a 190, K 243, R b 265, and C s 298. The atomic radii of the noble or inert gases included in the graph in picometers are: H e 31, N e 38, A r 71, K r 88, and X e 108.

    Figure \(\PageIndex{2}\): Within each period, the trend in atomic radius decreases as Z increases; for example, from K to Kr. Within each group (e.g., the alkali metals shown in purple), the trend is that atomic radius increases as Z increases.

    Video \(\PageIndex{1}\): Learn more about shielding.

    Thus, as we would expect, the outermost or valence electrons are easiest to remove because they have the highest energies, are shielded more, and are farthest from the nucleus. As a general rule, when the representative elements form cations, they do so by the loss of the ns or np electrons that were added last in the Aufbau process. The transition elements, on the other hand, lose the ns electrons before they begin to lose the (n – 1)d electrons, even though the ns electrons are added first, according to the Aufbau principle.

    Example \(\PageIndex{1}\): Sorting Atomic Radii

    Predict the order of increasing covalent radius for Ge, Fl, Br, Kr.

    Solution

    Radius increases as we move down a group, so Ge < Fl (Note: Fl is the symbol for flerovium, element 114, NOT fluorine). Radius decreases as we move across a period, so Kr < Br < Ge. Putting the trends together, we obtain Kr < Br < Ge < Fl.

    Exercise \(\PageIndex{1}\)

    Give an example of an atom whose size is smaller than fluorine.

    Answer

    Ne or He

    Variation in Ionic Radii

    Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it is smaller than the atom from which it is derived (Figure \(\PageIndex{3}\)). For example, the covalent radius of an aluminum atom (1s22s22p63s23p1) is 118 pm, whereas the ionic radius of an Al3+ (1s22s22p6) is 68 pm. As electrons are removed from the outer valence shell, the remaining core electrons occupying smaller shells experience a greater effective nuclear charge Zeff (as discussed) and are drawn even closer to the nucleus.

    The figure includes spheres in green to represent the relative sizes of A l and S atoms. The relatively large A l sphere in the upper left is labeled 118. The significantly smaller S sphere in the upper right is labeled 104. Beneath each of these spheres is a red sphere. The red sphere in the lower left is very small in comparison to the other spheres and is labeled, “A l superscript 3 plus 68.” The red sphere in the lower right is significantly larger than the other spheres and is labeled, “S superscript 2 negative 170. “

    Figure \(\PageIndex{3}\): The radius for a cation is smaller than the parent atom (Al), due to the lost electrons; the radius for an anion is larger than the parent (S), due to the gained electrons.

    Cations with larger charges are smaller than cations with smaller charges (e.g., V2+ has an ionic radius of 79 pm, while that of V3+ is 64 pm). Proceeding down the groups of the periodic table, we find that cations of successive elements with the same charge generally have larger radii, corresponding to an increase in the principal quantum number, n.

    An anion (negative ion) is formed by the addition of one or more electrons to the valence shell of an atom. This results in a greater repulsion among the electrons and a decrease in \(Z_{eff}\) per electron. Both effects (the increased number of electrons and the decreased Zeff) cause the radius of an anion to be larger than that of the parent atom ( Figure \(\PageIndex{3}\)). For example, a sulfur atom ([Ne]3s23p4) has a covalent radius of 104 pm, whereas the ionic radius of the sulfide anion ([Ne]3s23p6) is 170 pm. For consecutive elements proceeding down any group, anions have larger principal quantum numbers and, thus, larger radii.

    Atoms and ions that have the same electron configuration are said to be isoelectronic. Examples of isoelectronic species are N3–, O2–, F, Ne, Na+, Mg2+, and Al3+ (1s22s22p6). Another isoelectronic series is P3–, S2–, Cl, Ar, K+, Ca2+, and Sc3+ ([Ne]3s23p6). For atoms or ions that are isoelectronic, the number of protons determines the size. The greater the nuclear charge, the smaller the radius in a series of isoelectronic ions and atoms.

    1378px-Atomic_&_ionic_radii.svg.png

    Figure \(\PageIndex{4}\): Comparison of Ionic and Atomic Radius. Image Credit: By Popnose [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons

    Summary

    Video \(\PageIndex{2}\): A summary on atomic radius.

    Electron configurations allow us to understand many periodic trends. Covalent radius increases as we move down a group because the n level (orbital size) increases. Covalent radius mostly decreases as we move left to right across a period because the effective nuclear charge experienced by the electrons increases, and the electrons are pulled in tighter to the nucleus. Anionic radii are larger than the parent atom, while cationic radii are smaller, because the number of valence electrons has changed while the nuclear charge has remained constant.

    Glossary

    covalent radius
    one-half the distance between the nuclei of two identical atoms when they are joined by a covalent bond
    effective nuclear charge
    charge that leads to the Coulomb force exerted by the nucleus on an electron, calculated as the nuclear charge minus shielding
    isoelectronic
    group of ions or atoms that have identical electron configurations

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