The length that light has to travel in the atmosphere can affect the amount of electromagnetic radiation reaching a black body, but it does not directly influence the amount of radiation emitted by the black body itself. The radiation emitted by a black body is determined by its temperature alone, according to Planck's law.
When light travels through the atmosphere, it can be subject to various interactions and effects such as scattering and absorption. These interactions can affect the intensity and spectrum of the light reaching a particular location. However, the absorption and scattering processes in the atmosphere are not directly related to the radiation emitted by a black body.
In the context of a black body on a mountain versus one at sea level, the primary factors that could influence the amount of radiation reaching them are atmospheric conditions such as air density, composition, and presence of particulates or pollutants. These factors can influence the transmission, scattering, and absorption of light in the atmosphere, which could indirectly affect the amount of radiation incident on the black body.
In general, higher-altitude locations may have different atmospheric conditions compared to sea level, which can result in variations in the amount and characteristics of the incoming radiation. However, it's important to note that these effects are not directly related to the radiation emitted by the black body itself, which is solely determined by its temperature.