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प्रश्न
Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of 235U in a fission reactor.
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उत्तर
(a) Amount of hydrogen, m = 1 kg = 1000 g
1 mole, i.e., 1 g of hydrogen `(""_1^1"H")` contains 6.023 × 1023 atoms.
∴ 1000 g of `""_1^1"H"` contains 6.023 × 1023 × 1000 atoms.
Within the sun, four `""_1^1"H"` nuclei combine and form one `""_2^4"He"` nucleus. In this process 26 MeV of energy is released.
Hence, the energy released from the fusion of 1 kg `""_1^1"H"` is:
`"E"_1 = (6.023 xx 10^23 xx 26 xx 10^3)/4`
`= 39.1495 xx 10^26 " MeV"`
(b) Amount of`""_92^235"U"` = 1 kg = 1000 g
1 mole, i.e., 235 g of `""_92^235"U"` contains 6.023 × 1023 atoms.
∴ 1000 g of `""_92^235"U"` contains
`(6.023 xx 10^23 xx 1000)/235 "atmos"`
It is known that the amount of energy released in the fission of one atom of `""_92^235"U"` is 200 MeV.
Hence, energy released from the fission of 1 kg of `""_92^235"U"` is:
`"E"_2 = (6 xx 10^23 xx1000 xx 200)/235`
`= 5.106 xx 10^26 " MeV"`
`therefore "E"_1/"E"_1 = (39.1495 xx 10^26)/(5.106 xx 10^26) = 7.67 ~~ 8`
Therefore, the energy released in the fusion of 1 kg of hydrogen is nearly 8 times the energy released in the fission of 1 kg of uranium.
संबंधित प्रश्न
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(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
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\[{}_{1}^{2}\mathrm{H}+_{1}^{2}\mathrm{H}\rightarrow{}_{2}^{3}\mathrm{He}+\mathrm{n}+3.27\mathrm{MeV}\]
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