Choose the correct option regarding the following complex compound which follwos (F) and does not follow (NF) the Sidgwick EAN rule:
(I) `[Ph_(3)P)_(2)PdCl_(2)PdCl_(2)]`
(II) `[NiBrCl(en)]`
(III) `Na_(4)[Fe(CN)_(5)NOS]`
(IV) `Cr(CO)_(3)(NO)_(2)`

Options

A. (I)-NF,(II)-NF,(III)-NF,(IV)-NF
B. (I)-F,(II)-F,(III)-NF,(IV)-F
C. (I)-NF,(II)-NF,(III)-F,(IV)-F
D. (I)-NF,(II)-NF,(III)-F,(IV)-NF

Explanation

To determine which of the given complexes follow or do not follow the Sidgwick EAN rule, we will calculate the Effective Atomic Number (EAN) for each complex. The EAN is calculated using the formula:

\[ \text{EAN} = Z - O + L \]

Where:
- \( Z \) = Atomic number of the central metal atom
- \( O \) = Oxidation state of the metal
- \( L \) = Contribution from ligands (each ligand contributes based on its electron donation capacity)

Let's analyze each complex step by step.

### Step 1: Analyze Complex (I) `[Ph3P)2PdCl2]`

1. **Identify the central metal and its atomic number:**
- Palladium (Pd) has an atomic number \( Z = 46 \).

2. **Determine the oxidation state (O):**
- Let the oxidation state be \( x \).
- The contribution from two Cl ligands (each -1) is -2.
- The neutral ligand (PPh3) contributes 0.
- Overall charge = 0, so:
\[ x - 2 = 0 \Rightarrow x = +2 \]

3. **Calculate the contribution from ligands (L):**
- Each Cl contributes 2 electrons (2 Cl = 2 × 2 = 4).
- Each PPh3 contributes 2 electrons (2 PPh3 = 2 × 2 = 4).
- Total contribution from ligands = 4 + 4 = 8.

4. **Calculate EAN:**
\[ \text{EAN} = 46 - 2 + 8 = 52 \]

5. **Check against nearest noble gas atomic number:**
- Nearest noble gas atomic number is 54 (Krypton).
- EAN = 52 does not equal 54, hence **does not follow (NF)**.

### Step 2: Analyze Complex (II) `[NiBrCl(en)]`

1. **Identify the central metal and its atomic number:**
- Nickel (Ni) has an atomic number \( Z = 28 \).

2. **Determine the oxidation state (O):**
- Let the oxidation state be \( x \).
- Contribution from two Br ligands (-1 each) is -2.
- The neutral ligand (en) contributes 0.
- Overall charge = 0, so:
\[ x - 2 = 0 \Rightarrow x = +2 \]

3. **Calculate the contribution from ligands (L):**
- Each Br contributes 2 electrons (2 Br = 2 × 2 = 4).
- The bidentate ligand (en) contributes 4 electrons.
- Total contribution from ligands = 4 + 4 = 8.

4. **Calculate EAN:**
\[ \text{EAN} = 28 - 2 + 8 = 34 \]

5. **Check against nearest noble gas atomic number:**
- Nearest noble gas atomic number is 36 (Krypton).
- EAN = 34 does not equal 36, hence **does not follow (NF)**.

### Step 3: Analyze Complex (III) `Na4[Fe(CN)5NOS]`

1. **Identify the central metal and its atomic number:**
- Iron (Fe) has an atomic number \( Z = 26 \).

2. **Determine the oxidation state (O):**
- Let the oxidation state be \( x \).
- Contribution from five CN ligands (-1 each) is -5.
- The neutral ligands (NOS) contribute 0.
- Overall charge = -3 (from Na4), so:
\[ x - 5 = -3 \Rightarrow x = +2 \]

3. **Calculate the contribution from ligands (L):**
- Each CN contributes 2 electrons (5 CN = 5 × 2 = 10).
- NOS contributes 2 electrons.
- Total contribution from ligands = 10 + 2 = 12.

4. **Calculate EAN:**
\[ \text{EAN} = 26 - 2 + 12 = 36 \]

5. **Check against nearest noble gas atomic number:**
- Nearest noble gas atomic number is 36 (Krypton).
- EAN = 36 equals 36, hence **follows (F)**.

### Step 4: Analyze Complex (IV) `Cr(CO)3(NO)2`

1. **Identify the central metal and its atomic number:**
- Chromium (Cr) has an atomic number \( Z = 24 \).

2. **Determine the oxidation state (O):**
- Let the oxidation state be \( x \).
- The neutral ligands (CO and NO) contribute 0.
- Overall charge = 0, so:
\[ x = 0 \]

3. **Calculate the contribution from ligands (L):**
- Each CO contributes 2 electrons (3 CO = 3 × 2 = 6).
- Each NO contributes 3 electrons (2 NO = 2 × 3 = 6).
- Total contribution from ligands = 6 + 6 = 12.

4. **Calculate EAN:**
\[ \text{EAN} = 24 - 0 + 12 = 36 \]

5. **Check against nearest noble gas atomic number:**
- Nearest noble gas atomic number is 36 (Krypton).
- EAN = 36 equals 36, hence **follows (F)**.

### Summary of Results:
- Complex (I): NF
- Complex (II): NF
- Complex (III): F
- Complex (IV): F

### Final Answer:
- The complexes that follow the Sidgwick EAN rule are (III) and (IV), while (I) and (II) do not follow.