The current range of North Korean missiles sufficient to reach North America, and given the rate of progress they will likely be able to hit almost anywhere in the world by the end of the year.
But the more likely scenario is an atmospheric test of an H-bomb over the Pacific Ocean. That would demonstrate Pyongyang’s power without giving anyone sufficient excuse to shoot back.
While the potential health consequences of such a test are not trivial, neither are they dire.
The Partial Test Ban Treaty banned atmospheric tests in the early 1960’s, but prior to that hundreds of atmospheric tests were carried out, often in the megaton range:
Between 1951 and 1958, the US conducted 166 atmospheric tests, the Soviet Union conducted 82, and Britain conducted.
Humanity and civilization survived hundreds of massive atmospheric tests sixty years ago. Humanity and civilization will survive a single much smaller North Korean atmospheric test today. The underground test North Korea performed this month was well below a megaton, although much larger than anything they have done previously.
That said, it is worth keeping a few things in mind. Fallout takes a long time to circle the Earth. There will be days to prepare in most places. Months in the southern hemisphere, insofar as any preparation there is warranted.
Most fallout is in the form of dust, much like volcanic ash. It spreads through the upper atmosphere and drifts gently down to Earth, raising the level of background radiation a small but measurable amount.
As with all radioactivity, the more intense sources tend to be short-live: radioactive particles are literally destroying themselves as they decay. The more time that passes, the less radioactive fallout becomes. Furthermore, fallout tends to wash out of the environment over time as well, 70% of it over oceans.
For people well away from the point of explosion, the risk from additional background radiation due to fallout will be very small. If you don’t worry about traveling to Denver, you shouldn’t worry too much about fallout, unless you are very close to the explosion.
There will be a lot of fear-mongering about particular isotopes, especially strontium. Iodine isotopes have lifetimes from a few hours to about two months. Strontium isotopes range from a day to two months. Both tend to bio-accumulate: strontium in bones and teeth, iodine in the thyroid. Pay attention to local health authorities and behave accordingly, but be aware that the acute risk is low.
By far the greatest risk of such a test is that someone will use it as an excuse to attack North Korea. This is generally the human response to violence and conflict, which is why escalation is almost never in anyone’s interests.