Which of the following are low spin complexes which follow `EAN` rule?

Options

A. `Cr(CO)_(6)`
B. `[Cr(CN)_(6)]^(4-)`
C. `PtCl_(6)^(2-)`
D. `[Cu(NH_(3))_(3)CO]^(o+)`

Explanation

To determine which of the complexes are low spin complexes that follow the Effective Atomic Number (EAN) rule, we will analyze each complex step by step.

### Step 1: Understand Low Spin Complexes
Low spin complexes are formed when there is strong field ligand present, which causes the electrons to pair up in the lower energy orbitals before occupying the higher energy orbitals. This results in a lower total spin state.

**Hint:** Identify the ligands in the complexes to determine if they are strong field ligands.

### Step 2: Understand the EAN Rule
The EAN rule states that the effective atomic number (EAN) of a complex is calculated using the formula:
\[ \text{EAN} = Z - \text{oxidation state} + 2 \times \text{number of unidentate ligands} \]
Where \( Z \) is the atomic number of the central metal atom.

**Hint:** Calculate the EAN for each complex using the above formula.

### Step 3: Analyze Each Complex

#### Complex 1: \( \text{Cr(CO)}_6 \)
1. **Identify the ligand:** CO is a strong field ligand.
2. **Determine oxidation state of Cr:** Since CO is neutral, oxidation state of Cr = 0.
3. **Calculate EAN:**
\[ \text{EAN} = 24 - 0 + 2 \times 6 = 36 \]
(36 is the atomic number of Kr, a noble gas).

**Conclusion:** This is a low spin complex and follows the EAN rule.

#### Complex 2: \( \text{Cr(CN)}_6^{4-} \)
1. **Identify the ligand:** CN is a strong field ligand.
2. **Determine oxidation state of Cr:**
\[ \text{Oxidation state} = +3 \quad (\text{since } 6 \times (-1) + x = -4 \Rightarrow x = +2) \]
3. **Calculate EAN:**
\[ \text{EAN} = 24 - 2 + 2 \times 6 = 34 \]
(34 is not the atomic number of a noble gas).

**Conclusion:** This is a low spin complex but does not follow the EAN rule.

#### Complex 3: \( \text{PtCl}_6^{2-} \)
1. **Identify the ligand:** Cl is a weak field ligand.
2. **Determine oxidation state of Pt:**
\[ \text{Oxidation state} = +4 \quad (\text{since } 6 \times (-1) + x = -2 \Rightarrow x = +4) \]
3. **Calculate EAN:**
\[ \text{EAN} = 78 - 4 + 2 \times 6 = 86 \]
(86 is the atomic number of Rn, a noble gas).

**Conclusion:** This complex follows the EAN rule but is a high spin complex.

#### Complex 4: \( \text{Cu(NH}_3)_4^{+} \)
1. **Identify the ligand:** NH3 is a strong field ligand.
2. **Determine oxidation state of Cu:**
\[ \text{Oxidation state} = +1 \quad (\text{since } 4 \times 0 + x = +1 \Rightarrow x = +1) \]
3. **Calculate EAN:**
\[ \text{EAN} = 29 - 1 + 2 \times 4 = 36 \]
(36 is the atomic number of Kr, a noble gas).

**Conclusion:** This complex follows the EAN rule but cannot be a low spin complex due to its tetrahedral geometry.

### Final Conclusion
The only complex that is both a low spin complex and follows the EAN rule is:
- **Complex 1: \( \text{Cr(CO)}_6 \)**