To determine the number of U-235 nuclei that undergo fission when 1 gram of U-235 is subjected to a controlled nuclear reaction, we need to calculate the number of U-235 atoms in 1 gram and then divide it by the average number of U-235 nuclei that undergo fission per atom.

The molar mass of U-235 is approximately 235 grams/mol, so there are approximately 6.022 x 10^23 U-235 nuclei per mole.

Using the molar mass, we can calculate the number of moles of U-235 in 1 gram:

Number of moles = mass / molar mass
Number of moles = 1 gram / 235 grams/mol
Number of moles = 0.004255 moles

Since there are approximately 6.022 x 10^23 U-235 nuclei per mole, we can calculate the number of U-235 nuclei in 1 gram:

Number of U-235 nuclei = number of moles x Avogadro's number
Number of U-235 nuclei = 0.004255 moles x (6.022 x 10^23 nuclei/mol)
Number of U-235 nuclei = 2.563 x 10^21 nuclei

Now, assuming an average energy release per fission event, we need to divide the number of U-235 nuclei by the average number of U-235 nuclei that undergo fission per atom. This depends on the specific conditions of the controlled nuclear reaction.

Let's assume that on average, 2 U-235 nuclei undergo fission per atom in the reaction. So, the number of U-235 nuclei that undergo fission is:

Number of U-235 nuclei that undergo fission = Number of U-235 nuclei / Average number of U-235 nuclei that undergo fission per atom
Number of U-235 nuclei that undergo fission = (2.563 x 10^21 nuclei) / 2
Number of U-235 nuclei that undergo fission = 1.2825 x 10^21 nuclei

Therefore, approximately 1.2825 x 10^21 U-235 nuclei undergo fission when 1 gram of U-235 is subjected to a controlled nuclear reaction, assuming an average energy release per fission event.

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