There are many fallacious ideas surrounding the nuclear bombing of Hiroshima, the most prominent being that the bombing was necessary to end the war against Japan. Without the bombing, the myth goes, an invasion of the Japanese mainland with up to a million allied casualties would have been necessary. Over the past 25 years or so, a tremendous amount of scholarship has been devoted to understanding the circumstances surrounding the decision to bomb so that today no serious historian accepts at face value the popular myth (pushed ad nauseum by mainstream media) that the war would have continued for long without the bombing. I taught a course on the nuclear arms race for a number of years and wrote my own (unpublished) book on the subject, which I used in my classes. Here is a link to several questions and answers on the bombing of Hiroshima and Nagasaki:
A better understanding of the issue can be obtained from a chronology of events surrounding the A-bomb decision. Some might be surprised to find, for example, that the Japanese continued to refuse to surrender for nine days after Hiroshima and six days after Nagasaki. Indeed, they did not surrender until the U.S. sent assurances that Emperor Hirohito would be allowed to stay in place (with diminished powers, of course) subject to the occupation rule of General Douglas MacArthur. This puts the lie to the mythic claim that the A-bombs brought about the "unconditional" surrender of Japan. The most important condition, letting the Emperor stand, was agreed to. So anxious was the U.S. to extract a Japanese surrender that a fleet of 1014 aircraft was sent to bomb Tokyo on the evening of August 14-15 in the heaviest conventional bombing mission of the war. Here is a link to a detailed chronology of events from February to August 1945.
While the facts speak for themselves, I took care to provide students with enough arguments on both sides to make up their own minds about the justification of attacking Japan with A-bombs. Students were given class time to fill out the following survey on the issue which covers as many possible angles on the question as I was able to provide.