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 Si. Rationalize why these diagonal relationships hold for properties such as size, ionization energy, and electron affinity.

Short answer

Diagonal relationships in the periodic table, such as between Be-Al and B-Si, occur due to the balancing effects of increasing atomic number and the shielding effect of additional electron shells. These diagonal relationships result in elements with similar sizes, ionization energies, and electron affinities. This is because the effective nuclear charge and shielding effect of extra electron shells are balanced, which leads to similar atomic properties for these pairs of elements.

Step-by-step solution

Understanding Diagonal Relationships

Diagonal relationships in the periodic table occur when elements share similar properties due to their positions in the table. In this case, Be (beryllium) and Al (aluminum) are diagonal neighbors in groups 2 and 13, respectively, and B (boron) and Si (silicon) are diagonal neighbors in groups 13 and 14. These pairs of elements show similar properties due to the balance between the increase in atomic number and the shielding effect of additional electron shells.

Comparing Sizes of Elements

As we move across a period from left to right, the atomic number increases, and more protons are added to the nucleus. This increases the effective nuclear charge experienced by the outermost electrons, which results in a decrease in atomic size. As we move down a group, an additional electron shell is added, which means that electrons are further from the nucleus, and the atomic size increases due to the shielding effect. In the case of Be-Al and B-Si, since they are diagonal neighbors, the effects of additional protons and electron shells are balanced, resulting in elements with similar sizes.

Comparing Ionization Energies

Ionization energy is the energy required to remove an electron from an atom. As the atomic size decreases across a period, the ionization energy increases due to the increase in effective nuclear charge and stronger electrostatic attraction between the nucleus and the outermost electrons. On the other hand, ionization energy decreases down a group due to the increase in atomic size and the outermost electrons being further from the nucleus, making it easier to remove an electron. In the case of Be-Al and B-Si, the balance between the increase in atomic number and the shielding effect of additional electron shells results in similar ionization energies for these pairs of elements.

Comparing Electron Affinities

Electron affinity is the energy change that occurs when an electron is added to a neutral atom. It measures an atom's tendency to attract and bind with an extra electron. Across a period, electron affinity generally increases due to the smaller atomic size and stronger electrostatic attraction between the electrons and the nucleus. However, electron affinity decreases down a group due to the larger atomic size and shielded outer electrons being less attracted to the nucleus. For Be-Al and B-Si, the effective nuclear charge and shielding effect of extra electron shells are balanced, and they show similar electron affinities. In conclusion, diagonal relationships in the periodic table such as between Be-Al and B-Si occur due to the balancing effects of increasing atomic number and the shielding effect of additional electron shells. These diagonal relationships result in similar sizes, ionization energies, and electron affinities for these pairs of elements.

Key concepts

Atomic Size

In the periodic table, atomic size is an important property that helps us understand the behavior of elements. It refers to the distance from the nucleus of an atom to the outermost electron shell. Across a period, the atomic size generally decreases. This happens because as you move from left to right, more protons are added. More protons mean a greater effective nuclear charge—basically, the nucleus has a stronger "pull" on the electrons. This pulls the outer electrons closer to the nucleus, making the atom smaller.

However, things change as you move down a group. Moving down a column, atoms have more electron shells. These extra layers increase the distance between the nucleus and the outermost electrons, which makes the atomic size larger. The added layers also have a shielding effect. Despite more protons, the increased distance and shielding mean those outer electrons don't feel the nucleus's pull as strongly, so the atoms are bigger.

Diagonal relationships show that the effects of moving one step to the right and one step down almost cancel each other. For instance, while beryllium (Be) decreases in size as we move across a period, aluminum (Al), a larger atom due to adding one shell, balances it out. Therefore, their similar sizes make their properties more comparable.

Ionization Energy

Ionization energy is a measure of how strongly an atom holds on to its electrons. It is defined as the energy required to remove an electron from an atom in the gaseous state. As you progress across a period from left to right, ionization energy increases. This is because the atomic size decreases and the effective nuclear charge becomes stronger, holding onto electrons more tightly.

On the other hand, ionization energy decreases as you move down a group. The increase in atomic size and added electron shells means that outer electrons are further away from the nucleus. This distance reduces the hold of the nucleus on the outermost electrons, making it easier to remove them.

In diagonal relationships, like between Be and Al, or B and Si, the balance of these two trends can result in similar ionization energies. They both experience the effects of increasing nuclear charge along a period and of increased shielding and distance down a group, leading to a unique but balancing effect in their ionization energies.

Electron Affinity

Electron affinity is another critical concept in chemistry. It measures the energy change when an electron is added to a neutral atom, essentially indicating how much an atom "wants" an extra electron. As you move across a period, electron affinity tends to increase. This is due to the smaller atomic size and greater nuclear charge without added shielding effect, making outer electrons more attracted to the nucleus.

In contrast, as you move down a group, electron affinity generally decreases. The atomic size grows due to increased electron shells, and these shells "shield" the outer electrons from the nucleus's pull. Consequently, the draw towards gaining an extra electron isn't as strong.

Diagonal relationships reveal that these competing influences often reach a delicate equilibrium. For elements like Be and Al, or B and Si, the trend of increasing nuclear charge across a period and the addition of shielding shells down a column harmonize, resulting in electron affinities that are more similar than one might expect from their group trends alone.