No, an electron does not necessarily emit radiation with the same wavelength as it was absorbed. The wavelength of the radiation emitted by an electron depends on the specific electronic transition that occurs within the atom or molecule.
When an electron absorbs energy, it moves to a higher energy level or an excited state. Subsequently, the electron can return to a lower energy level by releasing the absorbed energy in the form of electromagnetic radiation. The emitted radiation may have a different wavelength than the absorbed radiation due to various factors, including the energy levels involved and the specific quantum transitions.
The energy levels in atoms and molecules are discrete, meaning they are quantized. Each energy level corresponds to a specific wavelength or set of allowed wavelengths for the emitted radiation. The emitted radiation may have a shorter or longer wavelength than the absorbed radiation, depending on the specific transition involved.
This phenomenon is fundamental to the study of atomic and molecular spectroscopy, where the absorption and emission spectra provide valuable information about the energy levels and transitions within a system.