The number of completely filled `pi` molecular orbitals in ground state of `C_(2)` is________.

Explanation

To determine the number of completely filled π molecular orbitals in the ground state of the C₂ molecule, we can follow these steps:

### Step 1: Determine the number of electrons in C₂
Each carbon atom has 6 electrons. Therefore, for the C₂ molecule:
\[ \text{Total electrons in C₂} = 2 \times 6 = 12 \text{ electrons} \]

### Step 2: Understand the molecular orbital (MO) configuration
The molecular orbital configuration for C₂ can be represented as follows:
1. σ1s
2. σ*1s
3. σ2s
4. σ*2s
5. π2px
6. π2py
7. σ2pz

The order of filling the molecular orbitals is based on their energy levels, and for C₂, the relevant orbitals are filled in the following order:
- σ1s (2 electrons)
- σ*1s (2 electrons)
- σ2s (2 electrons)
- σ*2s (2 electrons)
- π2px (2 electrons)
- π2py (2 electrons)

### Step 3: Fill the molecular orbitals with the electrons
Now, we fill the molecular orbitals with the 12 electrons:
- σ1s: 2 electrons (filled)
- σ*1s: 2 electrons (filled)
- σ2s: 2 electrons (filled)
- σ*2s: 2 electrons (filled)
- π2px: 2 electrons (filled)
- π2py: 2 electrons (filled)

### Step 4: Identify the completely filled π molecular orbitals
From the filling, we see that both π2px and π2py are completely filled with 2 electrons each.

### Conclusion
Thus, the number of completely filled π molecular orbitals in the ground state of C₂ is:
\[ \text{Number of completely filled } \pi \text{ molecular orbitals} = 2 \]

### Final Answer
The number of completely filled π molecular orbitals in the ground state of C₂ is **2**.

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