Electronic Configuration of Chromium (Cr)

Let's determine the electronic configuration of Chromium (Cr). Chromium is the element with atomic number 24. According to the Aufbau principle, electrons fill atomic orbitals in order of increasing energy. The expected electronic configuration for an element with 24 electrons would follow the pattern:

\(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^4\)

The part \(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6\) represents the electronic configuration of the noble gas Argon ([Ar]). So the expected configuration is \([\text{Ar}] \text{4s}^2 \text{3d}^4\). However, Chromium (Cr) is a notable exception to this rule.

The actual observed electronic configuration for Chromium is due to the extra stability associated with half-filled and completely filled d-orbitals. A half-filled 3d subshell (\(\text{3d}^5\)) is more stable than a \(\text{3d}^4\) configuration. To achieve this stability, one electron from the 4s orbital shifts to the 3d orbital.

Therefore, the actual electronic configuration of Chromium is:

\(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{3d}^5 \text{4s}^1\)

Using the noble gas configuration for Argon ([Ar]), this can be written as \([\text{Ar}] \text{3d}^5 \text{4s}^1\).

Now let's look at the given options:

• Option 1: \(\text{3s}^2\text{3p}^6\text{3d}^4\text{4s}^2\) - This represents \([\text{Ar}] \text{3d}^4 \text{4s}^2\). This is the expected configuration but not the actual stable one.
• Option 2: \(\text{3s}^2\text{3p}^6\text{3d}^5\text{4s}^1\) - This represents \([\text{Ar}] \text{3d}^5 \text{4s}^1\). This is the correct and stable electronic configuration for Chromium.
• Option 3: \(\text{3s}^2\text{3p}^6\text{3d}^6\) - This represents \([\text{Ar}] \text{3d}^6\). This configuration does not account for the 4s electrons and is incorrect for neutral Chromium.

Comparing the actual configuration \(\text{3s}^2\text{3p}^6\text{3d}^5\text{4s}^1\) with the options, Option 2 matches the correct electronic configuration of Cr.