I am pretty sure the first bomb dropping was justifiable on grounds that it shortened the war and the resultant loss of life from the bomb was less than the loss of life from a seaborne invasion of mainland Japan.
The second bomb is IMO not so easily justified. smacks more of a live experiment as it was a different type of bomb.
I'm not sure that this is wholly true. The first bomb didn't shorten the war in itself as Japan refused to surrender after it and a second bomb was required in order to convince them that it might be a good idea.
I've no doubt that the second bomb had a wider significance with the USSR suddenly looming large on the Manchurian horizon and declaring war on Japan the day before Nagasaki. However, the first and second bomb combined, saved the lives of millions of people both allied and Japanese that would have resulted from an invasion of Japan or from it's destruction from above by conventional arms.