During the Cold War the Premier of the Soviet Union threaten

During the Cold War, the Premier of the Soviet Union threatened the United States with 2.0 megaton 239 Pu warheads. (Each would have yielded the equivalent of an explosion of 2.0 megatons of TNT, where 1 megaton of TNT releases 2.6 times 1028 MeV.) If the plutonium that actually fissioned had been 8.00% of the total mass of the plutonium in such a warhead, what was that total mass?

Solution

Answer:

The yield of one warhead is 2.0 megatons of TNT, or

yield = 2(2.6×10²⁸ MeV) = 5.2×10²⁸ MeV           ( where 1 megaton of TNT releases 2.6×10²⁸ Mev)

Since each fission event releases about 200 MeV of energy, the number of fissions is

N = 5.2×10²⁸ Mev / 200 Mev = 2.6×10²⁶ .

However, this only pertains to the 8.0% of Pu that undergoes fission, so the total number of Pu is

N₀ = N/0.08 = (2.6×10²⁶) / (0.08) = 3.25×10²⁷ = 5.4×10³ mol.

With M = 0.239 kg/mol,

the mass of the warhead is m = (5.4×10³ mol)(0.239 kg/mol) = 1.3×10³ kg.