Assertion-The free gaseous `Cr` atom has six unpaired electrons.
Reason-Half-filled s-orbital has greater stability.

Options

A. If both assertion and reason are true and reason is the explaination of assertion.
B. If both assertion and reason are true but reason is not the correct explaination of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-step Solution:

1. **Understanding the Assertion**:
- The assertion states that the free gaseous chromium (Cr) atom has six unpaired electrons.
- To verify this, we need to look at the electronic configuration of chromium.

2. **Finding the Electronic Configuration of Chromium**:
- The atomic number of chromium (Cr) is 24.
- The expected electronic configuration based on the Aufbau principle would be:
\[ \text{Cr: } [\text{Ar}] 4s^2 3d^4 \]
- However, chromium is an exception to the expected configuration due to stability reasons. The actual electronic configuration is:
\[ \text{Cr: } [\text{Ar}] 4s^1 3d^5 \]
- This configuration shows that one electron from the 4s subshell has been promoted to the 3d subshell to achieve a half-filled d-subshell.

3. **Counting Unpaired Electrons**:
- In the configuration \(4s^1 3d^5\):
- The \(4s\) subshell has 1 unpaired electron.
- The \(3d\) subshell has 5 unpaired electrons (since all five d-orbitals can hold one electron each before pairing).
- Therefore, the total number of unpaired electrons in chromium is:
\[ 1 \text{ (from } 4s\text{)} + 5 \text{ (from } 3d\text{)} = 6 \text{ unpaired electrons} \]
- This confirms that the assertion is true.

4. **Understanding the Reason**:
- The reason states that a half-filled s-orbital has greater stability.
- In reality, half-filled orbitals (like \(3d^5\)) are indeed more stable due to symmetry and exchange energy, but the 4s orbital is not half-filled in chromium. It has only one electron, which does not confer the same level of stability as a half-filled orbital.

5. **Evaluating the Assertion and Reason**:
- The assertion is true (Cr has 6 unpaired electrons).
- The reason is false (it incorrectly states that half-filled s-orbitals are more stable, while it's actually the half-filled d-orbitals that confer stability).
- Thus, the correct conclusion is that the assertion is true, but the reason is false.

### Final Conclusion:
The correct option is **C**: Assertion is true, but the reason is false.

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