The most stable complex among the following is

Options

A. `[Pd(CN)_(4)]^(4-)`
B. `[Pd(CN)_(4)]^(3-)`
C. `[Ni(CN)_(4)]^(4-)`
D. `[Ni(CN)_(4)]^(3-)`

Explanation

To determine the most stable coordination complex among the given options, we can follow these steps:

### Step 1: Identify the Coordination Complexes
First, we need to identify the coordination complexes provided in the question. Let's assume the complexes are:
1. \( \text{Pd(CN)}_4^{2-} \)
2. \( \text{Ni(CN)}_4^{2-} \)
3. \( \text{Pd(CN)}_4^{3-} \)
4. \( \text{Ni(CN)}_4^{3-} \)

### Step 2: Determine the Oxidation States
Next, we calculate the oxidation states of the central metal in each complex:
- For \( \text{Pd(CN)}_4^{2-} \):
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- For \( \text{Ni(CN)}_4^{2-} \):
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- For \( \text{Pd(CN)}_4^{3-} \):
\[ x + 4(-1) = -3 \implies x - 4 = -3 \implies x = +1 \]
- For \( \text{Ni(CN)}_4^{3-} \):
\[ x + 4(-1) = -3 \implies x - 4 = -3 \implies x = +1 \]

### Step 3: Analyze the Charge on the Central Metal Atom
From the calculations:
- \( \text{Pd(CN)}_4^{2-} \) has \( \text{Pd}^{+2} \)
- \( \text{Ni(CN)}_4^{2-} \) has \( \text{Ni}^{+2} \)
- \( \text{Pd(CN)}_4^{3-} \) has \( \text{Pd}^{+1} \)
- \( \text{Ni(CN)}_4^{3-} \) has \( \text{Ni}^{+1} \)

### Step 4: Compare Stability Based on Charge
The stability of coordination complexes generally increases with the positive charge on the central metal atom. Therefore:
- \( \text{Pd(CN)}_4^{2-} \) and \( \text{Ni(CN)}_4^{2-} \) (both +2 charge) are more stable than \( \text{Pd(CN)}_4^{3-} \) and \( \text{Ni(CN)}_4^{3-} \) (both +1 charge).

### Step 5: Compare the Position in the Transition Series
Next, we compare the position of the metals in the periodic table:
- Palladium (Pd) is in the 4D transition series.
- Nickel (Ni) is in the 3D transition series.

As we move from 3D to 4D, the stability of the complexes increases. Thus:
- \( \text{Pd(CN)}_4^{2-} \) (4D) will be more stable than \( \text{Ni(CN)}_4^{2-} \) (3D).

### Conclusion
Based on the analysis of oxidation states, charge, and position in the transition series, the most stable complex among the given options is:
**Option B: \( \text{Pd(CN)}_4^{2-} \)**.

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