Meaning anything that could fall from the sky or get blown around in the air. The particles themselves are heavier than lead, but ash can act like a parachute, and the massive explosion created enormous heat sending everything upwards into the higher layers of the atmosphere.
Any time you see a mushroom cloud, the expanding top stops when it hits a layer of atmosphere that is the same temperature as the rising column. This is true of volcanic eruptions and enormous bombs. The atmosphere gets colder with height, but only for a limited amount of time before the density is too low. Once the density is low enough with elevation, the temperature goes back up from solar radiation. When a plume is powerful enough to punch through the cold and back out into the hot on the other side, that is what can carry heavy particulates quite a long distance. There are winds across these layers that are different and the winds play a role in keeping the layers divided. Think of it like the way Jupiter looks with the cloud layers but in miniature scale that is not easy for human eyes to see. The entire Earth has a similar wind banding structure in the atmosphere. If you ever see wind diagrams for the southern hemisphere the effect is more clearly seen. The northern is a bit less banded due to continuous landmass heating, the Himalayas, and the shallowness of the Gulf of Mexico causing enormous evaporation with an impact stretching all the way into Europe.
The wind patterns carry the little parachutes with heavy radioactive junk and it settles like dust. So like, when we say sealed inside your home, that means duck tape on every door seal, and nothing that could pull air into or out of the space. The pro hazmat setup is a positive pressure bunker where there is a complex filter or recycled air scrubbing system that maintains a higher pressure inside the enclosure so that any leaks present force material out instead of in.