Given below are two statements:

Statement I: A hypothetical diatomic molecule with bond order zero is quite stable.

Statement II: As bond order increases, the bond length increases.

In the light of the above statements, chose the most appropriate answer from the options given below:

To determine the validity of the given statements, let us analyze the concepts of bond order, molecular stability, and bond length step-by-step.

Analysis of Statement I:
According to Molecular Orbital (MO) Theory, the bond order of a diatomic molecule is calculated as:

$\text{Bond Order}=\frac{N_b-N_a}{2}$

where $N_b$ is the number of electrons in bonding molecular orbitals and $N_a$ is the number of electrons in antibonding molecular orbitals.
A bond order of zero implies that the net bonding forces in the molecule are zero (or the antibonding forces completely cancel out the bonding forces). For example, a helium dimer (${\text{He}}_2$) has a bond order of zero and does not exist under normal conditions. Therefore, a molecule with a bond order of zero is highly unstable and does not exist. Thus, Statement I is false.

Analysis of Statement II:
Bond order is a measure of the number of chemical bonds between a pair of atoms. As the bond order increases (for example, moving from a single bond to a double bond, and then to a triple bond), the electrostatic attraction between the nuclei and the shared electrons becomes stronger. This stronger attraction pulls the nuclei closer together, which causes the bond length to decrease. Therefore, as bond order increases, bond length decreases (and bond dissociation energy increases). Thus, Statement II is also false.

Conclusion:
Both Statement I and Statement II are false.