Problem 12 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

If the principal quantum number \(n=6\), the correct sequence of filling of electrons will be :[Main Online April 10,2015\(]\) (a) \(n s \rightarrow(n-2) f \rightarrow n p \rightarrow(n-1) d\) (b) \(n s \rightarrow(n-2) f \rightarrow(n-1) d \rightarrow n p\) (c) \(n s \rightarrow n p \rightarrow(n-1) d \rightarrow(n-2) f\) (d) \(n s \rightarrow(n-1) d \rightarrow(n-2) f \rightarrow n p\)

Step-by-Step Solution

Answer

The correct sequence is (b): \(n s \rightarrow(n-2) f \rightarrow(n-1) d \rightarrow n p\).

Step 1: Understand Electron Configuration Principles

Electron configurations follow the Aufbau principle, Hund's rule, and Pauli-exclusion principle. Electrons fill orbitals starting from the lowest energy to the highest energy

Step 2: Identify Available Sublevels for n=6

For the principal quantum number \(n=6\), the possible sublevels include \(6s\), \(6p\), \(5d\), and \(4f\).

Step 3: Order Sublevels by Increasing Energy

Arrange the sublevels based on the energy sequence: \(6s\), \(4f\), \(5d\), \(6p\). This follows from the Aufbau principle and common periodic table knowledge.

Step 4: Match Sequence with Given Options

Match this sequence with the given options. The correct sequence \(6s \rightarrow 4f \rightarrow 5d \rightarrow 6p\) corresponds to option (b): \(n s \rightarrow(n-2) f \rightarrow(n-1) d \rightarrow n p\).

Key Concepts

Aufbau Principle

In the world of electron configuration, the Aufbau Principle serves as a cornerstone. It guides how electrons arrange themselves within an atom. The term "Aufbau" comes from the German word meaning "building up". This principle suggests that electrons fill orbitals starting from the lowest energy level to the highest.
By filling from the lowest energy, atoms achieve the most stable configuration. This stability is essential because it allows atoms to maintain a minimized energy state.

• Electrons fill orbitals in an increasing order of energy levels.
• Each orbital can hold a specified number of electrons before moving to the next higher energy level.
• S orbitals fill first, followed by p, d, and then f.

Understanding the Aufbau Principle helps us know why, for instance, the 6s orbital fills before 4f. It's all about achieving the lowest possible energy first.

Principal Quantum Number

The Principal Quantum Number, represented as \( n \), provides vital information about the electron's location within an atom. Think of it as the electron's address indicating the energy level on which an electron resides.
The value of \( n \) starts from 1 and increases with higher energy levels. In our example, with \( n = 6 \), it denotes the atom's sixth energy level. Each principal quantum number encompasses different types of orbitals: s, p, d, and f.

• The larger \( n \), the further the orbital is from the nucleus.
• Larger \( n \), usually means a higher energy level.
• Each energy level can hold a distinct number of electrons.

By understanding \( n \), we grasp which orbitals are available for electron occupation, such as 6s, 6p, 5d, and 4f in the given solution.

Orbital Filling Order

Determining the order in which electrons occupy orbitals is crucial for correct electron configurations. The sequence relies on both energy levels and sublevels. The Aufbau principle primarily dictates this order. However, tools like the "n + l rule" help us predict it more intuitively.
According to this rule, orbitals are filled in order of increasing \( n + l \) values. If two orbitals have the same \( n + l \), the one with the lower \( n \) fills first. For instance,

• First, the 6s orbital fills.
• Next, the 4f, having a lower energy than 5d.
• Then, the 5d orbitals take their electrons.
• The 6p follows last among these options.

Mastering the orbital filling order helps avoid confusion and predict the electron configurations correctly.

Hund's Rule

Hund's Rule provides yet another crucial detail about electron configurations. It applies specifically when dealing with orbitals of the same energy level, known as degenerate orbitals. The rule states that electrons will fill these orbitals singly before any orbital gets a second electron.
This means that every orbital in a subshell receives one electron each before doubling up.

• Electrons prefer to maximize the number of parallel spins in separate orbitals.
• This results in the lowest energy state for the atom.
• Better symmetry of the electron distribution maximizes repulsion.”

By following Hund’s Rule, electrons enjoy a more balanced configuration, avoiding unnecessary electron pair repulsion immediately.

Pauli-Exclusion Principle

The Pauli-Exclusion Principle is fundamental in ensuring that no two electrons in an atom have identical sets of quantum numbers. It highlights the unique place every electron occupies. According to this principle, each orbital holds a maximum of two electrons, but these must have opposite spins.
This basic rule emphasizes a unique quantum identity for each electron and explains the variety in electron configurations.

• Only two electrons can occupy a single orbital.
• These occupants must differ by having opposite spins.
• Ensures all electrons in an atom have distinctive characteristics.

Understanding this principle reinforces why electrons within the same orbital exhibit opposite spins, playing a vital role in predicting how elements interact at an atomic level.