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The correct order of increasing bond length of C - H, C - O, C - C and C = C is:
(A) C - H < C = O < C - C < C = C
(B) C - H < C = C < C - O < C - C
(C) C - C < C = C < C - O < C - H
(D) C - O < C - H < C - C < C = C

Answer
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Hint: Consider the nature of various bonds present such as single bonds and double bonds. Also consider the size of the atoms, small or large. Also consider the electronegativity difference between two atoms joined by the bond.

Complete answer:
The bond length is the distance between the nuclei of two atoms joined by the bond. You can say that bond length is roughly equal to the sum of the covalent radii of two bonded atoms. Usually the unit of measurement of bond length is the angstrom unit. You can measure the bond length by using various techniques such as rotational spectroscopy, X-ray diffraction and neutron diffraction.
There are several factors that affect the bond length. These include bond order (single, double or triple), atomic/ionic radii and the electronegativity difference.
The force of attraction between two atoms joined by a double bond is more than the force of attraction present between two atoms joined by a single bond. A double bond is shorter than a single bond. Hence, the increasing order of bond length is C = C < C - C.
Among the bonds C - H < C - O < C - C, the C - H bond is shortest as both hydrogen and carbon atoms are small in size and have large electronegativity differences.
So C - H < C - O and C - H < C - C.
Hence, you can write the following order as the correct order of increasing bond length.
C - H < C = C < C - O < C - C.

Hence, the option (B) is the correct option.

Note: Bond length and bond strength have inverse relationship. Greater is the bond length, smaller is the bond strength and vice versa.
Hence, you can write the following order as the correct order of decreasing bond strength.
C - H > C = C > C - O > C - C