In the present work, the nanocrystalline particles of hydroxyapatite (HAp) using an easy alkoxide‐based sol–gel technique including triethyl phosphate [PO (OC2H5)3] and Ca (NO3)2·4H2O as P and Ca precursors have been synthesized. The sample characterization was performed by X‐ray diffraction, Fourier transform‐infrared analysis, scanning electron microscopy, thermal analysis (thermogravimetric analysis/differential thermal analysis), and elemental analysis of energy‐dispersive X‐ray analysis. It is interesting that single phase of HAp was obtained at a low firing temperature of 500°C. Modified Scherrer equation as the Williamson−Hall method was applied for the measurement of crystallite size distributions and micro‐strain of the sample. The determined crystallite size by complementary technique of transmission electron microscopy has good consistency with those obtained from the Scherrer formula. Moreover, we reported the one‐pot synthesis of 3,4‐disubstituted isoxazole‐5(4H)‐ones through the aqueous solution reaction of three components of ethyl acetoacetate, hydroxylamine hydrochloride and various aromatic aldehydes at room temperature. This protocol offers several advantages, including a simple work‐up procedure, very short reaction times (under 25 min), in accordance with the principles of green chemistry, recyclability, excellent yields (87–98%) and environmentally friendly.