According to the molecular orbital theory which of the following statement is incorrect?
[LUMO = lowest unoccupied molecular orbital]

Options

A. LUMO level for `C_(2)` molecule is `sigma2p_x`orbital.
B. In `C_(2)` molecules both the bonds `pi` are bonds
C. In `C_(2)^(2-)` ion there is one `sigma and "two "pi` bonds
D. `C_(2)` is paramagnetic but `C_(2)^(2-)` is diamagnetic.

Answer

To determine which statement is incorrect according to the molecular orbital theory (MOT) for the molecules C2 and C2^2-, we will analyze the molecular orbitals and the electron configurations for both species step by step.

### Step 1: Understand the Electron Configuration of C2
C2 has a total of 12 electrons. According to the molecular orbital theory, the molecular orbitals are filled in the following order for homonuclear diatomic molecules like C2:

1. σ1s
2. σ1s*
3. σ2s
4. σ2s*
5. π2px
6. π2py
7. σ2pz

For C2, the filling of electrons will be as follows:
- σ1s: 2 electrons
- σ1s*: 0 electrons
- σ2s: 2 electrons
- σ2s*: 0 electrons
- π2px: 2 electrons
- π2py: 2 electrons
- σ2pz: 0 electrons

Thus, the electron configuration for C2 is:
\[ \sigma 1s^2 \sigma 1s^{*0} \sigma 2s^2 \sigma 2s^{*0} \pi 2px^2 \pi 2py^2 \sigma 2pz^0 \]

### Step 2: Analyze the Bonding in C2
In C2, we have:
- 2 bonding σ bonds (from σ1s and σ2s)
- 4 bonding π bonds (from π2px and π2py)

The total number of bonds is:
- 2 (from σ) + 2 (from π) = 4 bonds

### Step 3: Understand the Electron Configuration of C2^2-
C2^2- has a total of 14 electrons. The filling of electrons will be similar, but we will have two additional electrons in the anti-bonding orbitals:

1. σ1s: 2 electrons
2. σ1s*: 0 electrons
3. σ2s: 2 electrons
4. σ2s*: 0 electrons
5. π2px: 2 electrons
6. π2py: 2 electrons
7. σ2pz: 2 electrons (2 additional electrons fill this orbital)

Thus, the electron configuration for C2^2- is:
\[ \sigma 1s^2 \sigma 1s^{*0} \sigma 2s^2 \sigma 2s^{*0} \pi 2px^2 \pi 2py^2 \sigma 2pz^2 \]

### Step 4: Analyze the Bonding in C2^2-
In C2^2-, we have:
- 2 bonding σ bonds (from σ1s and σ2s)
- 4 bonding π bonds (from π2px and π2py)
- 2 bonding σ bonds (from σ2pz)

The total number of bonds is:
- 2 (from σ1s) + 2 (from σ2s) + 2 (from σ2pz) + 2 (from π) = 6 bonds

### Step 5: Evaluate the Statements
Now we can evaluate the statements given in the question:

1. **C2 molecule has both bonds as π bonds.** - This is incorrect; C2 has both σ and π bonds.
2. **In C2 molecule, both π bonds are the same.** - This is correct; both π bonds are equivalent.
3. **In C2^- ion, there is 1 σ and 2 π bonds.** - This is incorrect; C2^- has more than that.
4. **C2 is paramagnetic, but C2 is diamagnetic.** - This is correct; C2 is indeed diamagnetic.

### Conclusion
The incorrect statements according to molecular orbital theory are:
- C2 molecule has both bonds as π bonds.
- In C2^- ion, there is 1 σ and 2 π bonds.