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Nuclear fallout - Wikipedia
So the asteroid itself would be converted into radioactive material from neutron-activation. However, The difference is that it would be distributed in the upper atmosphere rather than at ground level. I doubt most of it would be a problem though, as it would most likely decay faster than it would hit the ground. Possibly it would disrupt communication with satellites. The long-term isotopes would be from the bomb itself, and would be no different than any other airburst explosion.
The only way it would be an issue is if a large piece (20m or bigger) of irradiated material fell near a population center. Highly unlikely, as most nukes would entirely disintegrate a rocky body like that.
This is assuming that we do exactly nothing until there is no other choice than to nuke it. Bear in mind all we have to do is give it a gentle boop in 2028, or hit it with long-range rockets outside of geostationary orbit range. The only reason to use a nuke would be if we let it get into MEO or closer range before doing anything about it. Which would be kind of dumb.