Basicity in gaseous phase is determined by electron-donating ability of alkyl groups which increase electron density on nitrogen. The more alkyl groups attached, the higher the basicity:
- NH\(_3\): No alkyl group
- CH\(_3\)NH\(_2\): One methyl group
- (CH\(_3\))\(_2\)NH: Two methyl groups
- (CH\(_3\))\(_3\)N: Three methyl groups
Hence, basicity order increases as:
\[
\boxed{\text{NH}_3<\text{CH}_3\text{NH}_2<(\text{CH}_3)_2\text{NH}<(\text{CH}_3)_3\text{N}}
\]
Note: This is valid for gaseous phase. In aqueous phase, steric hindrance and solvation affect order.