Question
Assume one-fourth of the yield of a typical 320-kT strategic bomb comes from fission reactions averaging 200 MeV and the remainder from fusion reactions averaging 20 MeV.
1. Calculate the number of fissions and the approximate mass of uranium and plutonium fissioned, taking the average atomic mass to be 238.
2. Find the number of fusions and calculate the approximate mass of fusion fuel, assuming an average total atomic mass of the two nuclei in each reaction to be 5.
3. Considering the masses found, does it seem reasonable that some missiles could carry 10 warheads? Discuss, noting that the nuclear fuel is only a part of the mass of a warhead.
1. $1.0\times 10^{25}$ fissions from 4.1 kg of fissionable material.
2. $3.1\times 10^{26}$ fusions from 2.6 kg of fusion fuel.
3. The total nuclear payload is 6.7 kg which is a small mass for a rocket to carry. If this is only 10 percent of the total mass of a warhead, the warhead mass would be 67 kg. Ten warheads would be 670kg, which is a reasonable mass for a rocket to carry. Consider that two booster rockets can lift the massive space shuttle.
Solution Video

# OpenStax College Physics Solution, Chapter 32, Problem 57 (Problems & Exercises) (3:45)   