calculate the rate at which atoms of a particular fission product are being produced directly by 1 kg of 235U in a thermal neutron flux of 6.92x10^13 if the radionuclide's individual fission yield is .00536%
To calculate the rate at which atoms of a particular fission product are being produced directly by 1 kg of 235U in a thermal neutron flux, you need to follow these steps:
Step 1: Determine the number of uranium-235 (235U) atoms in 1 kg of uranium-235.
The molar mass of uranium-235 is approximately 235 g/mol.
Therefore, the number of uranium-235 atoms in 1 kg (1000 g) of uranium-235 can be calculated using Avogadro's number (6.022 × 10^23 atoms/mol):
Number of 235U atoms = (1000 g / 235 g/mol) × (6.022 × 10^23 atoms/mol)
Step 2: Calculate the rate of fission for 1 kg of uranium-235.
The rate of fission per second for 1 kg of uranium-235 can be calculated using the thermal neutron flux (number of neutrons per square centimeter per second) and the fission cross-section of uranium-235.
Fission rate = Thermal neutron flux × Cross-section of uranium-235
Step 3: Determine the number of fissions required to produce one atom of the fission product.
The individual fission yield is given as a percentage, which represents the fraction of fissions resulting in the production of the specific fission product. To find the number of fissions required to produce one atom of the fission product, we need to take the reciprocal of the individual fission yield:
Number of fissions required = 1 / (Individual fission yield as a fraction)
Step 4: Calculate the rate at which the atoms of the fission product are being produced.
The rate can be calculated by multiplying the number of fissions per second by the number of fission product atoms produced per fission:
Rate of fission product atoms produced = Fission rate × Number of fission product atoms per fission
Let's put these steps into practice using the given values:
Thermal neutron flux = 6.92 × 10^13 neutrons/cm^2/s
Individual fission yield = 0.00536% = 0.00536/100 = 0.0000536 (as a fraction)
Step 1: Number of 235U atoms in 1 kg of uranium-235:
Number of 235U atoms = (1000 g / 235 g/mol) × (6.022 × 10^23 atoms/mol)
Step 2: Rate of fission for 1 kg of uranium-235:
Fission rate = Thermal neutron flux × Cross-section of uranium-235
Step 3: Number of fissions required to produce one atom of the fission product:
Number of fissions required = 1 / (0.0000536)
Step 4: Rate at which the atoms of the fission product are being produced:
Rate of fission product atoms produced = Fission rate × Number of fission product atoms per fission
By following these steps, you can calculate the rate at which atoms of the fission product are being produced directly by 1 kg of uranium-235 in a thermal neutron flux.