It is hard to know for sure how something like the advent of the atomic age affects something as large as American society. We cannot be sure as to what factors cause what effects. However, we can speculate that the advent of the atomic age made American society somewhat more fearful as a whole.
When the atomic age dawned, Americans came to feel less secure. They soon felt that their very lives were in danger at any moment. This was the era in which Americans did things like building nuclear fallout shelters. It was the era in which children were taught to “duck and cover” in case of nuclear attack. The possibility of nuclear warfare hung over everyone, it seems, making them feel less secure and at ease.
The fear of nuclear weapons can be seen as part of the cause of anti-communism. The Red Scare also helped to reduce the degree to which people felt secure in the US. This gave rise to such movies as Invasion of the Body Snatchers, which depicted in various ways the feeling that Americans were in danger.
Thus, the 1950s seem to have been a decade in which there was some degree of fear and uncertainty in US society. Some of this was surely caused by the advent of the atomic age.