A 50 kiloton atomic bomb is fueled with pure 235 U, 4.0% of which actually under

Question

A 50 kiloton atomic bomb is fueled with pure 235U, 4.0% of which actually undergoes fission. (a) What is the mass of uranium in the bomb? (It is not 50 kilotons - that is the amount of 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.) 1 megaton of TNT produces 2.6 x 1028 MeV of energy. Assume each fission event releases 200 MeV of energy.

Explanation / Answer

given that ::

It is not 50 kilotons - that is the amount of released energy specified in terms of the mass of TNT required to produce the same amount of energy.

ton of TNT" is a unit of energy equal to 4.184 gigajoules.

kiloton of TNT = 4.184 x 1012 J or 4.184 terajoules.

(a) the mass of uranium in the bomb is given as ::

E = m c2                                      { eq. 1 }

where, c = speed of light = 3 x 108 m/s

E = energy required = 50 x 4.184 x 1012 J

inserting the value in above eq.

(50 x 4.184 x 1012 J) = m (3 x 108 m/s)2

m = 2.3 x 10-3 kg

(b) two primary fission fragments are produced.

(c) neutrons generated in the fissions are released to the environment is given as ::

U-235 + n ==> U-236

U-236 ===> fission fragments (+ 2 to 4 neutrons) (+ 200 MeV energy (approx.) )

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