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
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