[Harri (OP)]

Given that the race to build the atomic bomb was fueled by the fear that Hitler and his scientists were trying to build a bomb themselves, was it really necessary to drop 2 atomic bombs on Japan after Hitler had been defeated, the chance that Germany had developed a bomb was very low, and Japan was willing to accept defeat? Given that the populations of Hiroshima and Nagasaki consisted of mainly women, children and old people as most men were away in uniform, I personally find the decision difficult to justify.

[Bored chemist]

Japan was willing to accept defeat

That bit is debatable.

In any event, it's probably meaningless to judge the decisions made then, by the standards of today.

[syhprum]

Two bombs where dropped in rapid succession two convince the Russians that the USA had a plentiful supply of them, Stalin was not impressed he had better sources of information.
 

[Petrochemicals]

The argument was japan would never surrender, The allies would not accept this. The argument is that compared with okinawa or the tokyo firestorm  the two atom bombs saved millions of lives compared a conventional military campaign.

https://en.m.wikipedia.org/wiki/Battle_of_Okinawa

https://en.m.wikipedia.org/wiki/Bombing_of_Tokyo

[Bored chemist]

The argument was japan would never surrender, The allies would not accept this. The argument is that compared with okinawa or the tokyo firestorm  the two atom bombs saved millions of lives compared a conventional military campaign.

Actually, the argument was that it would save a lot of allied soldiers' lives.
They didn't worry too much about the opposition's casualties.
There was a war on.

[jimbobghost]

no, twice may not have been enough.

it was necessary to drop as many atomic bombs on Japan as required until they surrendered.

[David Cooper]

The best way to pretend that there were more bombs of the same kind available would have been to drop the first one over the sea fifty miles from the coast. If that had been done, the surrender might have come after the first bomb. (As it is, they tried to surrender between the two bombs but demanded that the emperor not be prosecuted, and given that he never was prosecuted, it makes you wonder why that surrender attempt wasn't accepted.) The disadvantage of that approach though is that the opportunity to test the bombs on real cities full of people would have been lost, and they must have been keen to compare the two as well because they were radically different in design.