720 energy are released when an unknown quantity of uraini um-238 isotope nuclear bomb is detonated. calculate the mass of urainium -238 isotope contained in the nuclear weapon.express your answer in grams
To calculate the mass of uranium-238 isotope contained in the nuclear weapon, we need to first determine the energy released per fission event of uranium-238.
The energy released per fission event of uranium-238 is approximately 200 MeV (million electron volts).
First, convert the energy released in the detonation from electron volts to joules:
1 eV = 1.602 x 10^-19 J, so 1 MeV = 1 x 10^6 eV = 1 x 10^6 x 1.602 x 10^-19 J = 1.602 x 10^-13 J
Therefore, 720 MeV = 720 x 1.602 x 10^-13 J = 1.154 x 10^-10 J
For uranium-238, the binding energy per nucleon is approximately 7.6 MeV. To calculate the number of fissions, divide the energy released by the energy per fission:
(Binding energy per nucleon) x (mass number) = energy per fission
7.6 MeV x 238 = 1812.8 MeV = 1.8128 x 10^-10 J per fission
Number of fissions = Energy released in detonation / Energy per fission
= 1.154 x 10^-10 J / 1.8128 x 10^-10 J
≈ 63.56
The average mass of uranium-238 is 238 g/mol. Therefore, the mass of uranium-238 isotope contained in the nuclear weapon is:
Mass of uranium-238 = Number of fissions x Atomic mass of Uranium-238
= 63.56 x 238 g/mol
≈ 15107.28 g or 15.10728 kg
Therefore, the mass of uranium-238 isotope contained in the nuclear weapon is approximately 15.11 kg.