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

The correct ground state electronic configuration for Z = 24 is \\([\text{Ar}]3d^{5}4s^1\\).

Step 1: Understand the Problem

We need to determine the correct ground state electronic configuration for the element with atomic number Z = 24. Atomic number corresponds to the number of electrons in a neutral atom, so we need to distribute 24 electrons according to the electronic configuration rules.

Step 2: Identify Element and Reference Configuration

For atomic number Z = 24, the element is Chromium (Cr). The closest noble gas preceding Chromium is Argon (Ar), with the electronic configuration \([\text{Ar}]3d^{10}4s^2\). We start with this noble gas core before adding any more electrons.

Step 3: Apply Aufbau Principle

According to the Aufbau principle, electrons are added to the lowest energy orbitals first. The order of filling after \([\text{Ar}]\) is 3d and then 4s. However, due to electron-electron interactions and stability considerations, sometimes there are exceptions to this rule.

Step 4: Recognize Chromium Exception

For Chromium, there is an exception to the standard filling order. Chromium (Cr) does not fill its 3d orbital as \([\text{Ar}]3d^{4}4s^2\) but instead fills as \([\text{Ar}]3d^{5}4s^1\). The reason is energetic stability gained by having a half-filled 3d subshell, which makes this configuration lower in energy.

Step 5: Verify Configuration

Among the given options, \([\text{Ar}]3d^{5}4s^1\) matches the known exception for Chromium's electronic configuration. This confirms it as the correct ground state configuration for Z = 24.

Key Concepts

Chromium Configuration

Chromium (Cr), with the atomic number 24, has a unique electronic configuration that diverges from the expected pattern. Normally, you'd anticipate it to follow the pattern of filling orbitals from lowest to highest energy with electrons. This would suggest a configuration of

• \( [\text{Ar}] 3d^{4} 4s^{2} \)

However, Chromium actually follows a special rule, resulting in

• \( [\text{Ar}] 3d^{5} 4s^{1} \)

This happens because Chromium gains additional stability from a half-filled 3d subshell. Deviating from the norm allows it to achieve a more stable electron arrangement, benefiting from the symmetric electron distribution and reduced electron repulsion.

Aufbau Principle

The Aufbau Principle guides us in determining the order in which electrons fill the atomic orbitals. According to this principle, electrons will first occupy the lowest available energy orbital. Typically, we follow a specific sequence to fill shells:

• 3d before the 4s, after filling the 3p orbital from Argon \([\text{Ar}]\)

Yet, the principle comes with exceptions. One such exception is the configuration of Chromium, where the 3d and 4s orbitals don't follow the expected order due to multiple factors, including energy preferences concerning electron interactions.
The principle serves as a flexible but often reliable guideline for electron configuration.

Electron Stability

Electron stability in atoms is a key concept to understand electron configuration exceptions. Electrons within an atom aim to be in the most stable configuration with the lowest energy. In Chromium, having five electrons in the 3d orbital \( (3d^{5}) \) leads to a very stable half-filled state. This state is preferable over strictly following the predicted order.

What makes a half-filled subshell particularly stable? Ul>

The symmetry in the half-filled configuration 

Decreased electron-electron repulsions

Enhanced exchange energy due to parallel spins

These factors collectively lower the total energy of the atom, making the half-filled arrangement more stable and energetically favorable.

Periodic Table Trends

The periodic table is an excellent tool for predicting electron configurations and understanding atom behavior. Atomic elements are organized in a manner that reflects the repeating pattern of electron filling. However, trends in the table sometimes have exceptions.

Take chromium's electron configuration, for example, which represents an anomaly. Such anomalies occur to maximize stability or due to specific interactions among electrons. When examining these trends, we observe:

• Horizontal rows (periods) helping infer electron shells filling up
• Vertical columns (groups) showing elements with similar chemical properties

While these trends are invaluable, knowing that exceptions can occur helps in understanding the dynamic nature of electron configurations across the periodic table.