Step 1: Understanding basic strength of amines.
The basic strength of alkylamines increases as the number of alkyl groups attached to the nitrogen increases. Alkyl groups donate electron density to the nitrogen, enhancing its ability to accept protons.
Step 2: Analyzing the options.
(A) CH\(_3\)NH\(_2\)>(CH\(_3\))\(_2\)NH>(CH\(_3\))\(_3\)N>NH\(_3\): Incorrect — While the order is partly correct, NH\(_3\) is less basic than alkylamines.
(B) (CH\(_3\))\(_2\)NH>(CH\(_3\))\(_3\)N>CH\(_3\)NH\(_2\)>NH\(_3\): Incorrect — The correct order should place (CH\(_3\))\(_3\)N lower than (CH\(_3\))\(_2\)NH.
(C) (CH\(_3\))\(_3\)N>(CH\(_3\))\(_2\)NH>CH\(_3\)NH\(_2\)>NH\(_3\): Incorrect — (CH\(_3\))\(_3\)N is less basic than (CH\(_3\))\(_2\)NH.
(D) (CH\(_3\))\(_2\)NH>CH\(_3\)NH\(_2\)>(CH\(_3\))\(_3\)N>NH\(_3\): Correct — This is the correct order, as the more alkyl groups on nitrogen, the more basic the amine.
Step 3: Conclusion.
The correct answer is (D) (CH\(_3\))\(_2\)NH>CH\(_3\)NH\(_2\)>(CH\(_3\))\(_3\)N>NH\(_3\), as this is the correct order of basic strength.