Problem 9 - A Complete Resource Book in Chemistry for JEE Main

Question

Chromium is represented by the electronic configuration (a) \([\mathrm{Ne}] 3 \mathrm{~s}^{2} 3 \mathrm{p}^{6} 3 \mathrm{~d}^{1} 4 \mathrm{~s}^{2}\) (b) \([\mathrm{Ne}] 3 \mathrm{~s}^{2} 3 p^{6} 3 \mathrm{~d}^{2} 4 \mathrm{~s}^{1}\) (c) \([\mathrm{Ne}] 3 \mathrm{~s}^{2} 3 \mathrm{p}^{6} 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) (d) \([\mathrm{Ne}] 3 \mathrm{~s}^{2} 3 \mathrm{p}^{6} 4 \mathrm{~s}^{2} 3 \mathrm{~d}^{4}\)

Step-by-Step Solution

Answer

The correct electronic configuration for chromium is given in option (c).

Step 1: Understand Chromium's Electron Count

First, find the atomic number of chromium, which is 24. This means chromium has 24 electrons, which we need to distribute into its atomic orbitals according to the order of filling.

Step 2: Recall Electron Configuration Order

Recall that electrons fill orbitals in order of increasing energy level: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc. This ordering is determined by the Aufbau principle.

Step 3: Apply Aufbau Principle for Chromium

Begin filling orbitals for chromium: \[1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^4\]This arrangement, however, is not the ground state configuration. For stability, one electron from the 4s orbital is transferred to the 3d orbital, due to the proximity in energy levels.

Step 4: Chromium's Actual Ground State Configuration

Chromium's electrons are rearranged to maximize stability, resulting in the unique configuration: \[[Ar] 3d^5 4s^1\]This configuration achieves half-filled d-orbitals, which is a stable arrangement.

Step 5: Identify the Correct Configuration

Compare the given configurations with the actual configuration of chromium:- Option (a): \([\mathrm{Ne}] 3s^2 3p^6 3d^1 4s^2\) - Option (b): \([\mathrm{Ne}] 3s^2 3p^6 3d^2 4s^1\) - **Option (c)**: \([\mathrm{Ne}] 3s^2 3p^6 3d^5 4s^1\) - This matches.- Option (d): \([\mathrm{Ne}] 3s^2 3p^6 4s^2 3d^4\)Thus, the correct configuration is option (c).

Key Concepts

Atomic Orbitals

Understanding atomic orbitals is crucial for exploring electron configurations. An atomic orbital is a region in an atom where there's a high probability of finding electrons. These orbitals are described in terms of energy levels and shapes, determined by the three quantum numbers: principal, angular momentum, and magnetic.
- **Principal Quantum Number ( ):** Indicates the main energy level. Larger values of correspond to orbitals that are farther from the nucleus.
- **Angular Momentum Quantum Number ( ):** Relates to the shape of the orbital. For instance, s-orbitals are spherical, p-orbitals are dumbbell-shaped, and d-orbitals are more complex.
- **Magnetic Quantum Number ( ):** Specifies the orientation of the orbital.
Each orbital can hold a maximum of two electrons with opposite spins. It's important to note that the type of orbital (s, p, d, f) affects how electrons fill up an atom, which is elaborated in the next sections.

Aufbau Principle

The Aufbau Principle is a fundamental concept guiding the electron configuration process. It states that electrons fill atomic orbitals in increasing order of their energy levels. This helps predict how electrons arrange themselves in an atom. When applying the Aufbau Principle, electrons start filling from the lowest possible energy level to the higher ones.
A simple way to determine the filling order under the Aufbau Principle is to remember the sequence: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on. In this sequence, the 4s subshell is filled before the 3d subshell due to its slightly lower energy. However, in certain atoms like Chromium, the electron configuration deviates slightly from the expected order to achieve greater stability, which is also influenced by Hund’s Rule and the Pauli Exclusion Principle.
The principle aids in systematically arranging electrons, ensuring better comprehension of an element's chemical properties.

Ground State Configuration

The ground state configuration of an atom is the most stable arrangement of its electrons. In this state, electrons are arranged in the lowest possible energy levels, adhering to the Pauli Exclusion Principle and Hund’s Rule for added stability. For Chromium, the ground state configuration is .
One unique feature of Chromium is its electron configuration doesn't follow the expected order as outlined by the Aufbau Principle. Typically, you'd expect , but Chromium has a special configuration: , where a 4s electron shifts to the 3d subshell.
This results in a half-filled d subshell, leading to extra stability due to exchange energy. Such configurations may appear puzzling initially, but they are significant for understanding exceptions in electron filling sequences.

Electron Filling Order

The order in which electrons fill atomic orbitals is crucial for determining an atom's electron configuration. This order relies heavily on the energy levels of the orbitals. Generally, orbitals are filled from the lowest to the highest energy level.
Yet, there can be exceptions due to the stability gained from specific electron arrangements, such as half-filled or fully filled subshells. For instance, despite the 3d orbital having a higher principal quantum number, its energy is slightly higher than 4s, which is why it fills after 4s according to the general rule. However, stability is further enhanced when d orbitals reach half or complete filling, as observed in Chromium.
This distinctive electron arrangement is why Chromium's electron configuration appears out of the usual order, shifting an electron from the 4s to the 3d subshell to achieve a half-filled state. Understanding this order aids in comprehending both the predicted and observed configurations, providing richer insights into electron distribution.