Question

Diagonal relationships in the periodic table exist as well as the vertical relationships. For example, Be and \(\mathrm{Al}\) 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, diagonal relationships in the periodic table, such as Be & Al and B & Si, arise due to the counterbalancing effects of periodic trends when an element is one period below and one group to the right of another. This leads to similarities in properties such as size, ionization energy, and electron affinity, demonstrating the existence and significance of these diagonal relationships.

Step-by-step solution

Understand Periodic Table Trends

First, let's recall the general trends in the periodic table: 1. Atomic size increases as we move from top to bottom and decreases from left to right. 2. Ionization energy typically decreases from top to bottom and increases from left to right. 3. Electron affinity usually decreases from top to bottom and increases from left to right.

Compare Be & Al Properties

Now let's examine the specific properties of Beryllium (Be) and Aluminum (Al): 1. Be: Group 2, Period 2 2. Al: Group 13, Period 3 Since Al is one period below and one group to the right of Be, we can observe the following trends in their properties: 1. Size: Both elements have relatively similar sizes. Al is one period below Be, so it's larger, but it's also one group to the right, counterbalancing the size increase. 2. Ionization energy: Both elements have similar ionization energies, since increasing one period and one group has a counterbalancing effect (decreased ionization energy by moving down a period, and increased ionization energy by moving right a group). 3. Electron affinity: Both elements have similar electron affinities, due to the same “counterbalancing” effect seen with ionization energy.

Compare B & Si Properties

Next, let's examine the specific properties of Boron (B) and Silicon (Si): 1. B: Group 13, Period 2 2. Si: Group 14, Period 3 Since Si is one period below and one group to the right of B, we can observe similar trends in their properties as seen with Be and Al: 1. Size: Both elements have relatively similar sizes due to the same "counterbalancing" effect. 2. Ionization energy: Both elements have similar ionization energies, experiencing the same counterbalancing effect when moving down a period and right a group. 3. Electron affinity: Both elements have similar electron affinities for the same reasons as ionization energy.

Conclude

In conclusion, the diagonal relationships in the periodic table arise due to the effects of horizontal and vertical periodic trends "counterbalancing" each other. This is seen in the examples of Be & Al, and B & Si, where both pairs exhibit similar properties in terms of size, ionization energy, and electron affinity. The counterbalancing effect occurs as one element is one period below and one group to the right of the other, demonstrating the existence and significance of these diagonal relationships in the periodic table.

Key concepts

Atomic Size Trends

Atomic size refers to the distance from the nucleus to the outermost shell of an electron. A few factors influence the atomic size across the periodic table.
When we talk about atomic size trends, we often think about how an atom's size changes as you move across or down the periodic table.

• As you move from left to right across a period, the atomic size decreases. This happens because electrons are added to the same energy level, while the number of protons in the nucleus also increases. The added positive charge pulls electrons closer to the nucleus, making the atom smaller.
• As you go down a group, atomic size increases. This is because each row adds a new shell to the atoms, making them larger.

The diagonal relationship, such as between Beryllium (Be) and Aluminum (Al), results from opposing trends. Despite Aluminum being one period lower (indicating it should be larger) and one group to the right (indicating it should be smaller), these factors "counterbalance," giving them similar sizes.

Ionization Energy Trends

Ionization energy is the amount of energy required to remove an electron from an atom. It provides an insight into the force of attraction between the nucleus and the electrons.
The periodic trend for ionization energy shows interesting patterns:

• Moving from left to right across a period, ionization energy increases. As more protons are added, electrons are held more tightly by the nucleus.
• Going down a group, ionization energy decreases since electrons are farther from the nucleus and experience less pull.

For elements like Be and Al or B and Si, diagonal relationships result from their positions in the periodic table. Be, for instance, is higher in ionization energy apart from its smaller atomic size, while Al is positioned such that its lower position and the enhanced pull due to additional protons counteract each other, leading to comparable ionization energies.

Electron Affinity Trends

Electron affinity is the energy change when an electron is added to a neutral atom, signifying how much an atom 'wants' an extra electron.
Across the periodic table, this property doesn't follow a strict trend but can be generalized:

• Typically, electron affinity becomes more negative or increases as you move from left to right across a period. More negative value means more energy is released and the atom "wants" the electron more.
• It generally decreases down a group because additional electron shells mean increased distance between added electrons and the nucleus, reducing pull.

In the context of diagonal relationships, elements like Be and Al or B and Si have comparable affinities. This "counterbalance" results from Be and B having higher electron affinities due to their position in the upper rows versus Al and Si, where lower proximity to the nucleus due to additional shells compensates, delivering similar affinities.