STATEMENT-1: Fe-CN bond length is smaller in `Fe(CN)_(6)^(-4)` than `Fe(CN)_(6)^(-3)`
and
STATEMENT-2: `Fe(CN)_(6)^(-3)` is more stable than `Fe(CN)_(6)^(-4)`

Options

A. Statement-1 is True , Statement-2 is True , Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True , Statement-2 is True , Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To analyze the statements given in the question, we can break down the problem step by step.

### Step 1: Determine the oxidation states of iron in both complexes.

For the complex \( \text{Fe(CN)}_6^{4-} \):
- Let the oxidation state of Fe be \( x \).
- The CN ligand has a charge of -1, and there are 6 CN ligands, so the total contribution from CN is \( 6 \times (-1) = -6 \).
- The overall charge of the complex is -4.

Setting up the equation:
\[ x + (-6) = -4 \implies x - 6 = -4 \implies x = +2 \]

For the complex \( \text{Fe(CN)}_6^{3-} \):
- Again, let the oxidation state of Fe be \( x \).
- The total contribution from CN is still \( 6 \times (-1) = -6 \).
- The overall charge of the complex is -3.

Setting up the equation:
\[ x + (-6) = -3 \implies x - 6 = -3 \implies x = +3 \]

### Step 2: Compare the oxidation states.

From the calculations:
- In \( \text{Fe(CN)}_6^{4-} \), the oxidation state of Fe is +2.
- In \( \text{Fe(CN)}_6^{3-} \), the oxidation state of Fe is +3.

### Step 3: Analyze the bond lengths.

Higher oxidation states typically lead to stronger metal-ligand bonds due to increased positive charge on the metal ion, which attracts the negatively charged ligands more strongly. Therefore:
- The bond length in \( \text{Fe(CN)}_6^{4-} \) (Fe at +2) is expected to be longer than in \( \text{Fe(CN)}_6^{3-} \) (Fe at +3) because the bond is weaker in the lower oxidation state.

### Step 4: Stability of the complexes.

Generally, complexes with higher oxidation states are more stable due to stronger metal-ligand interactions. Therefore:
- \( \text{Fe(CN)}_6^{3-} \) (Fe at +3) is more stable than \( \text{Fe(CN)}_6^{4-} \) (Fe at +2).

### Conclusion:

- **Statement 1**: "Fe-CN bond length is smaller in \( \text{Fe(CN)}_6^{4-} \) than \( \text{Fe(CN)}_6^{3-} \)" is **False**.
- **Statement 2**: "\( \text{Fe(CN)}_6^{3-} \) is more stable than \( \text{Fe(CN)}_6^{4-} \)" is **True**.

Thus, the correct answer is that Statement 1 is false, and Statement 2 is true.