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, we need to use a formula based on the fission yield and the neutron flux.
The formula for calculating the rate of fission product production is as follows:
Rate of fission product production = (fission yield * neutron flux * number of 235U nuclei) / atomic mass of 235U
Now, let's break down the calculation step-by-step:
1. Convert the fission yield to a decimal:
Fission yield = 0.00536% = 0.00536/100 = 0.0000536
2. Calculate the number of 235U nuclei:
Number of 235U nuclei = (mass of 235U / molar mass of 235U) * Avogadro's number
The molar mass of 235U is 235 g/mol, and Avogadro's number is 6.02214076 × 10^23 mol^-1.
Number of 235U nuclei = (mass of 235U / 235) * Avogadro's number
Given that the mass of 235U is 1 kg = 1000 g:
Number of 235U nuclei = (1000 / 235) * 6.02214076 × 10^23
3. Calculate the rate of fission product production:
Rate of fission product production = (fission yield * neutron flux * number of 235U nuclei) / atomic mass of 235U
Given that the neutron flux is 6.92 × 10^13:
Rate of fission product production = (0.0000536 * 6.92 × 10^13 * (1000 / 235) * 6.02214076 × 10^23) / 235
Now, you can plug in the numbers and calculate the rate at which atoms of the particular fission product are being produced directly by 1 kg of 235U in the given thermal neutron flux.