Final answer:
A grating with spacing greater than 800 nm would be most useful for analyzing infrared light because infrared wavelengths are on par with or longer than the spacing of the grating, matching well with its capabilities.
Step-by-step explanation:
For a grating with spacing greater than 800 nm to be used as an effective spectroscopic tool, it should match well with the wavelengths of the electromagnetic radiation it's meant to analyze. In the case of an 800 nm spacing, we're looking at wavelengths that are close to or longer than the spacing itself.
This would make such a grating most useful for analyzing infrared light, since infrared wavelengths range from about 700 nm to 1 mm, which are on par with or longer than the spacing of the grating.
It is important to note that a grating with a larger spacing is typically not suitable for shorter wavelengths, such as ultraviolet light, X-rays, or gamma rays, because they would require a spacing that's much smaller to effectively diffract those types of electromagnetic radiation.
Conversely, for radio waves, which have much longer wavelengths than infrared light, a grating with a spacing less than 800 nm would be too fine to effectively disperse the waves.