Problem 111 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statement (s) is /are true? (a) ionization energy \(\alpha \frac{1}{\text { Screening effect }}\) (b) The first ionization energies of Be and \(\mathrm{Mg}\) are more than ionization energies of \(\mathrm{B}\) and \(\mathrm{Al}\) respectively (c) Atomic and ionic radii of Niobium and Tantalum are almost same (d) Metallic and covalent radii of potassium are \(2.3 \mathrm{~A}\) and \(2.03 \AA\) respectively

Step-by-Step Solution

Answer

All statements (a), (b), (c), and (d) are true.

Step 1: Analyze Statement (a)

Statement (a) claims that ionization energy is inversely proportional to the screening effect. The screening effect refers to how the inner electrons reduce the effective nuclear charge experienced by the outer electrons. When there is higher screening, the nuclear charge felt by the outermost electrons is lessened, reducing the ionization energy. Thus, ionization energy is \(\propto \frac{1}{\text{Screening effect}}\), so this statement is true.

Step 2: Evaluate Statement (b)

Statement (b) compares the ionization energies of Be and Mg with B and Al respectively. Be and Mg belong to group 2, and B and Al belong to group 13. Generally, group 2 elements have higher ionization energies than group 13 elements within the same period due to having a full s-subshell. Hence, the first ionization energies of Be and Mg are indeed higher than B and Al respectively, making this statement true.

Step 3: Examine Statement (c)

Statement (c) concerns the atomic and ionic radii of Niobium (Nb) and Tantalum (Ta). These elements belong to the same group (group 5) and have similar electronic configurations. Due to the lanthanide contraction, these elements have almost the same atomic and ionic radii. Therefore, this statement is true.

Step 4: Assess Statement (d)

Statement (d) provides specific values for the metallic and covalent radii of potassium. Metallic radius is generally larger than the covalent radius. The given values, 2.3 Å for the metallic radius and 2.03 Å for the covalent radius, align with their expected trend, as the metallic radius should be larger. Hence, the statement is true.

Key Concepts

Screening Effect

The screening effect, also known as the shielding effect, plays a crucial role in determining the ionization energy of an atom. It refers to the ability of inner-shell electrons to decrease the effective nuclear charge felt by outer-shell or valence electrons. This happens because inner electrons repel outer electrons, reducing the full effect of the nucleus's positive charge on these outer electrons.

• Higher screening effect = Lower effective nuclear charge on outer electrons
• Results in a reduced ionization energy

In simpler terms, when inner electrons effectively "block" the outer electrons from feeling the full charge of the nucleus, it becomes easier to remove an electron, hence lower ionization energy. Therefore, ionization energy is inversely proportional to the screening effect. A high screening effect means lower ionization energy and vice versa.

Atomic and Ionic Radii

Atomic and ionic radii are important considerations when analyzing elements in the periodic table. These properties tell us about the size of an atom or ion, which can influence various chemical and physical behaviors. Atomic radius is the average distance from the nucleus to the boundary of the surrounding cloud of electrons. As we move down a group in the periodic table, this radius generally increases.

• Periodic trend: increase down a group, decrease across a period

Ionic radius changes when an atom gains or loses an electron. Cations (positive ions) have smaller radii than their parent atoms due to loss of electron(s), while anions (negative ions) have larger radii due to gain of electron(s). Niobium (Nb) and Tantalum (Ta) are examples of elements where atomic and ionic radii are almost the same because of similar electronic shells and the influence of the lanthanide contraction, which minimizes increase in size down a series.

Metallic and Covalent Radii

Understanding metallic and covalent radii can help explain the structure and bonding of elements. The metallic radius is half the distance between the nuclei of two adjacent atoms in a metallic lattice, while the covalent radius is half the distance between two atoms of the same element joined by a covalent bond.
Potassium is an example where we see the difference in these radii values. In metals, atoms are usually more loosely packed, leading to larger metallic radii compared to covalent radii.

• Metallic radius is seen in metals with free-moving electrons
• Covalent radius reflects a closer, shared bond

The given example values for potassium show that its metallic radius is 2.3 Å, which is larger than its covalent radius of 2.03 Å, consistent with these structural differences.

Group Trends in the Periodic Table

Understanding trends in the periodic table is key to mastering how elements behave and interact. These trends provide insights into atomic and physical properties such as ionization energy, atomic radius, and more.
As you move across a period from left to right, elements generally increase in ionization energy and decrease in atomic radius due to increasing nuclear charge without an accompanying increase in shielding. In contrast, as you move down a group, the atomic radius generally increases because additional electron shells are added.

• Ionization energy increases across a period, decreases down a group
• Atomic radius decreases across a period, increases down a group

These trends explain why elements like Be and Mg, which belong to group 2, have higher ionization energies than elements like B and Al in group 13. Additionally, understanding these trends helps explain why elements like Nb and Ta have almost equal atomic and ionic sizes due to effects like the lanthanide contraction.