Remember key exceptions in electronic configuration:
Cr = [Ar] $3d^5\,4s^1$
Cu = [Ar] $3d^{10}\,4s^1$
They occur due to extra stability of half-filled and fully filled $d$ subshells.
The question asks for the electronic configuration of chromium. Let's analyze why the correct configuration is \([Ar]\,3d^5\,4s^1\).
Understanding Basic Principles:
Electronic configuration follows the Aufbau principle, Hund's rule, and the Pauli exclusion principle.
The usual order of filling is that electrons fill the \(4s\) orbital before the \(3d\) orbital due to their respective energy levels.
Expected Configuration for Chromium:
According to the typical filling order, we would expect chromium to have the configuration of \([Ar]\,3d^4\,4s^2\).
This is because argon (\([Ar]\)) accounts for the first 18 electrons. Chromium, which has 24 electrons, would then fill the next 6 electrons.
Actual Configuration:
Chromium has an electronic configuration of \([Ar]\,3d^5\,4s^1\).
This configuration is an exception to the typical filling order due to electron stability, with half-filled subshells being more stable due to symmetrical distribution.
Increased stability arises from minimized electron repulsions and exchange energy.
Analyzing the Options:
Option 1: \([Ar]\,3d^4\,4s^1\) - Incorrect. This configuration does not conform to the correct electron filling order considering chromium's known exceptions.
Option 2: \([Ar]\,3d^4\,4s^2\) - Incorrect. While this might be expected without exception, it doesn’t account for stability preferences.
Option 3: \([Ar]\,3d^5\,4s^1\) - Correct. This is the known stable electron configuration of chromium due to half-filled \(d\) subshell stability.
Option 4: \([Ar]\,3d^5\,4s^2\) - Incorrect. Chromium doesn't have enough electrons to fill this configuration.\
Conclusion: The electron configuration \([Ar]\,3d^5\,4s^1\) is the most stable configuration for chromium, conforming with known principles of electronic stability and exceptions.