The electromagnetic spectrum is a range of all possible wavelengths of electromagnetic radiation, which includes various forms of energy such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The theoretical limits for the longest and shortest wavelengths in the electromagnetic spectrum are as follows:
Longest Wavelength: The longest wavelength in the electromagnetic spectrum is theoretically infinite. This is because there is no upper limit to the length of a wave. In theory, you could have a wavelength that extends indefinitely, but practically speaking, such extremely long wavelengths are not observed in nature.
Shortest Wavelength: The shortest wavelength in the electromagnetic spectrum is theoretically zero. A wavelength of zero would correspond to an infinitely high frequency, which is not physically possible. According to quantum mechanics, the shortest wavelength achievable is associated with the smallest unit of energy, known as a photon. The wavelength of a photon is inversely proportional to its energy, and the shortest possible wavelength is associated with the highest energy photons. However, there is a fundamental limit to the energy of a photon, called the Planck energy, beyond which our current understanding of physics breaks down. At this energy scale, the concept of spacetime becomes uncertain, and our understanding of the electromagnetic spectrum breaks down as well.
In summary, while there is no practical upper limit to the length of a wavelength, the shortest wavelength in the electromagnetic spectrum is limited by the Planck energy, beyond which our current understanding of physics cannot describe the behavior of electromagnetic radiation.