A : `K_(4)[Fe(CN)_(6)]` and `K_(3) [Fe(CN)_(6)]` have different magnetic moment..
R: Magnetic moment is decided by the number of unpaired electron and both have different number of unpaired electrons.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided in the question regarding the coordination compounds \( K_4[Fe(CN)_6] \) and \( K_3[Fe(CN)_6] \).

### Step 1: Analyze the Assertion
The assertion states that \( K_4[Fe(CN)_6] \) and \( K_3[Fe(CN)_6] \) have different magnetic moments.

1. **Determine the oxidation state of iron in \( K_4[Fe(CN)_6] \)**:
- The complex ion has a charge of -4 (from 4 K\(^+\) ions).
- Let the oxidation state of Fe be \( x \).
- The equation becomes:
\[ x + 6(-1) = -4 \implies x - 6 = -4 \implies x = +2 \]
- Thus, Fe is in the +2 oxidation state.

2. **Electron configuration of \( Fe^{2+} \)**:
- The electron configuration of Fe is \( [Ar] 3d^6 4s^2 \).
- For \( Fe^{2+} \), it loses 2 electrons (from 4s), leading to:
\[ [Ar] 3d^6 4s^0 \]

3. **Determine the number of unpaired electrons**:
- In the presence of strong field ligands (like CN\(^-\)), the electrons will pair up.
- The configuration will be \( (↑↓)(↑↓)(↑↓)(↑)(↑) \) in the 3d subshell.
- Therefore, there are **0 unpaired electrons**.

4. **Magnetic moment calculation**:
- The magnetic moment \( \mu \) is calculated using the formula:
\[ \mu = \sqrt{n(n+2)} \]
- Where \( n \) is the number of unpaired electrons. Here, \( n = 0 \):
\[ \mu = \sqrt{0(0+2)} = 0 \text{ Bohr magneton} \]

### Step 2: Analyze the Second Coordination Compound
Now, we analyze \( K_3[Fe(CN)_6] \).

1. **Determine the oxidation state of iron in \( K_3[Fe(CN)_6] \)**:
- The complex ion has a charge of -3 (from 3 K\(^+\) ions).
- Let the oxidation state of Fe be \( x \).
- The equation becomes:
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]
- Thus, Fe is in the +3 oxidation state.

2. **Electron configuration of \( Fe^{3+} \)**:
- The electron configuration of Fe is \( [Ar] 3d^6 4s^2 \).
- For \( Fe^{3+} \), it loses 3 electrons (2 from 4s and 1 from 3d), leading to:
\[ [Ar] 3d^5 4s^0 \]

3. **Determine the number of unpaired electrons**:
- In the presence of strong field ligands (like CN\(^-\)), the electrons will also pair up.
- The configuration will be \( (↑)(↑)(↑)(↑)(↑) \) in the 3d subshell.
- Therefore, there is **1 unpaired electron**.

4. **Magnetic moment calculation**:
- Using the formula:
\[ \mu = \sqrt{n(n+2)} \]
- Where \( n = 1 \):
\[ \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \text{ Bohr magneton} \]

### Conclusion
- \( K_4[Fe(CN)_6] \) has a magnetic moment of 0 Bohr magneton (diamagnetic) due to 0 unpaired electrons.
- \( K_3[Fe(CN)_6] \) has a magnetic moment of approximately 1.73 Bohr magneton (paramagnetic) due to 1 unpaired electron.
- Therefore, the assertion is true, and the reason is also true, as it correctly explains the assertion.

### Final Answer
The correct option is **1**: Both assertion and reason are true, and the reason is the correct explanation of the assertion.