The frequency of light that has the shortest wavelength corresponds to the highest frequency within the electromagnetic spectrum. This frequency belongs to the region of gamma rays. Gamma rays have the highest energy and shortest wavelengths among all the electromagnetic waves.
Gamma rays typically have frequencies on the order of 10^19 to 10^24 Hertz (Hz), which corresponds to wavelengths ranging from less than 0.01 nanometers (nm) to a fraction of a picometer (pm). These extremely short wavelengths make gamma rays highly energetic and capable of penetrating through materials, ionizing atoms, and causing significant damage to living tissues.
In summary, the frequency of light that has the smallest shortest wavelength belongs to the gamma ray region of the electromagnetic spectrum.