World is
4,000,000,000 years old
Radio Active Fall Out will kill humans and pollute the lands for 50-200 years.
Which is not even eye blink in term of age of earth.
So world will not be destroyed , it will wipe of all life no doubt but once the radioactivity will reside things will grow back, there would be plants but with out insects , they won't be able to grow or fertilize in numbers so life will reemerge in patches ...
But it won't be rich and diverse as it is know
Current Evolution Started as follow
> Water -> plants -> oxygen -> Diverse life -> ozone -> Land migration
If Nuclear weapons destroy life , alot of life forms will be gone for ever
may be only 1-2 % will be back and even those will lively be just plants and microbes for few billion years
Plant life is known to grow back rapidly