Danger of Lingering Radiation

The map that Dr Medford uses to find the location of Gramps' store shows that the latter is right next door to the area where nuclear tests were conducted in 1945.
Wouldn't that have put Gramps in danger of suffering radiation poisoning, as happened to the cast and crew of THE CONQUEROR in 1956?

God is subtle, but He is not malicious. (Albert Einstein)