How would the events of the Atomic Bombs be different had all of the fission material detonated?

by TKInstinct
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The Little Boy bomb had 64 kg of uranium in it. Less than 1 kg fissioned. Each kilogram of fissile material that fissions released on average around 17-18 kilotons worth of energy. So if all 64 kg had fissioned (which is not practical, but one could imagine more than the 1kg fissioning that did), it puts an upper-end of 1.2 megaton worth of energy. Which is a lot more than 15 kt. You can model it on the NUKEMAP. With today's Hiroshima population, it would result in the killing of something like 615,000 people out of a city of 1.2 million — so around 50% of the city would be fatalities, and 40% injured, so a total of about 90% of the city would be grievously affected. By contrast, the actual Hiroshima bombing killed about 120,000 people out of a city of around 340,000. So about a third. I don't know reliable numbers for injured.

As for environmental impact, not much different if it was detonated at a correspondingly high altitude. As for differences today, just more to rebuild.

We could run the same numbers with Nagasaki, but they are less interesting. The Fat Man bomb had about 6 kg of plutonium in it. If that all fissioned it would release around 110 kilotons worth of energy — "only" six times as much explosive power. Casualties would probably be similar to what actually happened.

You might be thinking, wait, how does a bomb 80X bigger not kill 80X more people, or a bomb 6X more powerful not kill 6X more people? This is because damage from bombs does not scale linearly with explosive power — the energy is radiated as a sphere, so it impacts the ground only a function of its cubic root. The rule of thumb is that if you want to increase the blast damage area by 2X, you need to increase the blast yield by 8X. So just linearly increasing the yields would not linearly increase the damage.