[20 points] How much is \"a lot?\" \"Little Boy,\" the gun-type nuclear weapon d
ID: 2304501 • Letter: #
Question
[20 points] How much is "a lot?" "Little Boy," the gun-type nuclear weapon dropped on Hiroshima, Japan on August 6, 1945 contained 64 kg of 80% enriched uranium. This is roughly the mass of an average man and may seem like a relatively small amount of material. With higher enrichment, as little as~20 kg could be enough to produce a weapon. a) As we've discussed, only a small fraction of natural uranium is U-235. What mass of 2. yellowcake would be required to produce the HEU used in Little Boy? (Recall that yellowcake is composed of both natural uranium and oxygen as U308.) b) The contentious Uranium One company (Google "Uranium One scandal") supplies about 8000 metric tons of yellowcake annually. How many Little Boys could this yield? c) We know from our studies of nuclear physics that very tiny amounts of mass equate to large releases of energy. Little Boy exploded with an energy of 16 kilotons of TNT (67 TJ). Using E-mc2, how much mass must have been converted into pure energy during detonation? d) The mass of a modern penny is 2.5 g. What fraction of a penny's mass does your answer from part (c) correspond to? (Via nuclear reactions, this miniscule mass provided Little Boy's enormous energy yield. A critical mass is required to initiate and sustain this reaction, but not nearly all of the material undergoes fission.)Explanation / Answer
Yellow cake is the uranium ore mainly contaning U3O8 , natural uranium
it contains 0.7% of U-235 and the rest U-238
by wieght yellow cake contains 238*3/ (238*3 + 16*8) * 0.7
= 0.59 % of U-235
little boy has 80% U-235 and wieghs 64 kg
to make little boy (80% U-235) we need 80/0.59 = 135.59 time of the yellow cake
for the little boy we need 135.59*64 = 8678 kg of yellow cake.
b) yellow cak supplied = 8000*1000 kg
little boys yield = 8000*1000/8678 = 921.9
c)energy of explosion with little boy = 67e+12 J
= mc2
m = 67e+12 * 9.0e-16 = 6.03e-2 kg
= 60.3 gms of the matter is converted to energy.
mass of penny = 2.5 gms
= 2.5/60.3 = 0.04 part of the mass destroyed in little boy explosion.
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