What is the smallest nuclear bomb that could be built and what kind of devastation would it produce?

Question
Mudassir Ali 8 months 1 Answer 91 views

Answer ( 1 )

  1. For U-235 (fission), the enthalpy is estimated to 83.24 * 10^12 J/kg.

    The (smallest) critical mass is about 57 kg.

    Then just multiply the two numbers: 57 kg * 83.24 * 10^12 J/kg

    = 4744.68 * 10^12 J.

    1 ton of TriNitroToluen makes 4.184 * 10^15 J.

    So the smallest bomb is about 1 ton of TNT.

    -The bomb left on Hiroshima was about 12 000 tons of TNT in energy.

    -Since the energy of a field is proportional to the reverse of the squared radius,

    12 000 tons-energy * 1/R^2 = 1 ton-energy * 1/r^2, where r < R.

    r^2/R^2 = 1/(12 000), r/R = SquareRoot(1/12000) = about 1%.

    -So the smallest nuclear bomb would destruct about the 12000th of the Hiroshima of 1945, if the structures were equally dispatched and that the actual bomb of these times destructed all the town (no more nor less).

    The population of this town was of 340 000. A proportion was survivant to this attack, but the comb was calculated enough, to make other damages. We could approximate hat the smallest bomb would kill about 30 people; that appears little, so the actual bomb of 1945 made other damages outside, for sure.

    Hiroshima was established over (about) 900 km^2. So let’s approximate it was on a disk:

    900 km^2 = Pi*R^2. R = SquareRoot(900 km^2/Pi) = 17 km (about).

    -The smallest bomb would make damages on 170 meters multiplied by 170 meters and Pi.

    Pi*(170m)^2 are about 9 hectares, and 30 people in it would be the same as the density of Hiroshima.

Leave an answer