[Stelios Chachadakis]

Lets suppose that we have an atom of an element which absorbs a certain wavelength of light "a", in the visible spectrum and reflects all other wavelengths. After absorbing light, its electrons get excited but after some time they get back to a lower state of energy emitting a photon with the same energy (this is equivalent to wavelength) as the photon they absorbed. This means that this atom actually emites back the radiaton it absorb. Then why do things have color? I get that we say that things have color because they reflect some wavelengths of radiations and absorb some others, but as it seems, they actually emite what they absorb back.

[Enthalpy]

Welcome, Stelios Chachadakis!

Re-emitting the same wavelength is only one possible process, called diffusion. Many other processes compete to dissipate the energy of the excited electron.

Other electrons get receive a part of the excitation energy. Or the movements of the atoms, as the vibration of the molecule or crystal for instance. If any energy is left for an emitted photon, it has a longer wavelength (fluorescence), possibly in the infrared region.

The atom or molecule can also emit several photons that share the energy, and have then a longer wavelength.

Combinations exist too.

As a sidenote, very few atoms are lone on Earth. Argon must be the most common ones. About all others form molecules. Often, valence electrons absorb the visible spectrum, and they spread over several atoms. This changes the energies electrons can have, so the absorption spectrum is typical of molecules rather than atoms.

[Corribus]

After absorbing light, its electrons get excited but after some time they get back to a lower state of energy emitting a photon with the same energy (this is equivalent to wavelength) as the photon they absorbed.

Even in an isolated atom in the gas phase, this doesn't happen. There's a finite probability that the excited atom can deactivate to any lower energy state, not necessarily the state it started in, provided the transition is allowed by selection rules.