How many atoms you need to break to make an atomic bomb?
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Little boy had 64 kg of uranium. At most 5% of that fissioned so some 3kg. Atomic weight of weapons grade uranium is 235, so 235 gram per mole. That means 3/0.235 moles or about 13 moles fissioned. 1 mole is 6×10^23 atoms so about 8×10^24 atoms for that one. Yes that is an 8 with 24 zeroes behind it.
The smallest production nuclear weapon was the US made Mk-54 known more commonly as the Davy Crockett. A 110 pound man portable nuclear weapon with an approximately 20 Ton yield.
It contained roughly 7 ounces of Uranium.
Of that between 1% and 15% of the material would undergo ~~fusion~~ fission during the detonation.
Exactly how much Uranium was in the Davy Crockett, and how much would fission I can’t say exactly because of lack of available documentation. The smaller and simpler nuclear weapons including Little Boy had only about 1% of it’s nuclear material undergo fission, while Fat Man and more more enriched weapons (Hydrogen bombs) are closer to 15%.
Smaller nuclear weapons than the Davy Crockett are theoretically possible, but not practical.
In terms of math:
7 oz of Uranium is about 10 cubic centimeters.
That’s about 190 grams
Uranium 235 has about 2.5626135×10^21 atoms per gram so 190 grams of U235 would be: 486,896,565,000,000,000,000,000 atoms or 486 sextillion
Since the smallest and simplest bomb type requires you to break 1% of those atoms, you would need to break
486,896,565,000,000,000,000 atoms or 486 Quintillion
Every atom of uranium you split releases about 200 MeV, which is a tiny unit of energy for a human being, but a lot for an atom. (It’s about as much energy as you’d need to visibly move a speck of dust, which doesn’t seem like much, but atoms are much, much smaller than specks of dust. In terms of scale it’s like an ant being able to make a Space Shuttle wobble by kicking it.) To make an explosion, you need to make lots and lots of atoms split.
You can use Google to tell you how many atoms you’d need to split to get a given amount of explosive output. For example, for the Hiroshima bomb, which was 15 kilotons of TNT, that is [~2 x 10^24 atoms](https://www.google.com/search?q=15+kilotons+of+TNT+%2F+200+MeV+%3D+%3F&oq=15+kilotons+of+TNT+%2F+200+MeV+%3D+%3F). If you want to know how much that might weigh, just multiply that number (2e24) by the weight of the atom you are splitting — [2e24 * 235 amu = ~0.8 kg](https://www.google.com/search?q=2e24+*+235+amu+%3D+%3F+kg&oq=2e24+*+235+amu+%3D+%3F+kg). (I think it is pretty neat that Google lets you convert the units this easily.)
So I usually just say “on the order of a trillion trillion” which gives a sense of the immensity of it, even for a relatively small (by modern standards) atomic bomb.
So it’s a lot of atoms. You can think of an atomic bomb as a very specialized engineering device designed to cause a trillion trillion atoms or more to split in less than a millisecond.
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