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 conclusion, the diagonal relationships between Be and Al, as well as B and Si, exist because the periodic trends in atomic size, ionization energy, and electron affinity are offsetting each other for these elements, making their properties similar. The atomic size of Be and Al, as well as B and Si, is relatively similar, which results from the balance between the increase in size down a group and the decrease in size across a period. Both Be and Al, as well as B and Si, have relatively high ionization energies and relatively low electron affinities compared to their respective neighbors, further emphasizing their diagonal relationship in the periodic table.

Step-by-step solution

Understand the concept of diagonal relationships in the periodic table

A diagonal relationship is the phenomenon where elements with similar properties are found diagonally adjacent to each other in the periodic table. This is primarily observed between elements in the second and third periods, such as Be and Al, as well as B and Si.

Examine the atomic size

As we move from left to right across a period, the atomic size generally decreases (due to increasing effective nuclear charge). When we move down a group, the atomic size increases as there is an extra energy shell. In the case of diagonal relationships, an increase in size down one group is offset by a decrease in size across the period. In the case of Be and Al, Be is in the second period and Al is in the third period and right next to Mg (group 2). The atomic size of Al is slightly larger than Be, which makes their sizes relatively similar. The same applies to B and Si, where B is in the second period and Si is in the third period, diagonally adjacent to B. The atomic size of Si is slightly larger than B, making them relatively similar in size.

Analyze the ionization energy

Ionization energy is the energy required to remove an electron from an atom. It generally increases as we move from left to right across a period and decreases down a group. In our case, Be and Al both have relatively high ionization energies compared to their neighbors Mg and Ga. Be in group 2 has an ionization energy higher than Mg and Al, while Al has a lower ionization energy than Mg but higher than Ga. Similarly, B and Si both have relatively high ionization energies compared to their neighbors C and Ge. B in group 13 has an ionization energy higher than Si, while Si has a lower ionization energy than C but higher than Ge. This explains the diagonal relationship between Be and Al, as well as B and Si in terms of ionization energy.

Discuss electron affinity

Electron affinity is the energy released when an electron is added to an atom. It generally increases as we move from left to right across a period and decreases down a group. Be and Al both have relatively low electron affinities compared to their neighbors, which are non-metals. This is because both Be and Al are metals and usually lose electrons. Similarly, B and Si both have relatively low electron affinities compared to their neighbors that are non-metals. As both B and Si are metalloids, their properties are intermediate between metals and non-metals. In conclusion, the diagonal relationships between Be and Al, as well as B and Si, exist because the periodic trends in atomic size, ionization energy, and electron affinity are offsetting each other in these elements making their properties similar.

Key concepts

Atomic Size

When discussing diagonal relationships in the periodic table, atomic size is a key factor. As we move left to right across a period, atomic size decreases. This is due to the increasing effective nuclear charge, which pulls the electrons closer to the nucleus. However, moving down a group increases atomic size since additional electron shells are added.

In the context of diagonal relationships, such as between Beryllium (Be) and Aluminum (Al), or Boron (B) and Silicon (Si), these size changes partially cancel each other out. For instance:

• Be is in the second period, while Al is in the third period. Although Al has additional electron shells making it larger, this increase is moderated by the larger effective nuclear charge Be experiences in its period.
• Similarly, B is small because of being in the second period, but Si in the third period has a larger size. Again, the increase in size related to the additional shell in Si partially offsets the decrease experienced across the period.

In these cases, atomic sizes are fairly similar across diagonal elements, showcasing a unique balance of periodic trends.

Ionization Energy

Ionization energy refers to the energy required to remove an electron from an atom. Typically, ionization energy increases across a period from left to right, due to the higher nuclear charge pulling electrons closer. On the other hand, it tends to decrease down a group as the outer electrons are further from the nucleus.

In diagonal relationships, such as Be with Al, these energies balance out:

• Be has a high ionization energy compared to its neighbor Magnesium (Mg), even though it's in a higher period. Al's ionization energy, while lower than Be, is still noteworthy when compared to both its neighbor Mg and Ga, due to its position in the third period.
• Likewise, Boron (B) and Silicon (Si) show a similar pattern. B has a higher ionization energy compared to Carbon (C), but its diagonal counterpart Si has an ionization energy sitting between its periods’ neighbors, offering a balanced relation in terms of diagonal opposition.

These findings highlight how ionization energy trends carefully balance, explaining the diagonal similarities.

Electron Affinity

Electron affinity is the energy change when an electron is added to an atom. Moving across a period, from left to right, generally increases electron affinities, while moving down a group decreases them. This trend is due to varying attractive forces for additional electrons influenced by electron configuration and nuclear charge.

Diagonal similarities between elements such as Be and Al, or B and Si, illustrate these affinities:

• Both Be and Al show lower electron affinities than their neighboring atoms, being metals that prefer to lose rather than gain electrons, highlighting their metallic nature in contrast to their non-metal neighbors.
• B and Si, being metalloids, exhibit electron affinities that are intermediate, fitting between metals and non-metals, hence showing low attraction towards additional electrons compared to their period neighbors.

In conclusion, the similarities in electron affinity along diagonals exemplify indirect relationships due to offsetting trends, making diagonal elements closer in properties despite their placements on the periodic table.