> Radiation is not "spread" in the manner you are suggesting
"[in] 1987 in Goiânia, Brazil [..] a forgotten radiotherapy source was stolen from an abandoned hospital site in the city. It was subsequently handled by many people, resulting in four deaths. About 112,000 people were examined for radioactive contamination and 249 of them were found to have been contaminated"
"In the consequent cleanup operation, topsoil had to be removed from several sites, and several houses were demolished. All the objects from within those houses, including personal possessions, were seized and incinerated"[0]
That incident would appear to confirm that radiation (from a radioactive source) is able to be "spread".
[0] https://en.wikipedia.org/wiki/Goi%C3%A2nia_accident