"Century"? Unless a cobalt-cased nuke, or large H-bomb, 5-10 yrs at most. Hiroshima is an inhabited city, and has been for a while.
I'm not just talking about the radiation. When you consider the condition of North Korea, if that happened there, they'd lose a lot of people and material that they can't replace. And it would take generations to recover the people lost. The loss of people and material and the overall effect it would have on the North's already terrible economy and infra structure would practically send the country back to the 1800's in some ways. And radiation drifts. Plus, we don't know 100% for certain what kind of radioactive material they're using for their nukes. The radioactivity in the area after detonation could be much longer than just a decade. Iran wouldn't suffer as bad as North Korea if that happened since it's a much larger nation, with more spread out population centers, and large uninhabited areas hundreds of miles from cities to build the weapons. North Korea could be damaged far more if they had a self-inflicted nuclear detonation.