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

Question

The correct ground state electronic configuration for the atom \((\mathrm{Z}=24)\) is (a) \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) (b) \([\mathrm{Ar}] 3 \mathrm{~d}^{4} 4 \mathrm{~s}^{2}\) (c) \([\mathrm{Ar}] 3 \mathrm{~d}^{6} 4 \mathrm{~s}^{\circ}\) (d) \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{2}\)

Step-by-Step Solution

Answer

(a) \([\mathrm{Ar}] 3\mathrm{d}^{5} 4\mathrm{s}^{1}\) is correct for chromium.

Step 1: Identify the Element

Element with atomic number \(Z = 24\) is chromium (Cr). Thus, we're tasked to find the ground state electronic configuration for chromium.

Step 2: Recall the Configuration Order

The general order of filling of electrons is governed by the Aufbau principle, in which electrons fill the 4s orbital before the 3d orbital. For elements near chromium, occasionally 3d and 4s have mixed filling sequences due to stability reasons.

Step 3: Determine Stability of Configurations

Chromium is an exception to the expected filling order. The actual configuration is due to the half-filled 3d subshell which imparts extra stability. Thus, it's more stable for Cr to have a configuration where 3d subshell is half-filled \((3d^5)\) and 4s has one electron \((4s^1)\).

Step 4: Write the Correct Configuration

Considering the above information, the correct ground state electronic configuration for chromium \((Z=24)\) is \([\mathrm{Ar}] 3\mathrm{d}^5 4\mathrm{s}^1\).

Key Concepts

Aufbau Principle

The Aufbau Principle is a fundamental concept in chemistry that guides the electronic configuration of atoms. It suggests that electrons fill atomic orbitals in order of increasing energy levels. This principle helps us predict the distribution of electrons among different energy orbitals in an atom.
The order generally followed is:

• The lowest energy orbitals fill first before higher energy ones.
• Electrons fill the 1s orbital, then 2s, followed by 2p, 3s, and so on.

According to the Aufbau Principle, electrons should fill the 4s orbital before the 3d orbital. This is because 4s is slightly lower in energy than 3d for calcium and potassium. However, right around chromium, this sequence can get slightly altered.
In the case of transition metals, particularly chromium, the actual sequence deviates slightly. This deviation happens as a result of additional stability achieved by having a certain number of electrons in the 3d subshell. This principle is essential in understanding why certain elements, like chromium, have unique electron configurations that contribute to their chemical properties.

Chromium

Chromium, with atomic number 24, is an element known for its unique electronic configuration. Unlike most elements that follow the typical filling order predicted by the Aufbau Principle, chromium is an exception due to its inclination towards stability.
While you might expect chromium to have the configuration \([ ext{Ar}] 3d^4 4s^2\), which follows the order of filling 4s before 3d, this is not the case. Chromium actually has the electronic configuration \([ ext{Ar}] 3d^5 4s^1\). This is because the 3d subshell achieves a half-filled state, which provides additional stability and slightly lowers the energy of the electron arrangement.
This particular arrangement allows chromium to maintain a lower energy and more stable ground state than expected. Such exceptions illustrate the intricacies of atomic structure and show how stability factors can sometimes override general rules like the Aufbau Principle.

Ground State Stability

Atoms generally strive to reach a state of minimal energy, known as the ground state. The ground state configuration corresponds to the most stable electron arrangement that an atom can achieve. For chromium, achieving a half-filled 3d subshell lends significant stability to its ground state.
This half-filled stability is characterized by:

• Symmetrical electron distribution, which minimizes repulsion between electrons.
• Magnetic properties imparted by unpaired electrons in the 3d subshell.
• Lower total energy compared to other configurations.

The electron configuration \([ ext{Ar}] 3d^5 4s^1\) allows chromium to benefit from these attributes. Although it departs from what the Aufbau Principle might predict, this configuration exemplifies the importance of considering both electron repulsion and sub-energy levels stability. Understanding such exceptions is crucial for grasping fundamental concepts of electronic structures and their effects on an element's chemical behavior.