Roaches can survive atomic bombs, depending on the distance between them and the bomb, they can survive.
The Mythbusters tested this myth and found that fruit flies have a better chance of surviving when exposed to high levels of radiation more than cockroaches.
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Underground vault
Far from any explosion, so you only have to handle fallout
HEPA filtered forced air supply that does not depend on external power and can run for up to 3 months without maintenance of any kind (the filter cartridges may become too radioactive to safely replace, etc.) It must have enough air changes per hour to support all the people in the shelter
3 months supply of food and water for each person in shelter
Reliable survey RADIAC for checking outside radiation dose rate, to find out when it is safe to leave
It might also help to have a hand cranked AM/SW radio to get information on state of things outside your shelter.
The best is to prevent the use of this weapon, as it is extremely destructive immediately, has lingering radiation danger at the blast site, and can spread radioactive particles over a wide area - including particles transferred by wind or water.
If you have to plan to defend against a nuclear detonation, massive concrete bunkers that are sealed from outside air could work, but then you need to stay in the bunker for anywhere from weeks to many months before it would be only marginally dangerous to leave the bunker for short periods.
Nuclear based weapons, (atomic, hydrogen, neutron bombs) are so destructive that their use should only be an absolute last resort - and even then it might not be worth it. It is conceivable that a 'nuclear war' might eradicate the entire human race.
Well lots of people survived the actual bomb blast and the following shock and heat wave. It the radiation and the radiated fall out that killed many survivors of the initial blast, heat, shock waves. Part of the survival rate was due to location and prevailing winds, so long as one was up wind from the fallout and got away from the epicenter of the blast as soon as possible, your chances were better than staying close to the epicenter and being subjected to the fallout of the radioactive dust.
yes and no if the bomb went off and you were on the other side of the state yes underground depends 500 miles away no 15,000 yes
It is possible to survive the radiation if you are surronded by a layer of lead. The thicker, the better.