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Why didn’t the Americans use it?
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Why weren’t the North Koreans afraid of it?
Because we believed that the USSR would retaliate by dropping one on us, or on one of our Allies.
Even as late as the 1950s atomic bombs were in very, very short supply. We are talking handfuls of bombs that might not work when you want 'em to. You could not use them willy-nilly.
Further, nuclear weapons are more useful as a threat than as a boom. Once you bust that particular cap the other guy realizes “hey, I can deal with that.” (In Navy talk we call the idea a “force in being.”)
As it was the Chinese were forced to fight a war under nuclear condition, dispersal, lots of troublesome camouflage and whatnot. This reduced the effect of a blast and increased the overall bother level even without the Americans dropping the hammer.
Finally, this was not (as the OP stated) a North Korea thing. The DPRK had lost all sembelence of control of the war by '51 or so. It was a Russia/China thing. The PDRK was not a player.
Also, when North Korea invaded the south, it did so on the assumption that the US would NOT intervene. (US Sec. of State Dean Acheson had recently given a speech outlining the key areas of interest in the Pacific and South Korea went unmentioned.)
By the time the war was down to the China/ US battle of attrition, virtually everything aboveground between the 38th parallel and the Yalu had been bombed to rubble already. The North Koreans were living in caves. An atomic bomb will obliterate any target it’s dropped on, but moderately hard targets (bunkers, soldiers in trenches) can survive suprisingly close to a multikiloton explosion. And as said upthread, military planners didn’t want to risk losing the “mystique” of nuclear weapons as ultimate doomsday weapons. Their main use was to threaten China with a widening of the war if they didn’t get serious about peace talks.
But they made huge use of camouflage and night movements right from the get-go, and were very successful as a result. I was under the impression that this was primarily to defeat UN air power and reconnaisance which had proved so effective against the Koreans (as well as the Germans/Japanese a few years earlier). To a certain extent it’s irrelevant if the B-29s are dropping A-bombs or massive amounts of conventional ordnance, the response is still to scatter, dig and hide. It would be interesting to know if the Chinese have released any documents that indicate which they were most worried about, but as Lumpy says, conventional air power was plenty enough to ravage the peninsula.
There does not seem to be consensus about this. The chinese do not seem to have been particularly impressed, possibly because they were well prepared for bombing of whatever kind, possibly because of the expected Soviet response. The last two years of the war (after the chief bruhaha about possible nuclear escalation) consisted of two years of stalemate and interminable peace talks that didn’t really go anywhere. So The Bomb may have had very limited utility in this situation.
For an outstanding analysis of the Korean War, everyone should read the late David Halberstam’s excellent book, The Coldest Winter. He discusses each of these issues in great detail.