A 77 kiloton atomic bomb is fueled with pure^235 U, 4.0% of which actually under

Question

A 77 kiloton atomic bomb is fueled with pure^235 U, 4.0% of which actually undergoes fission. (a) What is the mass of uranium in the bomb? (It is not 77 kilotons-that is the amount released energy specified in terms of the mass of TNT required to produce the same amount of energy.) (b) How many primary fission fragments are produced? (c) How many neutrons generated in the fissions are released to the environment? (On average, each fission produces 2, 5 neutrons, Assume 2 neutrons per fission create further fissions.) 1 megaton of TNT produces 2.6 times 10^MeV of energy. Assume each fission event releases 200 MeV of energy.

Explanation / Answer

a)

The energy yield of the bomb is

E=(77*10-3Megaton)(2.6*1028MeV/megaton)=2.002*1027 MeV

at 200 MeV per fission event

(2.002*1027)/200=1.001*1025 fission events takes place,

only 4% of 235U nuclei originally present undergo fission there must have been

=1.001*1025/0.04=2.5025*1026 nuclei originally present

the mass of 235U is

m=2.5025*1026*235*1.661*10-27=97.68 kg

m=97.7 kg (approx)

b)

two fragments are produced in each fission event ,so total number of fragments are

=2*(1.001*1025)=2.002*1025

c)

one neutron produced in each fission event is used to trigger the next fission event ,so the average number of neutrons released to the environment in each event is 2.5.the total number released is

=(1.001*1025)*2.5=2.5025*1025

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