Final answer:
To find the energy released by 0.4 kg of a material undergoing fission, the mass is converted to atomic mass units, the number of nuclei is calculated using Avogadro's number, and the total energy is found by multiplying the number of nuclei by 180 MeV.
Step-by-step explanation:
The question is asking how much energy in megaelectronvolts (MeV) would be released if 0.4 kg of a material with an atomic mass of 239.7 u undergoes fission, given that the fission of one nucleus of this material releases 180 MeV. To find the total energy released from 0.4 kg of the substance, we need to calculate the number of nuclei in 0.4 kg and then multiply this by the energy released per nucleus.
First, we convert the mass from kilograms to grams, and then to atomic mass units (u). We then divide by the atomic mass of the substance to get the number of moles, and finally use Avogadro's number to find the number of nuclei. The energy released is the number of nuclei times 180 MeV per nucleus.
0.4 kg is equal to 400 grams, and since 1 gram is equal to 6.022×10²23 u, we have 400 × 6.022×10²23 u in 0.4 kg. Then divide by the atomic mass of the nucleus (239.7 u) to get the number of moles. Multiply the number of moles by Avogadro's number (6.022×10²23) to find the number of nuclei. Finally, multiply the number of nuclei by 180 MeV to find the total energy released.
The solution involves calculations of mass-to-energy conversion and utilizes the concepts of nuclear fission and Avogadro's number.