The smallest size an atom can be and still be visible to the naked eye is generally considered to be around 0.1 micrometers (μm) or 100 nanometers (nm). This corresponds roughly to the wavelength of visible light, which ranges from about 400 to 700 nanometers.
Visible light interacts with matter through a process called scattering, where photons are deflected by the electrons in atoms or molecules. When light encounters an object smaller than its own wavelength, such as an atom, it tends to scatter in various directions. This scattering can cause the object to become visible to the human eye.
However, it's important to note that individual atoms are far smaller than this visible range. For example, the radius of a hydrogen atom is about 0.1 nm. But due to their small size and the limitations of our eyes' sensitivity, we cannot directly observe individual atoms without the use of advanced techniques such as scanning tunneling microscopy or atomic force microscopy.
In everyday life, we perceive macroscopic objects made up of vast numbers of atoms. The collective scattering of light from these objects gives rise to their visibility. Thus, while atoms themselves are too small to be seen, their presence and arrangement contribute to the visibility of the objects they compose.