How long would it take for the effects of a nuclear weapon to wear off?

I would like to know how long it would take for the plant life in an area to recover from an explosion from a nuclear bomb exploding.

Parameters for questions:

• The bomb is a 100 megaton nuclear bomb

• The area is 50 square miles

• Let's say for simplicity the bomb was on the ground and it suddenly exploded and the entire area was wiped of life, so the ground was barren and irradiated

• Assume no intervention from humans

I would like to know how many years it would take when the area would look unaffected, like the explosion had never occurred. (Meaning plant life has returned)

Additionally, I would also appreciate knowing how long it would take so that any effects from the bomb have a minimal effect on plants and humans (Like radiation shortening lifespan or the likes)

• One important factor is the material being used. What kind of nuke? Fission, or fusion? Then what elements? Uranium, Plutonium, Hydrogen? The material will dictate the product element, or nuclear waste, which will determine the Half-Life, and how well the environment can deal with it. – Iter Aug 5 '17 at 16:57
• Hiroshima and Nagasaki are large, thriving cities... Plant life will return in a few years if not immediately. Health and safety regulations may prevent human habitation for quite longer; look at Chernobyl -- still considered unsafe for humans, but wildlife is abundant, and there is even talk of making the area a permanent natural reserve. – AlexP Aug 5 '17 at 17:40
• 100 MT? You may want to scale that back a little, unless you're making a point of total, utter destruction. Wikipedia puts the Tsar Bomba, "the single most physically powerful device ever deployed by mankind", at a 51 MT yield (originally estimated at 55-60 MT by the US). It destroyed brick buildings 55 km from the detonation, and damaged windows 900 km away. The shock wave travelled around the world at least three times. And for extra effect, its mushroom cloud was about 64 km high. (Airliners fly at around 10 km altitude.) – a CVn Aug 5 '17 at 22:24
• Well, based on yield, it is not a fission weapon, the most practical fusion weapon being hydrogen bombs, it would be a safe working assumption. – Gary Walker Aug 5 '17 at 22:43
• I think you need a more exact definition of exactly what you mean by recover. You'd get some plant life in the next growing season - see e.g. the recovery after the Mt. St. Helens volcanic eruption. To get back to where it'd be indistinguishable would take several centuries, if you need to grow full-sized trees. The forests hereabouts still haven't recovered from logging in the latter half of the 19th century. – jamesqf Aug 6 '17 at 4:15

o.m.'s answer is pretty good, but does neglect one detail of the original question - this is a 100 megaton bomb.

The fireball alone would have a radius of 8km, which would sweep out an area greater than the 50 square miles stated in the initial question (about 60 square miles, in fact). It would result in a crater 10 miles wide. The depth is somewhat more problematic, as there have never been any ground-burst tests in the thermonuclear range (atoll tests don't really count because of the water all around). I don't think it's unreasonable to estimate that at least at ground zero you could expect it to carve out a space a kilometre deep.

Fallout would be astonishing, since all the dirt and rock that used to be in that crater would be scooped up in the enormous mushroom cloud and distributed over an absolutely enormous area (that is, in fact, one of the reasons that Tsar Bomba was limited to 50 MT). Depending on prevailing winds, you could see an area as large as the eastern seaboard of the United States rendered uninhabitable for decades.

But even after the radiation had died down to levels that were within an order of magnitude of the background radiation for the region, I don't know if the results of a ground-burst full-yield 100 MT nuclear detonation would ever fade to the degree where the area would look "unaffected". In that power range, it's comparable to a meteor strike, so it would take thousands or tens of thousands of years of erosion and deposition before the crater was worn down and the bedrock eroded and re-covered with the soil and plants scythed from it by the blast.

(All back-of-the-envelope calculations regarding radius and fallout spread provided by NukeMap, a fantastic resource for this sort of thing.)

Edit:

For comparison there's Lake Bosumtwi. It is the middle of an impact crater that is approximately the same size as this 100 MT bomb's hypothetically would be. It has also been around for approximately 1.1 million years. The area is green and fertile, yes, but geographically, any event of that magnitude will leave the area changed effectively forever.

Any amount of radiation is bad for your health. On the other hand, there is natural background radiation on Earth, so the question would be when do the weapon effects become so low that it takes a systematic scientific study to tell the difference?

• It depends on the design of the weapon. Salted weapons were designed to produce extra fallout. Ground bursts also produce more fallout than air bursts.
• Bikini is still considered too unhealthy to live. But pictures of the plant life look normal to the layman.

So less than a century for a slightly bigger bomb, if significantly increased cancer risks are ignored.

• It also depends in which kind of "salt" you are using; "standard" design, using cobalt, would produce heavy radiation via Co-60, but that has a half life just over 5 years, so it wouldn't add much to "clean out" time. – ZioByte Aug 5 '17 at 19:24
• Re "Any amount of radiation is bad for your health", this is certainly not proven, and probably not true. People who live in areas with higher than average natural background radiation tend to be healthier than those who live in low radiation areas: en.wikipedia.org/wiki/Radiation_hormesis – jamesqf Aug 6 '17 at 4:10