Which of the follownig complexes have a maximum number of unpaired electrons?

Options

A. `[Ni(CN)_(4)]`
B. `[Co(NH_(3))_(4)(NO_(2))_(2)]^(+)`
C. `[Ag(CN)_(2)]^(-)`
D. `[CuBr_(4)]^(2-)`

Explanation

To determine which of the given complexes has the maximum number of unpaired electrons, we will follow these steps:

### Step 1: Identify the complexes and their oxidation states
We will analyze the oxidation states of the metals in each complex.

1. **Ni(CN)₄²⁻**:
- Let the oxidation state of Ni be \( x \).
- CN is a -1 charge, and there are 4 CN ligands.
- The equation is: \( x + 4(-1) = -2 \) (since the overall charge is -2).
- Solving gives \( x = +2 \).

2. **CuBr₄²⁻**:
- Let the oxidation state of Cu be \( x \).
- Br is -1 charge, and there are 4 Br ligands.
- The equation is: \( x + 4(-1) = -2 \).
- Solving gives \( x = +2 \).

3. **Ag(CN)₂⁻**:
- Let the oxidation state of Ag be \( x \).
- CN is -1 charge, and there are 2 CN ligands.
- The equation is: \( x + 2(-1) = -1 \).
- Solving gives \( x = +1 \).

4. **Co(NH₃)₆³⁺**:
- Let the oxidation state of Co be \( x \).
- NH₃ is neutral, and there are 6 NH₃ ligands.
- The equation is: \( x + 0 = +3 \).
- Solving gives \( x = +3 \).

### Step 2: Determine the electron configurations
Next, we will write the electron configurations for the metal ions in their respective oxidation states.

1. **Ni²⁺**:
- Atomic number of Ni = 28, configuration: [Ar] 4s² 3d⁸.
- For Ni²⁺: [Ar] 3d⁸ (4s is empty).

2. **Cu²⁺**:
- Atomic number of Cu = 29, configuration: [Ar] 4s¹ 3d¹⁰.
- For Cu²⁺: [Ar] 3d⁹ (4s is empty).

3. **Ag⁺**:
- Atomic number of Ag = 47, configuration: [Kr] 5s¹ 4d¹⁰.
- For Ag⁺: [Kr] 4d¹⁰ (5s is empty).

4. **Co³⁺**:
- Atomic number of Co = 27, configuration: [Ar] 4s² 3d⁷.
- For Co³⁺: [Ar] 3d⁶ (4s is empty).

### Step 3: Determine the number of unpaired electrons
Now we will determine the number of unpaired electrons in each complex based on the electron configurations.

1. **Ni²⁺ (3d⁸)**:
- The 3d subshell can hold 10 electrons. The configuration is:
- ↑↓ ↑↓ ↑↓ ↑ ↑ (paired electrons).
- **Unpaired electrons = 0**.

2. **Cu²⁺ (3d⁹)**:
- The configuration is:
- ↑↓ ↑↓ ↑↓ ↑ ↑ (1 unpaired electron).
- **Unpaired electrons = 1**.

3. **Ag⁺ (4d¹⁰)**:
- The configuration is:
- ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ (all paired).
- **Unpaired electrons = 0**.

4. **Co³⁺ (3d⁶)**:
- The configuration is:
- ↑↓ ↑↓ ↑ ↑ ↑ (paired electrons).
- **Unpaired electrons = 0**.

### Conclusion
The complex with the maximum number of unpaired electrons is **Cu²⁺** with **1 unpaired electron**.

### Final Answer
The complex with the maximum number of unpaired electrons is **CuBr₄²⁻**.

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