\(C_6H_5NH_2<NH_3<C_2H_5NH_2<C_6H_5CH_2NH_2\)
Step 1: Aniline (\(C_6H_5NH_2\)) is less basic than ammonia (\(NH_3\)) due to the electron-withdrawing nature of the phenyl group via resonance.
Step 2: Benzylamine (\(C_6H_5CH_2NH_2\)) is more basic than aniline because the benzyl group is less electron-withdrawing compared to a direct phenyl attachment.
Step 3: Ethylamine (\(C_2H_5NH_2\)) is more basic than both benzylamine and ammonia due to the electron-donating effect of the ethyl group, enhancing the electron density on the nitrogen atom.
Step 4: The correct order of increasing basicity, considering the electronic effects, is therefore aniline, ammonia, benzylamine, and ethylamine.
Kepler's second law (law of areas) of planetary motion leads to law of conservation of