Covalent Bond Length and Total Length of AB Molecule

To determine the covalent bond length and the total length of the heteronuclear diatomic molecule $AB$:

1. Covalent Bond Length:

   • The covalent bond length ($d_{AB}$) of a diatomic molecule $AB$ is defined as the internuclear distance between the nuclei of atoms $A$ and $B$.
   • Given that the covalent radius of atom $A$ is $r_A$ and that of atom $B$ is $r_B$, the internuclear distance (covalent bond length) is given by: $\text{Covalent bond length} = r_A + r_B$

2. Total Length of the $AB$ Molecule:

   • The total length (overall end-to-end span) of the $AB$ molecule along the internuclear axis extends from the outer boundary of atom $A$ to the outer boundary of atom $B$.
   • Considering the atoms as spheres of radii $r_A$ and $r_B$:
     • The distance from the outer boundary of atom $A$ to its nucleus is $r_A$.
     • The internuclear distance between nucleus $A$ and nucleus $B$ is $(r_A + r_B)$.
     • The distance from the nucleus of atom $B$ to its outer boundary is $r_B$.
   • Thus, the total length of the molecule $AB$ is: $\text{Total length} = r_A + (r_A + r_B) + r_B = 2r_A + 2r_B = 2(r_A + r_B)$
   • Equivalently, the total length is the sum of the diameters of atom $A$ ($2r_A$) and atom $B$ ($2r_B$), which equals $2(r_A + r_B)$.

Therefore, the covalent bond length and the total length of the $AB$ molecule are $(r_A + r_B)$ and $2(r_A + r_B)$, respectively.

Correct Option: A [$(r_A + r_B), 2(r_A + r_B)$]