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what would’ve happened if challenger was carrying nuclear material? (i’m actually asking)

It would depend a great deal on what it was and how it was packaged. This seems to have some good discussion:

https://space.stackexchange.com/questions/16608/how-does-the...

The Earth would be immeasurably more radioactive than today.

Usually immeasurably means infinite, I'm guessing that's not what you meant?

Immeasurably means "incapable of being measured", which could refer to too small to measure or too large to measure, because English is fun like that. It does generally refer to the latter, though.

The Earth would in fact be the same radioactive as today, assuming we had used stockpiled Pu.

It's the distribution that matters. A little bit of ocean floor over Florida would be much more radioactive than today if it was scattered with Pu-238.

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