Variation in Covalent Radius

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This figure has two parts: a and b. In figure a, four diatomic molecules are shown to illustrate the method of determining the atomic radius of an atom. The first model, in light green, is used to find the F atom radius. Two spheres are pushed very tightly together. The distance between the centers of the two atoms is indicated above the diagram with a double-headed arrow labeled “128 picometers (pm).” The end points of this arrow connect to line segments that extend to the atomic radii below. Beneath the molecule is the label, “F radius equals 128 pm divided by 2 equals 64 pm.” The next three models are similarly used to show the atomic radii of additional atoms. The second diatomic molecule is in a darker shade of green. The distance between the radii is 198 pm. Beneath the molecule is the label, “Cl radius equals 198 pm divided by 2 equals 99 pm.” The third diatomic molecule is in red. The distance between the radii is 228 pm. Beneath the molecule is the label, “Br radius equals 228 pm divided by 2 equals 114 pm.” The fourth diatomic molecule is in purple. The distance between the radii is 266 pm. Beneath the molecule is the label, “I radius equals 266 pm divided by 2 equals 133 pm.” In figure b, a periodic table layout is used to compare relative sizes of atoms, using green spheres. No spheres are provided for the noble or inert gas—group 18 elements. General trends noted are increasing circle size moving from top to bottom in a group, with a general tendency toward increasing atomic radii toward the lower left corner of the periodic table.

Figure 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. Source: OpenStax Chemistry 2e

Variation in Covalent Radius (OpenStax Chemistry 2e)

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 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). 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 1 and Figure 1. The trends for the entire periodic table can be seen in Figure 1.

Source: OpenStax Chemistry 2e
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 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. Source: OpenStax Chemistry 2e

As shown in Figure 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, Zeff. 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:

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.

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.

Related Research: Research Article: Deducing chemical structure from crystallographically determined atomic coordinates

Source:

Flowers, P., Theopold, K., Langley, R., & Robinson, W. R. (2019, February 14). Chemistry 2e. Houston, Texas: OpenStax. Access for free at: https://openstax.org/books/chemistry-2e

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Related External Link:

Ionocovalency and Applications 1. Ionocovalency Model and Orbital Hybrid Scales