Assertion : Magnetic moment of `Mn^(2+)` is less than `Cr^(2+)`
Reason: Higher the atomic number smaller is the magnetic moment.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason not is the correct explanation of assertion.
C. If assertion is trun 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 magnetic moment of \( \text{Mn}^{2+} \) is less than that of \( \text{Cr}^{2+} \).

2. **Determine the Electronic Configuration**:
- For \( \text{Mn}^{2+} \):
- Manganese (Mn) has an atomic number of 25. Its electronic configuration is \( [\text{Ar}] 4s^2 3d^5 \).
- In \( \text{Mn}^{2+} \), two electrons are removed from the \( 4s \) orbital, resulting in \( [\text{Ar}] 3d^5 \).
- This means \( \text{Mn}^{2+} \) has 5 unpaired electrons.

- For \( \text{Cr}^{2+} \):
- Chromium (Cr) has an atomic number of 24. Its electronic configuration is \( [\text{Ar}] 4s^1 3d^5 \).
- In \( \text{Cr}^{2+} \), one electron is removed from the \( 4s \) orbital and one from the \( 3d \) orbital, resulting in \( [\text{Ar}] 3d^4 \).
- This means \( \text{Cr}^{2+} \) has 4 unpaired electrons.

3. **Calculating the Magnetic Moment**:
- The formula for magnetic moment (\( \mu \)) is given by:
\[ \mu = \sqrt{n(n + 2)} \]
- For \( \text{Mn}^{2+} \) (5 unpaired electrons):
\[ \mu_{\text{Mn}^{2+}} = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \mu_B \]
- For \( \text{Cr}^{2+} \) (4 unpaired electrons):
\[ \mu_{\text{Cr}^{2+}} = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.90 \, \mu_B \]

4. **Comparing the Magnetic Moments**:
- From the calculations, we find that:
- \( \mu_{\text{Mn}^{2+}} \approx 5.92 \, \mu_B \)
- \( \mu_{\text{Cr}^{2+}} \approx 4.90 \, \mu_B \)
- Therefore, the assertion that \( \mu_{\text{Mn}^{2+}} < \mu_{\text{Cr}^{2+}} \) is **false**.

5. **Understanding the Reason**:
- The reason states that "higher the atomic number, smaller is the magnetic moment."
- This statement is also **false** because the magnetic moment depends on the number of unpaired electrons, not directly on the atomic number.

6. **Conclusion**:
- Both the assertion and the reason are false.

### Final Answer:
Both assertion and reason are false.