There was one more bomb and Col. Tibbets had sent three B-29’s back the United States to bring it out to Tinian. However, General Groves (The head of the Manhattan Engineer District) had ordered all shipments of atomic weapons to the Pacific halted for several days to see if Japan would surrender.
At the same time, the scientists at Los Alamos were working to construct new bombs are rapidly as possible. They would have had anywhere from 4 to 10 completed by the end of 1945.
That fits with what I was taught.
As the invasion of Japan was scheduled for November of 1945 there was time to have atomized at least 4 more Japanese cities before the invasion was even possible.
Even if the coup had succeeded I don't think it would have been able to hold on to power with the destruction of four more cities.
Thanks, apparently that a-bomb had no name (?).