Oh, that's just silly. No atmosphere, no fallout. The effects would be felt in a few kilometers' radius only.

More, the astronauts were already being exposed to a huge amount of electromagnetic radiation of all types, nearly all of which was blocked by their space suits.

Overall, am I surprised that learn that humans once planned to nuke the moon? No. Humans are extremely intelligent creatures, but pathologically unwise.

Compared to destroying our own biosphere, something we're engaged in literally as I write this, dropping an atom bomb on the moon is the height of wisdom and dignity.