Arrange the given dicarbon species in order of their bond lengths giving reasons L `C_(2), C_(2)^(-), C_(2)^(2-)` .

Explanation

To arrange the given dicarbon species \( C_2 \), \( C_2^- \), and \( C_2^{2-} \) in order of their bond lengths, we first need to determine their bond orders. The bond length is inversely proportional to the bond order; that is, a higher bond order corresponds to a shorter bond length, and a lower bond order corresponds to a longer bond length.

### Step 1: Determine the number of electrons in each species
- For \( C_2 \): Each carbon atom has 6 electrons, so for two carbon atoms, the total number of electrons is \( 6 + 6 = 12 \).
- For \( C_2^- \): This species has one additional electron due to the negative charge, so the total number of electrons is \( 12 + 1 = 13 \).
- For \( C_2^{2-} \): This species has two additional electrons due to the two negative charges, so the total number of electrons is \( 12 + 2 = 14 \).

### Step 2: Calculate the bond order for each species
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