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Answer :
To match the energy released by 1 metric ton of TNT, a minuscule amount of ²³⁵U is required, far less than the smallest provided option of 10 grams. Therefore, the correct option is 1) 10 grams.
To determine approximately how many grams of ²³⁵U (uranium-235) are needed to provide the same amount of energy as 1 metric ton of TNT by fission reactions, we need to understand the energy released by the fission of ²³⁵U and compare it to the energy released by TNT.
One gram of ²³⁵U has 1.42 × 10^{26} atoms. From the provided references, we know that each fission of ²³⁵U releases about 200 MeV (megaelectron volts) or 3.2 × 10^{-11} joules of energy, and the detonation of 1 metric ton of TNT releases about 4.184 × 10^{9} joules. Now we can calculate the number of fissions and the corresponding mass of ²³⁵U required to match the energy of TNT.
First, calculate the number of fission events needed for the same energy as TNT:
4.184 × 10^{9} joules (TNT energy) / 3.2 × 10^{-11} joules (energy per fission) = 1.31 × 10^{20} fissions required.
Next, determine the mass of ²³⁵U for these many fissions:
1.31 × 10^{20} fissions / 1.42 × 10^{26} atoms per gram = 9.23 × 10^{-7} grams of ²³⁵U.
Since this number is much less than even the smallest option provided (10 grams), it indicates that a tiny amount of ²³⁵U is needed to release the same amount of energy as 1 metric ton of TNT. Thus, the correct option is 1) 10 grams.
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