Step 1: Understanding the Concept:
Basicity of amines depends on the availability of the lone pair of electrons on the Nitrogen atom. It is influenced by inductive effects (\(+I\)), steric hindrance, and solvation effects in aqueous solution.
Step 3: Detailed Explanation:
In aqueous solution, the basic strength is determined by a combination of the electron-donating \(+I\) effect of alkyl groups and the stabilization of the conjugate acid by hydration.
Alkyl groups (\(R\)) increase electron density on Nitrogen through the \(+I\) effect, making alkyl amines more basic than \(NH_3\).
However, as the number of alkyl groups increases to three (\(R_3N\)), steric hindrance to hydration and crowding around Nitrogen reduces its basicity compared to secondary amines (\(R_2NH\)).
Thus, the general order in aqueous phase follows: \(Secondary>Primary>Tertiary>Ammonia\), which matches option (D): \(NH_3<R-NH_2<R_2NH>R_3N\).
Step 4: Final Answer:
The correct order is \(NH_3<R-NH_2<R_2NH>R_3N\).