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Answer :
Final answer:
The energy comparison between fusion of 1 kg of hydrogen and fission of 1 kg of U-235 is made using Einstein's mass-energy equivalence principle. Fusion yields about 0.7% of the mass as energy, notably more than the energy produced per mass in fission reactions. The ratios of mass destroyed to the original mass indicate that fusion is a more potent energy source than fission.
Explanation:
Energy Comparison between Fusion and Fission
To compare the energy released by fusion of 1.0 kg of hydrogen and the fission of 1.0 kg of U-235, we first need to understand the mass-energy equivalence principle given by Einstein's equation, E=mc^2, where E represents energy, m is mass, and c is the speed of light.
For fusion:
- Fusion of hydrogen into helium yields about 0.7% of the mass as energy.
- Therefore, by converting 1.00 kg of hydrogen, (1.00 kg * 0.007) of mass is converted into energy.
- Using Einstein's equation, we calculate the energy produced.
For fission:
- An average nuclear fission reaction of 235U produces roughly 200 MeV of energy.
- To find the total energy produced by fissioning 1.00 kg of U-235, we multiply the number of atoms in 1 kg by the energy per reaction.
The ratio of mass destroyed to the original mass (Am/m) can be calculated for both processes and compared. The
Am/m ratio for fusion is 0.007, and the Am/m ratio for fission can be determined if we know the total number of fissions occurring in 1 kg of U-235 based on its atomic weight.
In conclusion, fusion of hydrogen releases significantly more energy per kilogram than fission of uranium-235, as demonstrated by the
Am/m ratios and calculations described above. This comparison highlights the potential of fusion energy as a much more potent source than fission.
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