Use molecular orbital theory to determine which of the following dicarbon species is expected to have the longest bond length. Use the following valence MO order: σ2s < 'σ*2s < π2py = π2pz < σ2px < π*2pz < σ*2px. a. C2^-2
b. C2^-
c. C2
d. All the dicarbon species have the same bond length
e. C2+

Applying molecular orbital theory the dicarbon specie that has the longest bond length is ; ( E )  C₂⁺

The valence electrons in molecules fill up molecular orbits in accordance to Pauli exclusion theory  and Hund's  rule.  while

The bond order is the difference between bonding and antibonding electrons found in a molecule divided into half. while the molecule orbitals are filled according to increasing energy in accordance to Aufbau principle

The bond order of a molecule is inversely proportional to the bond length of the molecule. Therefore the dicarbon specie that has the longest bond length is C₂⁺ because it has the shortest bond length of approximately 1.5.

Hence we can conclude that Applying molecular orbital theory the dicarbon specie that has the longest bond length is ; ( E )  C₂⁺

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e. C2+

Explanation:

In the molecular orbital theory, the valence electrons in molecules are filled into molecular orbitals in accordance with Hund's rule and Pauli exclusion theory.

The orbitals are filled in order of increasing energy (Aufbau principle) as shown in the question. The bond order refers to half the difference between the number of bonding and antibonding electrons in the molecule.

The smaller the bond order the longer the bond length and vice versa. The specie having the least bond order is C2+ with a bond order of 1.5. This specie certainly has the longest bond length also. Hence the answer.

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