Answer :
Final answer:
The energy released by the fusion of 1.0 kg of hydrogen and the fission of 1.0 kg of U-235 is calculated using Einstein's equation E=mc^2. The ratio of mass converted to energy (
Δm/m
) is computed to compare the efficiency of these processes, with fusion typically being more efficient than fission.
Explanation:
Calculating Energy from Nuclear Reactions
To calculate the energy released by the fusion of 1.0 kg of hydrogen and the fission of 1.0 kg of uranium-235 (U-235), we use Einstein's equation E=mc2. This establishes a relationship between mass (m) and energy (E), with c representing the speed of light in a vacuum.
For hydrogen fusion, the process that occurs in the Sun, we know from nuclear physics data that the fusion of deuterium and tritium (isotopes of hydrogen) yields approximately 17.6 MeV for each reaction. If we assume a similar yield per nucleon for fusion reactions involving pure hydrogen, we can estimate the total energy released with the given mass.
Nuclear fission of U-235, on the other hand, releases about 200 MeV of energy per fission. By calculating the number of atoms in 1.0 kg of U-235 and multiplying it by the energy per fission, we find the total energy released.
To compare the efficiency of these processes, we would calculate the ratio of mass converted to energy (
Δm/m
), where
Δm
is the mass converted to energy and
m
is the original mass. This ratio is higher for fusion than for fission, indicating that fusion is a more efficient process for converting mass into energy, although both processes release significant amounts of energy.
