How many atomic bombs will it take to destroy the world?
An air burst (detonating a bomb above the surface) would produce far more damage and death via radioactive fallout than one detonating at ground level.
A single 100 megaton air burst would be enough to cause a nuclear winter and pollute the Earth for many many years. Theoretically, a 100 megaton bomb detonated below ground could produce a massive earthquake and the constant explosions of a full blown nuclear war may also cause numerous earthquakes around the globe. But this would not destroy the world nor all human life.
Globally there are not enough nuclear bombs to completely kill every human. The Tsar Bomb (largest bomb ever detonated) had a fallout of 1000 square kilometres, and was 50 MT. The world is close to 150 million square kilometres, and the human population covers close to 18 million square kilometres.
Therefore to get a rough idea we can say hypothetically that the 5000 megatones of nuclear warheads was 100 Tsar Bombs (the same value in megatons). If these bombs were detonated their total radioactive fallout would cover 100,000 square kilometres.
It may be surprising to hear that this covers less than 1% of the area that the human population covers, which should give a general idea of the miniscule size of impact this would have on the total world's surface. Therefore it can be shown that we do not have the capacity at the moment to destory the world with nuclear warheads.
However, there are factors we have overlooked, which include:
- Tsar Bomb has a very small radioactive fallout in comparison with its megatone value
- Nuclear wardheads can be assumed to target densly populated locations, and
- Nuclear winter which would result in the radioactive fallout
To put curiousty to rest, even if we replaced our Tsar Bomb equation with nuclear warheads that had a higher radioactive yield to fulfill the 5000 megatons gloabl nuclear arsenal we would still not come close to the amount of radioactive fallout required to cover the area the human population covers, let alone destroy the world.
If nuclear warheads were targeted at densly populated locations it would increase the fatalities of a nuclear war, however this would still not wipe out humanity, let alone destory the world.
Nuclear winter can in lamer terms be contrasted with the ice age. The ice age did not destory the world, and did not wipe out all life, therefore neither would nuclear winter. Humanity is extremley resilient, and although many of the world's population die due to starvation if they did not die from the initial nuclear war or radiation, life will find a way.
You forgot to take into account the amount of radiation there would be if more than one detonated at a single time.
My U.S. History teacher told us that if 8 nuclear bombs went off at roughly the same time, it would kill 95% of life in planet Earth.