I wonder if it really scared Stalin. He knew that the Allies had the atomic bomb, thanks to his spy rings. When Truman announced at Potsdam, they had the bomb, Stalin didn't bat en eyelid, suprising the Americans who thought he would have shown at least a mild reaction to the news.
Brad, that 100% correct, and the Russians soon obtained information on how to build their own atomic weapons via spies in the US.