Question

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

Short answer

Using the periodic table trends, the order of increasing atomic radius for each set of atoms is: (a) Na, Ca, Ba; (b) As, In, Sn; (c) Be, Al, Si.

Step-by-step solution

(a) Ba, Ca, Na - Increasing Atomic Radius

First, locate the positions of Ba, Ca, and Na in the periodic table. - Ba (Barium) is in group 2 and period 6 - Ca (Calcium) is in group 2 and period 4 - Na (Sodium) is in group 1 and period 3 Since all elements are in period 3 or further down, we prioritize the group trend (atomic radius increases going down a group). Hence the order of increasing atomic radius is: Na, Ca, Ba.

(b) In, Sn, As - Increasing Atomic Radius

Locate the positions of In, Sn, and As in the periodic table. - In (Indium) is in group 13 and period 5 - Sn (Tin) is in group 14 and period 5 - As (Arsenic) is in group 15 and period 4 In and Sn are in the same period, so we prioritize the period trend (atomic radius decreases as we go left to right across a period). As is one period above In and Sn; hence, it will be the smallest among three. The order of increasing atomic radius is: As, In, Sn.

(c) Al, Be, Si - Increasing Atomic Radius

Locate the positions of Al, Be, and Si in the periodic table. - Al (Aluminum) is in group 13 and period 3 - Be (Beryllium) is in group 2 and period 2 - Si (Silicon) is in group 14 and period 3 No two elements are in the same period, so we need to consider both group and period trends. The order of increasing atomic radius due to both effects is: Be, Al, Si.

Key concepts

Periodic Table

The periodic table is an organized chart of chemical elements, arranged in order of increasing atomic number, which corresponds to the number of protons in an atom's nucleus. This arrangement shows recurring "periodic" trends in the properties of the elements. It consists of rows, known as periods, and columns, called groups or families.

Each element in a period has one more proton and is slightly more massive than the element before it. Elements in the same group share chemical properties, primarily because they have the same number of valence electrons that participate in chemical reactions. The periodic table helps chemists understand and predict the behavior of elements in chemical reactions. Its organization is crucial for studying trends and patterns in atomic structure and properties.

Group and Period Trends

In the periodic table, understanding trends within groups and periods helps predict element properties like atomic radius, ionization energy, and electronegativity.

• **Group Trends:** As you move down a group (a column) in the periodic table, the atomic radius of an element increases. This happens because each subsequent element has an additional shell of electrons, which makes the atom larger despite an overall increase in nuclear charge.


• **Period Trends:** Moving across a period (a row) from left to right, the atomic radius tends to decrease. This is because electrons are added to the same shell while protons are being added to the nucleus, increasing the nuclear charge which pulls the electron cloud closer to the nucleus, making the atom smaller.

These trends are essential for predicting the size of an atom compared to others when arranging them in order of increasing atomic radius.

Atomic Size

Atomic size, often referred to as atomic radius, is a measure of the size of an atom's electron cloud, which surrounds the nucleus. Since the precise edge of an atom is difficult to define, atomic size is typically approximated by measuring the distance between the nuclei of two bonded atoms and dividing by two.

The atomic radius can be affected by:

• **Number of Electron Shells:** More electron shells mean a larger atomic radius, as seen when moving down a group.


• **Nuclear Charge:** A higher number of protons (atomic number) results in a stronger pull on electrons, which decreases the atomic radius as you move across a period.

Understanding atomic size is fundamental in explaining the reactive nature of an element. It helps in determining how elements interact with one another and their positioning in the periodic table aids in predicting atomic size.