Hi there, while you await an answer to your question, you may also be interested in this section of our FAQs which deals with the "need" for the atomic bomb. In particular, these threads may be of interest:

https://www.reddit.com/r/AskHistorians/comments/u6qqo/there_has_been_some_controversy_on_the_true/c4sthrz/

https://www.reddit.com/r/AskHistorians/comments/2todt6/did_the_us_have_to_nuke_japan_in_wwii/co17rtk/

https://www.reddit.com/r/AskHistorians/comments/24gvwd/are_tsuyoshi_hasegawas_conclusions_about_the/ch71h0y/

I highly recommend the other material that's already been posted by others, but I thought I would add an additional note from a recent book by James D. Hornfischer (The Fleet at Flood Tide).

The Atomic Bomb ended up being a very specific target - not a city - but the heart and mind of a single individual - Emperor Hirohito. The view of all involved is that the critical impact was the nuclear bomb. The United States was reading the diplomatic ciphers, and knew that the Japanese cabinet was deadlocked. It was hoped (and the Japanese emperor and cabinet confirmed) that the shock of the atomic bomb would be enough to break the deadlock permanently.

This just establishes that the nuclear bomb was sufficient, not that it was necessary. There are several more ways that the war could have ended:

1. After a starvation blockade caused a revolt or starvation of the entire Japanese population (endorsed by King and Nimitz)
2. After a ground invasion (endorsed by Marshall and MacArthur)
3. After the firebombing had reduced the remaining cities in Japan.

The other point that James D. Hornfischer made that I thought was very good is that the Japanese strategy of causing casualties to be so high that the US would reconsider invading, or offer better negotiating terms that allows Japan to keep parts of China and the dutch east Indies was working.

The battles were becoming bloodier and bloodier, and the the Allied planning had moved from a "Saipan ratio" to estimate casualties at a acceptable level with the "sinister ratio" that was projecting casulties greater then the casualties inflicted by the end of the war in Germany. Worse the greater then anticipated build up by the Japanese was causing the navy in particular to walk away from the idea of a invasion as the Japanese were outnumbering their invaders in Kyushu. The Kamikaze problem was significant as well, and the United States had no answer to the sudden spike in ship losses due to the tactic.

Does that mean that the Nuclear bomb was the only viable path? No, air bombing and blockade was the alternative to invasion, and even a invasion would be feasible with Soviet assistance.

The other points about the use of nuclear bombs is better addressed by other posts.