Question

If the interatomic distance between ${{A}_{2}}$ and ${{B}_{2}}$ is 74 pm and 198 pm, then the bond length of AB will be-
(A)- 136 pm
(B)- 68 pm
(C)- 272 pm
(D)- 363 pm

Answer 1

Hint: In molecular geometry, the average distance between the nuclei of two bonded atoms in a molecule is known as bond length or bond distance. The distance between the nuclei of atoms in a material or a compound is known as atomic spacing.

Complete Step by step answer:
-In solid materials, the atomic spacing refers to the bond lengths of its atoms.
-In a bond between two identical atoms, half the bond distance is equal to the covalent radius.
-Bond length of a compound or element is measured either by X-ray diffraction or approximated in the gas phase by microwave spectroscopy.
-A bond between a pair of atoms may vary with different molecules because of various factors affecting it like a steric hindrance, electronegativity, etc.
-Let the radius of two atoms ${{A}_{2}}$ and ${{B}_{2}}$ be ‘r’ and ‘r’ respectively which combines to form the molecule AB whose interatomic distance will be 2r.
$r=\dfrac{\text{interatomic distance}}{2}$
-The radius of atom A $=\dfrac{74}{2}=37pm$
-The radius of atom B \[=\dfrac{198}{2}=99pm\] (pm = picometer)
-The bond length of the molecule AB will be the summation of the radius of A and radius of B.
-Bond length of AB = 37 + 99 = 136 pm
-Hence the calculated bond length of AB will be 136pm.

Therefore, the correct answer is option A.

Note: Bond length or bond distance is a transferable property of a bond between atoms of fixed types, which are relatively independent of the rest of the molecules. When more electrons participate in bond formation, the bond is shorter, which implies that bond length is related to bond order. Bond length is inversely proportional to the bond strength and the bond dissociation energy.