It is possible to follow the mixing by tracers like the 14C bomb spike and CFC's, both increased rapidely after WWII. (joannenova.com.au)
Fossil fuel combustion has dispersed fly ash particles worldwide, pretty well coincident with the peak distribution of the «bomb spike» of radionuclides generated by atmospheric testing of nuclear weapons, Dr Waters says. (climatenewsnetwork.net)
Different half lives: the 5 year calculated from the bomb spike is about how fast 14C (natural or not) disappears out of the atmosphere, but is not destroyed: it simply is gone into other reservoirs (oceans and plants) and / or replaced by stable carbon (12C and 13C) from the other reservoirs. (wattsupwiththat.com)