Final answer:
The calculation of the energy released by the fusion of a 2.25-kg mixture of deuterium and tritium can be done using the equation E = mc². The energy per reaction is given as 17.59 MeV, which can be converted to joules. By calculating the energy released per nucleus and multiplying it by the total number of nuclei in the mixture, we can determine the total energy released in joules.
Step-by-step explanation:
The energy released by the fusion of a 2.25-kg mixture of deuterium and tritium can be calculated using the equation E = mc², where E is the energy, m is the mass, and c is the speed of light. The energy per reaction for deuterium and tritium fusion is given as 17.59 MeV. To convert this energy to joules, we can use the conversion factor of 1 MeV = 1.602 × 10^-13 J. Since there are equal numbers of deuterium and tritium nuclei in the mixture, we can calculate the energy released per nucleus and then multiply it by the total number of nuclei.
Step 1: Calculate the energy released per nucleus:
E = 17.59 MeV × 1.602 × 10^-13 J/MeV = 2.814 × 10^-12 J
Step 2: Calculate the total number of nuclei:
Number of nuclei = mass of the mixture / (mass of one nucleus × Avogadro's number)
Number of nuclei = 2.25 kg / (5 g/mol × 6.022 × 10^23 nuclei/mol)
Step 3: Calculate the total energy released:
Total energy released = Energy released per nucleus × Number of nuclei
Total energy released = 2.814 × 10^-12 J × Number of nuclei