Question

There are certain similarities in properties that exist between the first member of any periodic family and the element located below it and to the right in the periodic table. For example, in some ways Li resembles \(\mathrm{Mg}\), Be resembles \(\mathrm{Al}\), and so forth. This observation is called the diagonal relationship. Using what we have learned in this chapter, offer a possible explanation for this relationship.

Short answer

The diagonal relationship in the periodic table can be explained by the similar atomic properties, like atomic radius, ionization energy, and electronegativity, of diagonally related elements. When moving diagonally down and to the right, the changes in these properties while moving across a period are countered by the opposite changes when moving down a group, causing the properties to remain similar for the diagonally related elements, leading to the observed diagonal relationship.

Step-by-step solution

Review periodic properties

Before we analyze the diagonal relationship, let's review the periodic trends in atomic properties to be considered in this explanation: 1. Atomic radius: It decreases across a period (left to right) and increases down a group (top to bottom). 2. Ionization energy: It increases across a period (left to right) and decreases down a group (top to bottom). 3. Electronegativity: It increases across a period (left to right) and decreases down a group (top to bottom). These trends will play a key role in understanding the diagonal relationship in the periodic table.

Consider the examples

As given in the exercise, we have some examples that exhibit diagonal relationships: Li and Mg, Be and Al. We can observe that these elements are present diagonally in the periodic table. For example: - Li is in group 1, period 2, and Mg is in group 2, period 3. - Be is in group 2, period 2, and Al is in group 13, period 3.

Analyze the properties of diagonally related elements

Now, let's analyze the properties of the diagonally related elements. 1. Atomic radius: Considering Li and Mg as an example, when we move from Li to Mg in the periodic table, we go down in a group and across a period. As a result, the atomic radius will decrease when we move from Li to Be (across a period), but it will increase when we move from Be to Mg (down a group). The net effect is that the atomic radii of Li and Mg are similar. 2. Ionization energy: Using the same example, the ionization energy decreases when we move from Li to Be (down a group), but it increases when we move from Be to Mg (across a period). As a result, the ionization energies of Li and Mg are also similar. 3. Electronegativity: As with the other two properties, the electronegativities of Li and Mg are also similar, given that the electronegativity decreases when we move from Li to Be (down a group) and it increases when we move from Be to Mg (across the period).

Offer a possible explanation for the diagonal relationship

Based on the similarities in atomic properties between diagonally related elements in the periodic table, we can offer the following possible explanation for the diagonal relationship: When we move diagonally down and to the right in the periodic table, the properties such as atomic radius, ionization energy, and electronegativity do not change significantly. The reason is that the changes in these properties while moving across a period (left to right) are countered by the opposite changes in them while moving down a group (top to bottom). As a result, the net effect is that the properties remain similar for the diagonally related elements, which leads to the diagonal relationship observed in the periodic table.

Key concepts

Understanding Periodic Trends

Periodic trends refer to patterns in the properties of elements that occur in the periodic table. These patterns arise due to the periodic nature of the atomic structure of the elements. The periodic table is designed in such a way that elements with similar properties fall into the same column (groups), while horizontal rows (periods) denote increasing atomic number and mass.

Some of the most significant periodic trends include changes in atomic radius, ionization energy, and electronegativity when moving across a period (from left to right) or down a group (from top to bottom). Understanding these trends is fundamental when studying the chemical behavior of elements and helps explain the diagonal relationship between certain pairs of elements.

Atomic Radius

The atomic radius is a measure of the size of an atom, typically the distance from the nucleus to the outermost electrons. Here's how it changes in the periodic table:

• Across a Period: The atomic radius generally decreases as you move from left to right across a period. This is due to the increased number of protons in the nucleus, causing a stronger attraction to the electrons and pulling them closer.
• Down a Group: The atomic radius increases as you go down a group. This increase is because each subsequent element has an additional electron shell, making the atom larger.

These opposing trends combine in a particular way for diagonally related elements, such as lithium (Li) and magnesium (Mg), leading to similar atomic sizes despite their different positions in the periodic table.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. It's a critical indicator of an element's reactivity. Here are the trends for ionization energy:

• Across a Period: Ionization energy increases from left to right across a period. As the atomic radius decreases and nuclear charge increases, electrons are more strongly attracted to the nucleus, making them harder to remove.
• Down a Group: Ionization energy decreases as you move down a group. Larger atoms with more electron shells have electrons that are farther from the nucleus and less tightly held, thus requiring less energy to remove.

Diagonally related elements like beryllium (Be) and aluminum (Al) exhibit similar ionization energies since the increase in ionization energy due to decreasing radius is offset by the decrease due to the added electron shell.

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons when it is part of a compound. Similar to other periodic trends, electronegativity is influenced by the atomic structure:

• Across a Period: Electronegativity tends to increase moving from left to right. Atoms with higher nuclear charge and smaller radii can more effectively attract electrons in bonds.
• Down a Group: Electronegativity decreases moving down a group because the additional electron shells reduce the nuclear pull on bonding electrons.

In terms of the diagonal relationship, these opposing trends result in diagonally positioned elements like lithium (Li) and magnesium (Mg) having similar abilities to attract electrons in chemical bonds, despite their different locations on the periodic table.