How many carbon atoms lie in a plane in `[Ni(dmg)_(2)]`?

Options

A. 8
B. 4
C. 6
D. none of these

Explanation

To determine how many carbon atoms lie in a plane in the coordination complex `[Ni(dmg)_(2)]`, we can follow these steps:

### Step 1: Understand the Structure of the Complex
The complex `[Ni(dmg)_(2)]` consists of nickel (Ni) and two dimethylglyoxime (dmg) ligands. Each dimethylglyoxime ligand has a specific structure that includes carbon (C), nitrogen (N), and oxygen (O) atoms.

### Step 2: Identify the Dimethylglyoxime Structure
The structure of dimethylglyoxime can be represented as:
```
CH3
|
C=C
|
CH3
```
In this structure, there are two carbon atoms involved in the double bond (C=C) and two methyl (CH3) groups, making a total of 4 carbon atoms per dimethylglyoxime ligand.

### Step 3: Count the Total Number of Carbon Atoms
Since there are two dimethylglyoxime ligands in the complex, we multiply the number of carbon atoms in one ligand by two:
- 4 carbons per ligand × 2 ligands = 8 carbon atoms in total.

### Step 4: Determine the Hybridization of Carbon Atoms
In the dimethylglyoxime structure:
- The two carbon atoms involved in the C=C double bond are sp² hybridized.
- The two methyl (CH3) carbon atoms are sp³ hybridized.

### Step 5: Identify the Planar Carbons
- The sp² hybridized carbon atoms (the two from the double bond) lie in the same plane.
- The sp³ hybridized carbon atoms (the two CH3 groups) are also in the same plane due to their connection to the double bond.

### Conclusion
Thus, all 8 carbon atoms (4 from each dimethylglyoxime ligand) lie in the same plane in the `[Ni(dmg)_(2)]` complex.

### Final Answer
The total number of carbon atoms that lie in a plane in `[Ni(dmg)_(2)]` is **8**.

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