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NCERT Class XII Chapter
Nuclei
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Question : 30 of 31
Marks: +1, -0
Calculate and compare the energy released by (a) fusion of 1.0 kg of hydrogen deep within the Sun and (b) the fission of 1.0 kg of  235U\,{}^{235}\mathrm{U} in a fission reactor.
Solution:  
(a) In the fusion reactions taking place within core of sun, 4 hydrogen nuclei combines to form a helium nucleus with the release of 26 MeV of energy.
4 11H4\,{}^{1}_{1}\mathrm{H} →  24He+2e+\,{}^{4}_{2}\mathrm{He} + 2e^{+} + 26 MeV
Number of atoms in 1 kg of  11H\,{}^{{\underset{1}{1}}}\mathrm{H} ,
n = 1000 g×6×1023Atomic mass\frac{1000\,\mathrm{g} \times 6 \times 10^{23}}{\text{Atomic mass}} = 1000 g1 g\frac{1000\,\mathrm{g}}{1\,\mathrm{g}} × 6 × 102310^{23} = 6 × 102610^{26} atoms
Energy released in the fusion of 1 kg of  11\,{}^{\underset{1}{1}} H,
E1E_1 = 6×1026×264\frac{6 \times 10^{26} \times 26}{4} MeV = 39 × 102610^{26} MeV
(b) Energy released per fission of U-235 is 200 MeV.
Number of atoms in 1 kg of U-235,
n = 1000 g×6×1023235 g\frac{1000\,\mathrm{g} \times 6 \times 10^{23}}{235\,\mathrm{g}} = 25.53 × 102310^{23} atoms
Total energy released for fission of 1 kg of uranium,
E2E_2 = 25.53 × 102310^{23} × 200 MeV = 5.1 × 102610^{26} MeV
E1E2\frac{E_1}{E_2} = 39×10265.1×1026\frac{39 \times 10^{26}}{5.1 \times 10^{26}} = 7.65 = 8
So the energy released in fusion of 1 kg of Hydrogen is nearly 8 times the energy released in fission of 1 kg of uranium-235.
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