Definitely. There were no other options that would have been any better for anyone.
From the American point of view, using the atomic bomb made sense. The number of Americans who would have died in an invasion of Japan would most likely have been huge (judging from how many Americans died taking relatively small islands like Saipan, Iwo Jima and Okinawa).
But even from the point of view of Japanese civilians, it's hard to imagine what would have been more humane. They would have suffered horribly from more conventional bombings and then from an invasion of their home islands.
So the atomic bomb was horrible for the people of Hiroshima and Nagasaki, but it was better for the rest of Japan and for the US, in my view.
This is a fairly profound question. I am not sure anyone can answer it with a sense of complete absolutism, especially given the massive cost of human life and implications on the world stage, of which no one could have foreseen. There is enough evidence which indicates that the use of the bomb was the only option for Truman and the United States, who sought an end to the fighting in the Pacific. Being oppositional, I tend to examine the other side, which indicated that the blockade of the Japanese and the overall military strength of the United States, with the European Theatre having come to a close, would have overpowered the Japanese. I think that the human cost of dropping the bomb and the legacy Oppenheimer's creation left afterwards has to cause some level of analysis as whether or not it should have been done. This might be confirmed when so many who worked on the project became avid opponents of it after seeing the cost of their creation.
It's difficult to imagine any responsible person not dropping the bomb. This may seem terrible to some, but the truth is that more people were killed in the firebombing of Tokyo than in either of the atomic blasts. With a projected one million US casualties for the invasion and the Japanese population being propagandized with the slogan "Ten Million Die Together," an actual invasion would have been horrific. When you add to that the fact that the Japanese Imperial Army had a million troops still under arms on the mainland of China, and troops in Korea, and troops in Vietnam, etc., it's essentially a no-brainer. The Japanese army would simply have moved the government to the mainland if it looked like the invasion forces were winning, and the war could have dragged on not only another year for the invasion but for years in China. It's hard to come up with any alternative to the bomb that could have been acceptable.
Hindsight is 20/20, and some historians have suggested that alternatives could have been explored. What if, instead of dropping the bomb on a Japanese city, there was a demonstration over open ocean or even over Mt. Fuji, a very important religious symbol to the country? What if we never dropped it and just blockaded Japan into surrender?
While they are interesting alternatives to consider, they would not have been decisions that were possible in 1945. There was virtually no one in government or the military that would have hesitated to use the bomb at all, and had I lived in 1945 and just gone through the Pacific War, I'm sure I wouldn't have either.
I believe you are asking me to decide this as a person in a position to decide on behalf of USA.
It is a very difficult question. Most certainly the nuclear weapons, and the nuclear arms race that has resulted from it are not very much in the interest of the Humanity and therefor cannot be in the long term interest of USA. But there is no clear evidence or logic to suggest that restraint in using atom bomb in 1945 would have resulted in less aggressive competition in nuclear arms race, or would have prevented any other country from ever developing or using the nuclear bomb.
Very difficult decision. May be I would have spent a sleepless night or two mulling over this question and would have consulted some very close and very wise people. I may have even tried to give some kind of credible warnings to Japan. But I do not know what would have been the result of all these. But if nothing worked, I would have perhaps used the atom bomb. On possible advantage of doing this is perhaps that it helped to end the war. If it was not used then, and the war ended in some other way, perhaps the chances of it being used subsequently would have been much more, and the consequences of that later use would have resulted in a war that would have been much more horrible than the war that ended with dropping of nuclear bomb.