Ok heres how this would happen:
Cherynobal (im a bad speller k?) was a reactor malfuction that caused it to leak or explode a small part of the reactor realesing nuclear dust or fallout, when after a short while (a couple monthes to 10 years) this dust settles down and gets washed away or just looses radation. causing life to return quite fast. Also they tried to make it go away and made sure it wouldnt kill anyone and they treated people fast. Ok thats chernobal
Fallout 3's world was nuked, go wacth some nuclear bomb tests on youtube to see what they look like. When the bombs fell they were mostly trying to hit large populated centers (hmm... ney york.. wonder whats going on there *wink* ) trying to kill as many restince as possible. People ran for cover and failed due to the fact that the light that is generated from an atomic weapon burns just about everything and melts everything, cause most houses to burn down and/or get totally blown away from the force of the blast. Making underground seem more better. So as people went underground to seek shelter (vaults) they were protected from most nuclear fallout. Back on track nukes will take your breath away (no i am serious) because of the blast creating so much o2 needs (see when a nuke goes off theres 2 blasts a strong foward blast and a reverse blast of the O2 suction effect), causing most fires unless at the epicenter of the blast (which actually wouldn't have anything there due to the fact that it would A: evaporate due to heat B: atoms are broken apart *insat kill* C: the intense blast knocks you out and u burn/radiate/melt). So most wouldnt survie, thats when the vaults come in most of the world would actually be black, the sky, ground,water would be grey beacuse of the blasts (this is also why it doesnt rain/snow/hail/sleet in fallout all clouds water sources were instally burned when the nukes went off, now the rivers probley came from the ice caps on both bottom and top as the world probley heated well above 1000F (degrees) or about 200C causing them to melt then evaporate and rain causing a massive world ecosystem change. making it all most impossiable for anything to live throught the blast.) also it would be impossiable to do anything becuase of the radiontion of the blasts would murder the upper atmopshere and kill everything with cancer, and anyoen whom would step outside would breath the dust like in chernobal but only 100x stronger.) when your 200 years ahead of this terriable stuff the dust is gone and most things would be dead.... thus making everyone a scavenger or a mutent trying to kill them, making life hard and tuff. So that makes my point
P.s. this was made by a 12 year old
got out smarted bah me!