which statement is incorrect about the peptide bond $O = C - NH - $ ?
A) $C - N$ bond length in proteins is longer than the usual bond length of $N - $bond
B) Spectroscopic analysis shows planar structure $O - CO - NH - $ group
C) $C - N$ bond length in proteins is smaller than the usual bond length of $C - N$ bond
D) None of the above

Hint: In the question, the incorrect option has been asked which means the other remaining three options are correct and one can relate this information to find out the correct option. The bond length $C - N$ has been asked which can get affected by many factors and one needs to analyze if there is the presence of any factor which gives the incorrect option

Complete step by step answer:
1) First of all we will learn about what peptide bonds are and they can be described as a type of chemical bond which is formed between the two molecules when the carboxyl group of one molecule gets reacted with the amino group of another molecule.
2) This reaction involves the dehydration reaction which means the removal of a molecule of water. This type of reaction is also known as a condensation reaction and it is a very common type of reaction which occurs between amino acids which leads to the formation of proteins.
3) The peptide bond has a nitrogen atom in its structure which has the lone pair of electrons on it. Besides the nitrogen atom, the carbonyl group is present which means the lone pair present on the nitrogen atom can form the resonance with the carbonyl group forming the double bond in between the carbon and nitrogen forming an anion on the oxygen atom.
4) The spectroscopic data shows the presence of a peptide bond as it shows the data for the presence of groups in the structure. Hence, option B is also the correct choice. The double bond formed between the carbon and nitrogen will have less bond length than a single bond as there is the involvement of $\pi $ bond which makes the bond length less. Therefore, option C is also correct.
5) The $C - N$ bond length in proteins is never longer than the usual bond length of $N - $bond

which shows the option A as an incorrect option.

Note:
The single bond between two atoms is larger than the double bond as the double bond is a stronger bond and has $\pi $ a bond in it the length is small. Spectroscopic analysis is a method that is used to determine the structure and the functional groups present in the molecule. The amino acids are attached to each other by a peptide bond to form protein molecules.