High School

Determine the energy released from the fission reaction of 1.0 kg of uranium-235, which is the critical mass of uranium-235.

a) \(3.8 \times 10^{13} \, \text{J}\)

b) \(6.3 \times 10^{13} \, \text{J}\)

c) \(9.1 \times 10^{13} \, \text{J}\)

d) \(1.2 \times 10^{14} \, \text{J}\)

Answer :

Final answer:

The energy released from the fission of 1.0 kg of uranium-235 is calculated by determining the number of atoms in 1.0 kg of uranium-235 and then multiplying by the average energy per fission reaction of 200 MeV. This is converted to joules using the conversion factor for MeV to joules.

Explanation:

To determine the energy released from the fission reaction of 1.0 kg of uranium-235, we use the given average energy per fission reaction of uranium-235, which is 200 MeV. First, we need to calculate the number of uranium-235 atoms in 1.0 kg. Since 1 mole of uranium-235 has a mass of 235.04 g, 1.0 kg equals 1000 g, which gives us approximately 4.25 moles of uranium-235.

Next, we multiply the number of moles by Avogadro's number to find the total number of atoms, then we multiply that number by the energy per reaction, taking into consideration the conversion from MeV to joules. The energy released in joules (J) is then found by:

  1. Number of moles = 1000 g / 235.04 g/mol = 4.25 mol
  2. Number of atoms = 4.25 mol × 6.02 × 10²³ atoms/mol
  3. Total energy in MeV = Number of atoms × 200 MeV/atom
  4. 1 MeV = 1.602 × 10⁻¹³ J
  5. Total energy in joules = Total energy in MeV × 1.602 × 10⁻¹³ J/MeV

Performing this calculation should give us the energy released from the fission of 1.0 kg of uranium-235.

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