The covalent radii of atoms A and B are $r_A$ and $r_B$, respectively. The covalent bond length and total length of AB molecule are respectively :
- $(r_A + r_B), 2(r_A + r_B)$
- $\frac{1}{2}(r_A + r_B), (r_A + r_B)$
- $(r_A + r_B), (r_A + r_B)$
- $2(r_A + r_B), \frac{1}{2}(r_A + r_B)$
The Correct Option is C
Solution and Explanation
Covalent radius is defined as half of the distance between the nuclei of two bonded atoms in a homonuclear molecule. For a heteronuclear molecule AB, the bond length is approximately the sum of the covalent radii of the two atoms.
Step 2: Detailed Explanation:
The covalent bond length ($d_{AB}$) in a molecule AB is the distance between the centers of the nuclei of atom A and atom B.
By definition, if $r_A$ is the covalent radius of atom A and $r_B$ is the covalent radius of atom B, then:
\[ \text{Covalent Bond Length} = r_A + r_B \]
In a simple diatomic molecule model, the "total length" of the molecule (from the outer boundary of the electron cloud of A to that of B) is effectively defined by the distance spanning both covalent radii when bonded. Thus, it is also taken as $(r_A + r_B)$.
Step 3: Final Answer:
Both the covalent bond length and the total length of the AB molecule are represented as $(r_A + r_B)$.
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