Question

Using only the periodic table, arrange each set of atoms in order of increasing radius: (a) \(\mathrm{Ba}, \mathrm{Ca}, \mathrm{Na} ;\) (b) \(\mathrm{Sn}, \mathrm{Sb}\), As; (c) \(\mathrm{Al}, \mathrm{Be}, \mathrm{Si}\).

Short answer

(a) Using the periodic table, arrange Ba, Ca, and Na in order of increasing atomic radius: \(Ca < Na < Ba\) (b) Arrange Sn, Sb, and As in order of increasing atomic radius: \(As < Sn < Sb\) (c) Arrange Al, Be, and Si in order of increasing atomic radius: \(Be < Si < Al\)

Step-by-step solution

Identify Positions in the Periodic Table

Locate Ba, Ca, and Na in the periodic table. They belong to Group 2 (alkaline earth metals) and Group 1 (alkali metals). Ba is in period 6, Ca is in period 4, and Na is in period 3.

Compare Periods and Groups

Going down a group increases atomic radius, while going across from left to right decreases atomic radius. As Na and Ca belong to Group 1 and 2 respectively, Na has a larger atomic radius than Ca. Ba, being in the same group as Ca but with a higher period, has a larger atomic radius.

Arrange Atoms in Order

In order of increasing atomic radius: \(Ca < Na < Ba\) (b) Arrange Sn, Sb, and As in order of increasing atomic radius

Identify Positions in the Periodic Table

Locate Sn, Sb, and As in the periodic table. They belong to Group 14 (carbon group), Group 15 (nitrogen group), and Group 16 (oxygen group). Sn is in period 5, Sb is in period 6, and As is in period 4.

Compare Periods and Groups

As Sn and As belong to the same period but different groups, As has a smaller radius than Sn. Sb is in the same group as As but has a higher period, which makes its radius larger than that of As.

Arrange Atoms in Order

In order of increasing atomic radius: \(As < Sn < Sb\) (c) Arrange Al, Be, and Si in order of increasing atomic radius

Identify Positions in the Periodic Table

Locate Al, Be, and Si in the periodic table. They belong to Group 13 (boron group), Group 2 (alkaline earth metals), and Group 14 (carbon group). Al is in period 3, Be is in period 2, and Si is in period 3.

Compare Periods and Groups

As Al and Si belong to the same period but different groups, Al has a larger atomic radius than Si. Be belongs to Group 2 and is in a lower period than Al, which means it has a smaller atomic radius than Al.

Arrange Atoms in Order

In order of increasing atomic radius: \(Be < Si < Al\)

Key concepts

Periodic Table

The periodic table is a comprehensive chart organizing elements according to their atomic structure and chemical properties. Given its systematic layout, it's possible to discern trends, like atomic radius, as you move across periods (horizontal rows) and down groups (vertical columns).

For instance, atomic radius tends to decrease across a period from left to right, as additional protons in the nucleus create a stronger pull on the electrons, drawing them closer. Conversely, atomic radius increases down a group due to additional electron shells, which increase the distance from the nucleus, despite the higher nuclear charge.

Alkali Metals

Alkali metals are found in Group 1 of the periodic table. These elements include lithium, sodium, potassium, rubidium, cesium, and francium. They are characterized by having a single electron in their outermost shell, which makes them highly reactive. They are also notable for having large atomic radii within their respective periods, which is attributed to their single valence electron experiencing a relatively weak electrostatic pull from the nucleus.

Within the context of the problem where we are comparing Na (sodium) with other elements, Na is an alkali metal with a larger atomic radius compared to elements in other groups of the same period.

Alkaline Earth Metals

Adjacent to the alkali metals in Group 2 are the alkaline earth metals, which include beryllium, magnesium, calcium, strontium, barium, and radium. Each atom has two electrons in its outer shell. They are less reactive than alkali metals and have slightly smaller atomic radii than their Group 1 counterparts in the same period due to the stronger effective nuclear charge experienced by the electrons.

In the provided exercise, calcium (Ca) is an alkaline earth metal, which we see has a smaller atomic radius than sodium (Na) when compared within the same period.

Atomic Radius Comparison

When comparing atomic radii among different elements, it's crucial to consider their group and period. Atomic radius generally increases down a group because each successive element has an additional electron shell, which leads to a greater distance from the nucleus. However, within a period, atomic radius decreases as electrons are added to the same shell while the nuclear charge increases.

Looking at the exercise example, barium (Ba) has a larger atomic radius than both calcium (Ca) and sodium (Na) because it's located in a higher period. This means it has more electron shells, leading to a greater atomic radius.

Group and Period Properties

Understanding group and period trends is essential for predicting and comparing the properties of elements. Groups indicate how many valence electrons are present in an element, which significantly affects its chemical reactivity. For instance, all alkali metals in Group 1 are very reactive due to their single valence electron.

Periods indicate the number of electron shells. Elements within the same period will have the same number of electron shells, affecting properties like atomic radius. As seen in the exercise, arsenic (As), tin (Sn), and antimony (Sb) exhibit increasing atomic radii with higher periods, despite belonging to different groups.