Concept:
The Hofmann bromamide reaction (also called Hofmann degradation or Hofmann rearrangement) is a reaction in which a primary amide is converted into a primary amine containing one carbon atom less.
The reaction takes place in the presence of bromine and aqueous sodium hydroxide.
The general reaction is
\[
\boxed{
RCONH_2+Br_2+4NaOH
\rightarrow
RNH_2+Na_2CO_3+2NaBr+2H_2O
}
\]
Thus, the amide loses its carbonyl carbon as carbonate.
Step 1: Identify the reactants.
The given reactants are
\[
RCONH_2,\;Br_2,\;\text{and}\;NaOH.
\]
A primary amide reacts with bromine in an alkaline medium.
Step 2: Identify the product formed.
The product is
\[
RNH_2,
\]
which is a primary amine.
The amine contains one carbon atom less than the original amide.
This is the characteristic feature of the Hofmann bromamide reaction.
Step 3: Compare with the given options.
• Hinsberg reaction is used to distinguish primary, secondary and tertiary amines.
• Carbylamine reaction is used for the identification of primary amines.
• Sandmeyer reaction converts diazonium salts into haloarenes.
• Hofmann bromamide reaction converts amides into amines with one less carbon atom.
Therefore,
\[
\boxed{\textbf{Option (D)}}
\]
is the correct answer.