Arrange the following species in order of their in-creasing bond lengths and explain: `C_(2),C_(2)^(-) and C_(2)^(2-)`.

Explanation

`C_(2):K K(sigma_(2s))^(2)(sigma_(2s)^(**))^(2)(pi_(2p_(x)))^(2)(pi_(2p_(y)))^(2)`,
`C_(2)^(-): K K (sigma_(2s))^(2)(sigma_(2s)^(**))^(2)(pi_(2p_(x)))^(2)(pi_(2p_(y)))^(2)(sigma_(2p_(z)))^(1)`
`C_(2)^(2-): K K(sigma_(2s))^(2)(sigma_(2s)^(**))^(2)(pi_(2p_(x)))^(2)(pi_(2p_(y)))^(2)(sigma_(2p_(z)))^(2)`.

Since bond length is inversely proportional to bond order, the increasing sequence of bond length of the given species: `C_(2)^(2-) lt C_(2)^(-) lt C_(2)`.