Why did Truman decide to use the atomic bomb against Japan? Were there any reasons other than showing the Soviet Union what we were capable of, and getting even for the Japanese bombing Pearl Harbor?
Getting even for the Japanese bombing of Pearl Harbor was not an important consideration by the time the U.S. dropped the atomic bombs on Hiroshima and Nagasaki. They were already devastating Japanese cities with conventional bombing raids and would have completely destroyed all Japan's major cities without using atomic bombs. Once they had captured Okinawa they were within easy bombing range of Japan and could have continued massive air raids indefinitely, just as they were doing in Germany.
Japanese cities were far more vulnerable to explosive and incendiary bombs than European cities because most of the buildings were made of wood. The houses typically had interior walls made of wood and paper. The floors were covered with dried grass matting. The roofs were thatched with straw.
Showing the Soviet Union what we were capable of was probably not a strong consideration at the time, since, for one thing, we didn't really know what we were capable of, and, for another thing, we were not on hostile terms with the Soviet Union. We were encouraging them to come into the war against Japan, and we didn't know what their plans were for the years following World War II.
The most important consideration--and it wasn't entirely Truman's thinking but that of his many advisers--was that it would end the war quickly and save as many as a million American lives. It would give the Japanese an opportunity to "save face," even though they had to accept the demand for "unconditional surrender." Proof that Truman, and his advisers, were right was the fact that Japan surrendered almost immediately aboard the U.S.S. Missouri in Tokyo harbor. The surrender not only saved a million or more American lives but saved even more Japanese lives.
Perhaps one of the reasons that motivated the Americans to drop the atomic bombs on Japan was the fact that by using the bombs, the US could seek to control the circumstances of post-war Japan and to impose American control in the redesigning of Asia. The sheer costs and effort spent on developing the nuclear warhead during the Manhattan Project also meant that the concentration of cutting-edge scientists and engineers employed were generating a momentum that could not be stopped - they wanted to see the atomic bombs in use and Japan provided the best opportunity, at that time, to do so. Casualties were also a key factor. Truman had been informed by his military advisers that it was necessary to invade the Japanese mainland since the imperial army would fight on a suicidal scale to counter the American troops. Due to such a tenacity in fighting, a high casualty count was to be expected from the American forces. This estimation greatly influenced Truman in his decision-making, since the operationally-ready nuclear weapons could be used to force Japan to surrender without an invasion of the mainland and the incursion of high casualty numbers - they could be used to preserve American life.