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Question 53

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  :

To understand the relationship between covalent radii and bond length, we use the fundamental definition of covalent radius in molecular geometry.

The covalent bond length between two atoms $$A$$ and $$B$$ is defined as the sum of their individual covalent radii when they are joined by a single covalent bond. Therefore, the bond length is given by

$$d_{AB}=r_A+r_B.$$

The total length of the diatomic molecule $$AB$$ refers to the distance from the outer edge of atom $$A$$ to the outer edge of atom $$B$$. Since this includes the radii of both atoms on either side of the bond, the total molecular length is

$$L=2(r_A+r_B).$$

Hence, the covalent bond length of the molecule is

$$r_A+r_B,$$

and the total length of the molecule is

$$2(r_A+r_B).$$

Therefore, the correct option is the one corresponding to

$$\boxed{\text{Bond length}=r_A+r_B,\qquad \text{Total length}=2(r_A+r_B).}$$

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