Step 1: Understanding the Concept:
The basicity of amines depends on the availability of the lone pair of electrons on the Nitrogen atom.
Factors affecting basicity include:
1. Inductive effect (+I effect of alkyl groups increases electron density).
2. Solvation effect (hydrogen bonding with water stabilizes the cation).
3. Steric hindrance (bulky groups hinder the approach of protons).
Step 2: Detailed Explanation:
In the gas phase, the order is strictly \( 3^\circ>2^\circ>1^\circ>NH_3 \).
However, in aqueous solution, the interplay of the +I effect and solvation/steric factors makes the secondary ($2^\circ$) amine the most basic.
For Methyl groups ($R = CH_3$): \( (CH_3)_2NH>CH_3NH_2>(CH_3)_3N>NH_3 \)
For Ethyl groups ($R = C_2H_5$): \( (C_2H_5)_2NH>(C_2H_5)_3N>C_2H_5NH_2>NH_3 \)
In general, ammonia ($NH_3$) is always the least basic because it lacks the +I effect of alkyl groups. The secondary amine ($R_2NH$) is generally the most basic.
Option (d) correctly places $NH_3$ at the bottom and $R_2NH$ as greater than $RNH_2$ and $R_3N$.
Step 3: Final Answer:
The order is \( NH_3<R-NH_2<R_2NH>R_3N \).