The maximum wavelength of electromagnetic radiation that can cause a transition depends on the specific system or material undergoing the transition. In general, the energy required to cause a transition between energy levels or states in a system is inversely proportional to the wavelength of the radiation. This relationship is governed by the equation:
E = hc / λ
where E is the energy of the transition, h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds), c is the speed of light (approximately 3 x 10^8 meters per second), and λ is the wavelength of the radiation.
To determine the maximum wavelength, you need to consider the energy difference between the initial and final states of the system. If the energy difference is small, then the maximum wavelength that can cause the transition will be longer.
For example, in atomic systems, transitions between energy levels are typically associated with the absorption or emission of photons. The maximum wavelength that can cause a transition would occur when the energy difference between the levels is smallest, which generally happens for transitions involving the outermost electrons or higher energy levels. In such cases, the maximum wavelength can be in the range of infrared or microwave radiation.
However, it's important to note that there are various systems and materials with different energy level structures, so the specific maximum wavelength of radiation that can cause a transition will vary depending on the context.