What was president Truman's chief priority in using the atomic bomb against japan

The atomic bomb is the result of the Manhattan Project, which Albert Einstein was actually a part of as well. As to why Truman decided to use the atomic bomb against Japan, the answer is involved by several factors.

1. Location, Japan is isolated, so any harm done would have "directly" been restrained to Japan.

2. A show of military might, The atomic bomb was the USA's ace in the hole. The adverse effects of this though is that an arms race for nuclear weapons began after WW2 and resulted in The Cold War.