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 Total Number of Electrons
The atomic number of carbon (C) is 6, which means each carbon atom has 6 electrons. Since C₂ has two carbon atoms, the total number of electrons in C₂ is:
\[ \text{Total electrons} = 2 \times 6 = 12 \]

### Step 2: Write the Molecular Orbital Configuration
According to molecular orbital theory, the molecular orbitals for C₂ are filled in the following order:
1. σ1s
2. σ*1s
3. σ2s
4. σ*2s
5. π2px
6. π2py
7. σ2pz
8. π*2px
9. π*2py
10. σ*2pz

For C₂, the molecular orbital filling will be:
- σ1s: 2 electrons
- σ*1s: 0 electrons
- σ2s: 2 electrons
- σ*2s: 0 electrons
- π2px: 2 electrons
- π2py: 2 electrons
- σ2pz: 2 electrons
- π*2px: 0 electrons
- π*2py: 0 electrons
- σ*2pz: 0 electrons

### Step 3: Fill the Molecular Orbitals
Now, we fill the molecular orbitals with the 12 electrons:
- σ1s (2)
- σ*1s (0)
- σ2s (2)
- σ*2s (0)
- π2px (2)
- π2py (2)
- σ2pz (2)
- π*2px (0)
- π*2py (0)
- σ*2pz (0)

### Step 4: Identify the Completely Filled π Molecular Orbitals
From the filling, we can see that:
- π2px is filled with 2 electrons (completely filled)
- π2py is filled with 2 electrons (completely filled)

Thus, there are a total of **2 completely filled π molecular orbitals** in the ground state of C₂.

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

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