Answer :
The energy released when 1.00 kg of uranium-235 undergoes fission is approximately 2.81 × 10¹² joules.
Initial mass = Mass of Uranium-235 + Mass of Neutron
Final mass = Mass of Iodine-136 + Mass of Yttrium-96 + 4 × Mass of Neutron
Mi = 234.9935 + 1.00867 = 235.00217 amu
Mf = 135.8401 + 95.8629 + 4 × 1.00867
= 135.8401 + 95.8629 + 4.03468
= 235.73768 amu
Mass defect (Δm):
Δm = Mi - Mf
= 235.00217 - 235.73768
= -0.73551 amu
1 amu = 1.660539 × 10⁻²⁷ kg
Mass defect (kg) = -0.73551 × 1.660539 × 10⁻²⁷
= -1.221 × 10⁻²⁸ kg
E = Δm × c²
where c = speed of light = 3 × 10⁸ m/s
E = 1.221 × 10⁻²⁸ kg × (3 × 10⁸ m/s)²
= 1.221 × 10⁻²⁸× 9 × 10¹⁶
= 1.099 × 10⁻¹² J per fission event
Molar mass of U-235 = 235.9935 g/mol
Number of moles in 1 kg = 1000 g / 235.9935 g/mol
= 4.236 mol
Number of atoms = 4.236 mol × 6.022 × 10²³ atoms/mol
= 2.55 × 10²⁴ atoms
Total Energy = 2.55 × 10²⁴ atoms × 1.099 × 10⁻¹² J/atom
= 2.81 × 10¹² J
Note the complete question is:
