A nuclear bomb costs 12,000 gold pieces and weighs 120 stones.
It is titled "a very dangerous bomb" before identification and is precious.
It can be purchased from Noel in Derphy after accepting the Red Blossom in Palmia quest.
Setting off a bomb in a town causes serious karma loss (-100), setting it off anywhere else causes -20 Karma. The bomb can only detonate when the player is in the same area - leaving will only stall the countdown. Obviously not good for your health. A (usually) reliable workaround is to read a Scroll of Contingency, which should allow you to survive the blast. Alternatively, you can drop the bomb in one corner of an area, leave the area, and re-enter from another direction. If the map is large enough, you'll be outside the blast radius. It would be smart to activate it during a storm so you can safely loot the town without catching fire.
A nuclear blast deals 1000 fire damage.