Problem 24 - A Complete Resource Book in Chemistry for JEE Main

Question

The order of first ionization energies of the elements \(\mathrm{Li}, \mathrm{Be}, \mathrm{B}, \mathrm{Na}\) is (a) \(\mathrm{Be}>\mathrm{Li}>\mathrm{B}>\mathrm{Na}\) (b) \(\mathrm{B}>\mathrm{Be}>\mathrm{Li}>\mathrm{Na}\) (c) \(\mathrm{Na}>\mathrm{Li}>\mathrm{B}>\mathrm{Be}\) (d) \(\mathrm{Be}>\mathrm{B}>\mathrm{Li}>\mathrm{Na}\)

Step-by-Step Solution

Answer

The correct order is (d) Be > B > Li > Na.

Step 1: Understanding First Ionization Energy

Ionization energy is the energy required to remove the outermost electron from a neutral atom in its gaseous state. First ionization energy generally increases across a period and decreases down a group in the periodic table.

Step 2: Analyzing Periodic Table Trends

Lithium (Li), Beryllium (Be), and Boron (B) are all in the second period, with Be having the highest first ionization energy due to its filled s-orbital, followed by B and then Li. Sodium (Na), being in the third period, typically has a lower ionization energy than elements in the second period.

Step 3: Creating the Ionization Energy Sequence

Considering the order within the second period, the order is typically Be > B > Li, since filling and effective nuclear charge considerations place B slightly below Be. When comparing Li and Na, the typical trend is Li > Na due to Na being lower in the periodic table.

Step 4: Matching with Given Options

Given the analysis, the order of the first ionization energies is Be > B > Li > Na. This corresponds to option (d).

Step 5: Verification of Trends

We've verified the trends: across a period, ionization energy generally increases, and down a group, it decreases. Be > B > Li > Na follows these expected trends, confirming option (d) is correct.

Key Concepts

Periodic Table Trends

The periodic table is a valuable tool that helps us understand and predict various chemical behaviors of elements, such as ionization energy. Ionization energy is the energy required to remove an outermost electron from a neutral atom. It is useful to know that as you move across a period in the periodic table from left to right, the first ionization energy typically increases. This happens because elements have more protons, leading to a greater nuclear charge which holds onto the electrons more tightly.

Conversely, as you move down a group in the periodic table, the first ionization energy decreases. This is due to the increasing atomic size where added energy levels push outer electrons further from the nucleus. Thus, these electrons are not as tightly held and can be removed with less energy. These trends help explain why elements like Lithium (Li) have lower ionization energies compared to elements positioned further right in the same row such as Beryllium (Be) and Boron (B).

• Across a period: Ionization energy increases.
• Down a group: Ionization energy decreases.

Second Period Elements

The second period of the periodic table includes elements like Lithium (Li), Beryllium (Be), Boron (B), and so on. These elements are of particular interest when studying periodic trends because they exemplify changes in electron configuration and nuclear attraction as you move across the period. Each step to the right in this period typically adds a proton and an electron.

For example, Beryllium, which comes after Lithium in the second period, has a filled s-orbital. This provides greater stability and thus higher ionization energy compared to Boron, where the additional electron goes into a p-orbital, slightly reducing its ionization energy despite having one more proton than Beryllium. Understanding these subtle changes in structure with each subsequent element in the period helps explain their varying ionization energies.

• Li < Be due to increased nuclear charge and filled s-orbital.
• Be > B despite Boron's additional p-electron.

Effective Nuclear Charge

Effective nuclear charge ( Z_eff) is a concept that helps us understand how the positive charge from the nucleus affects outer electrons. While the number of protons gives the nucleus a positive charge, inner electrons can shield outer electrons from this charge. Z_eff becomes an important factor when analyzing elements across a period or down a group.

A stronger effective nuclear charge means electrons are held more tightly to the nucleus, which usually means higher ionization energy. For instance, in the second period, as you move from Lithium (Li) to Beryllium (Be) to Boron (B), the effective nuclear charge increases. This increase is because electrons being added do not completely cancel out the additional positive charge from the protons.

However, even with Boron having a higher number of protons than Beryllium, its additional electron in the p-orbital experiences slightly less nuclear charge due to orbital penetration effects. Thus, Beryllium typically shows a higher ionization energy than Boron.

• Higher Z_eff leads to higher ionization energy.
• Inner electrons shield outer electrons from full nuclear charge.