The electronic configuration of carbon is `1s^(2) 2s^(2) 2p^(2)`.
There are 12 electrons in `C_(2)` . The correct electronic configuration of `C_(2)` molecule is

Options

A. `(sigma1s^(2))(sigma^(**)1s^(2))(sigma2s^(2))(sigma^(**)2s^(2))(sigma2p_(z)^(2))(pi2p_(x)^(2))`
B. `(sigma1s^(2))(sigma^(**)1s^(2))(sigma2s^(2))(sigma^(**)2s^(2))(pi2p_(x)^(2)=pi2p_(y)^(2))`
C. `(sigma1s^(2))(sigma^(**)1s^(2))(sigma2s^(2))(sigma^(**)2s^(2))(sigma2p_(z)^(2))(pi2p_(x)^(1)=pi2p_(y)^(1))`
D. `(sigma1s^(2))(sigma^(**)1s^(2))(sigma2s^(2))(sigma^(**)2s^(2))(pi2p_(x)^(2)=pi2p_(y)^(1))`

Explanation

To determine the electronic configuration of the C2 molecule, we will follow the steps outlined below:

### Step 1: Determine the Total Number of Electrons
The C2 molecule consists of two carbon atoms. Each carbon atom has 6 electrons, giving a total of:
\[ \text{Total electrons in C}_2 = 6 \text{ (from first C)} + 6 \text{ (from second C)} = 12 \text{ electrons} \]

### Step 2: Use Molecular Orbital Theory (MOT)
According to Molecular Orbital Theory, we will fill the molecular orbitals based on their energy levels. The order of filling for diatomic molecules like C2 is as follows:
1. σ(1s)
2. σ*(1s)
3. σ(2s)
4. σ*(2s)
5. π(2p_x), π(2p_y)
6. σ(2p_z)
7. π*(2p_x), π*(2p_y)
8. σ*(2p_z)

### Step 3: Fill the Molecular Orbitals
1. **1s Orbitals**:
- 2 electrons in σ(1s)
- 2 electrons in σ*(1s)

Configuration so far:
\[ \sigma(1s)^2 \sigma^*(1s)^2 \]

2. **2s Orbitals**:
- 2 electrons in σ(2s)
- 2 electrons in σ*(2s)

Configuration so far:
\[ \sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \]

3. **2p Orbitals**:
- There are 4 electrons to place in the 2p orbitals. According to Hund's rule, we will fill the degenerate orbitals (π(2p_x) and π(2p_y)) first before pairing them.
- 2 electrons will go into π(2p_x) and 2 electrons will go into π(2p_y).

Final configuration:
\[ \sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2 \]

### Step 4: Write the Complete Electronic Configuration
The complete electronic configuration of the C2 molecule is:
\[ \sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2 \]

### Conclusion
Thus, the correct electronic configuration of the C2 molecule is:
\[ \sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2 \]