Question

Diagonal relationships in the periodic table exist as well as the vertical relationships. For example, Be and Al are similar in some of their properties, as are \(\mathrm{B}\) and \(\mathrm{Si}\). Rationalize why these diagonal relationships hold for properties such as size, ionization energy, and electron affinity.

Short answer

In the periodic table, diagonal relationships exist between elements with similar electronic configurations and sizes, such as Be and Al, and B and Si. These similarities arise due to comparable atomic sizes, ionization energies, and electron affinities, all of which are influenced by the effective nuclear charge. Diagonal relationships occur as the atomic size generally decreases across a period and increases down a group, while ionization energy decreases down a group and increases across a period. Consequently, diagonally adjacent elements like Be and Al or B and Si share more similar properties than if they were directly below each other.

Step-by-step solution

1. Understanding Diagonal Relationships

Diagonal relationships in the periodic table occur between elements that are located diagonally from one another. They share similar properties due to their similar electronic configuration and size. In this case, we are comparing beryllium (Be) with aluminum (Al), and boron (B) with silicon (Si).

2. Size Comparison

In the periodic table, the atomic size generally decreases across a period due to an increase in the effective nuclear charge, which pulls the outer electrons closer to the nucleus. However, it increases down a group due to a gradual increase in the principal quantum numbers. For Be and Al, their smaller size compared to their neighbors in their respective groups contributes to their similarities. The same applies to B and Si as their sizes are also comparable. As both pairs of elements are diagonally adjacent, they share a more similar size than if they were directly below each other.

3. Ionization Energy Comparison

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. Generally, ionization energy decreases down a group and increases across a period. Both Be and Al have similar ionization energies because they are diagonally adjacent, and both B and Si also share similar values. These similarities in the ionization energies arise due to the similar effective nuclear charge and size between the respective pairs (Be and Al, B and Si).

4. Electron Affinity Comparison

Electron affinity is the energy change when an electron is added to a neutral atom in its gaseous state to form a negative ion. Generally, electron affinity increases across a period and decreases down a group. For the diagonal pairs of Be and Al, and B and Si, their electron affinities are comparable because of their similar effective nuclear charge and sizes.

5. Conclusion

In conclusion, diagonal relationships in the periodic table, such as between Be and Al, and B and Si, exist due to their comparable sizes, ionization energies, and electron affinities. These similarities in properties arise from their similar electronic configuration and the effect of the effective nuclear charge on the elements.

Key concepts

Atomic Size

The term **atomic size** refers to the average distance from the nucleus of the atom to the outer shell of electrons. In the periodic table, atomic size decreases across a period from left to right because of the increasing effective nuclear charge. This means that the nucleus is pulling the electrons more closely in, compacting the atom. Conversely, atomic size increases as you move down a group, due to an increase in the principal quantum number. This means electrons are found in shells farther from the nucleus, making the atom larger.
Be and Al, as well as B and Si, demonstrate diagonal relationships because their atomic sizes are closer compared to elements directly vertically or horizontally adjacent on the periodic table. The similar sizes mean that these diagonal elements can exhibit similar chemical behavior, thanks in part to having similar electron densities around the nucleus as well.

Ionization Energy

**Ionization energy** is the amount of energy needed to remove an electron from a gaseous atom. It's a key indicator of how tightly an atom's electrons are bound to its nucleus. Ionization energy generally increases when moving across a period due to rising effective nuclear charge, causing the electrons to be held more tightly.
As you travel down a group, the ionization energy decreases. This results from the increased distance between the nucleus and the valence electron, which weakens the nucleus' hold on the electrons. However, in a diagonal relationship, like that of Be and Al, or B and Si, ionization energy remains more comparable because these elements have similar atomic sizes and effective nuclear charges. Such similarities lead to parallel energy requirements for losing an electron, making their chemical behavior similar.

Electron Affinity

**Electron affinity** measures how much energy is released when an electron is added to a gaseous atom. It's closely related to the atom's desire to gain electrons and is influenced by the nuclear charge and atomic radius. Typically, electron affinity increases as you move across a period because atoms tend to pull in electrons more avidly, attributed to more positive effective nuclear charges.
In contrast, electron affinity decreases as you descend a group, since added electrons would be further from the nucleus and experience less attraction. For elements like Be and Al and B and Si, even though they align diagonally rather than directly across a period or group, electron affinities remain close. This similarity arises from their similar atomic sizes and effective nuclear charges. Despite differing positions, their diagonal alignment results in affinity values close enough to produce analogous chemical traits.