I want to make the point that the bombs didn't matter in the Japanese emperor's decision to surrender.
1. The a-bombs did terrible destruction, but the incendiary bombs we dropped, like on Tokyo, did the same scale of damage. The incendiary bombs just took longer.
2. Several cities had been fire bombed by that point. People were used to it.
3. Nagasaki was bombed August 9.
4. The Japanese surrendered September 6. That's like a month from the a-bombs to the surrender. The Japanese weren't all that impressed by the a-bombs. The bombs certainly didn't speed up their surrender.
5. Even after Hiroshima and Nagasaki were nuked, the Japanese still would not surrender.
6. America sent the Japanese this note
https://www.ibiblio.org/pha/policy/1945/1945-08-11a.html
7. This is the key phrase from the note: "The ultimate form of government of Japan shall, in accordance with the Potsdam Declaration, be established by the freely expressed will of the Japanese people."
8. That told the emperor, he could keep his job.
9. Japan surrendered.