The shortest possible wavelength for electromagnetic radiation is associated with the highest energy photons in the electromagnetic spectrum. These photons have extremely high frequencies, corresponding to very short wavelengths.
In modern physics, the theoretical limit for the shortest wavelength is believed to be the Planck length. The Planck length is approximately 1.616 × 10^-35 meters. It is a fundamental constant derived from Planck's constant (h), the speed of light (c), and the gravitational constant (G).
However, it's important to note that our current understanding of physics and our ability to experimentally probe such extreme scales is limited. At the Planck length scale, the effects of quantum gravity are expected to become significant, and our current theories do not provide a complete description of the behavior of spacetime at such small distances.
In practical terms, the shortest wavelengths of electromagnetic radiation that have been observed and studied in experiments are in the range of gamma rays. Gamma rays have wavelengths shorter than about 10 picometers (10^-12 meters) or frequencies higher than about 30 exahertz (3 × 10^19 Hz).
To summarize, the Planck length sets a theoretical lower limit for the shortest possible wavelength of electromagnetic radiation, but our current understanding of physics and experimental capabilities prevent us from directly probing or observing phenomena at that scale.