Problem 66 - A Complete Resource Book in Chemistry for JEE Main

Question

The configuration of inert gas with smallest size and highest IE is (a) \(1 \mathrm{~s}^{2}\) (b) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{6}\) (c) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{3}\) (d) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{6} 3 \mathrm{~s}^{2} 3 \mathrm{p}^{6}\)

Step-by-Step Solution

Answer

The configuration corresponds to (b) \(1 \, ext{s}^2 \, 2 \, ext{s}^2 \, 2 \, ext{p}^6\), which is Neon with smallest size and highest IE.

Step 1: Identify Inert Gas Configurations

First, recognize that inert gases – also known as noble gases – have completely filled outer electron shells. This means their electron configurations will have full s and p orbitals in their outermost shells. The typical configuration pattern is of the form \( ext{ns}^2 ext{np}^6 \). Analyze each option to identify which have this pattern.

Step 2: Analyze Given Configurations

Review the provided electron configurations:- (a) \(1 \, ext{s}^2\) is the configuration for Helium, which is not a noble gas with fully filled p orbital but belongs to the group due to full s orbital.- (b) \(1 \, ext{s}^2 \, 2 \, ext{s}^2 \, 2 \, ext{p}^6\) corresponds to Neon, a noble gas.- (c) \(1 \, ext{s}^2 \, 2 \, ext{s}^2 \, 2 \, ext{p}^3\) corresponds to an incomplete p orbital, thus not a noble gas.- (d) \(1 \, ext{s}^2 \, 2 \, ext{s}^2 \, 2 \, ext{p}^6 \, 3 \, ext{s}^2 \, 3 \, ext{p}^6\) corresponds to Argon, a noble gas.

Step 3: Determine Smallest Size and Highest Ionization Energy

Ionization energy (IE) tends to increase across a period and decreases down a group. Smaller atomic size generally correlates with higher ionization energy. Between the options, Helium in (a) has the smallest atomic size and highest ionization energy, but lacks a filled p orbital. Ne (b) and Ar (d) both have full p orbitals, but Ne (b) is smaller and has a higher IE than Ar (d) due to its position in Period 2 compared to Period 3.

Key Concepts

Electron Configuration

Electron configuration is a representation of how electrons are distributed within an atom's orbitals. Each atom has a unique electron configuration, which determines its chemical properties and behavior.
Understanding how to read and write electron configurations is essential for identifying elements and predicting their interactions. The configurations are typically written using a sequence of numbers and letters, such as \(1s^2\), \(2s^2\), \(2p^6\), etc. Each symbol represents:

• The number denotes the principal energy level, or shell.
• The letter indicates the type of orbital (s, p, d, or f).
• The superscript shows the number of electrons in those orbitals.

For noble gases, the electron configurations end with a filled p orbital, like \(ns^2 np^6\). This full s and p configuration in the valence shell grants them stability, making noble gases unreactive under normal circumstances.

Ionization Energy

Ionization energy (IE) reflects the energy needed to remove an electron from an atom or ion in its gaseous state. It serves as an indicator of an atom's tendency to resist losing electrons.
Noble gases have particularly high ionization energies due to their full valence shells, which make removing an electron energetically unfavorable.
Here’s why ionization energy is important:

• Across a period, IE increases as the effective nuclear charge attracting the outer electrons becomes stronger.
• Down a group, IE decreases since the outer electrons are further from the nucleus and are more easily removed.
• Smaller atomic size typically means a higher ionization energy, since electrons are closer to the nucleus.

Understanding ionization energy helps in explaining the stability of noble gases like Neon and Argon.

Atomic Size

Atomic size, often referred to as atomic radius, pertains to the physical size of an atom. It is influenced by the number of electron shells and the effective nuclear charge.
Here are the key points to understand about atomic size:

• Across a period, atomic size decreases because the effective nuclear charge increases, pulling electrons closer to the nucleus.
• Down a group, atomic size increases as additional electron shells are added, distancing the outer electrons from the nucleus.
• Smaller atoms, such as Helium and Neon, have higher ionization energies due to their compact size.

This concept is crucial for understanding why Neon, with fewer electron shells compared to Argon, also possesses a higher ionization energy.

Noble Gases

Noble gases, which include Helium, Neon, Argon, and others, are characterized by their full valence electron shells. This full configuration is denoted as \(ns^2 np^6\) for those beyond Helium, giving them stability and making them mostly non-reactive.
Here are the unique features of noble gases:

• They are located in Group 18 of the periodic table.
• Possess a complete s and p orbital in their outermost energy level.
• Exhibit high ionization energies due to their stable electron configurations.
• They have very low chemical reactivity, often described as inert.

Recognizing noble gases' configurations and properties is essential for understanding why they do not readily form compounds under normal conditions.