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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 ^{235}U in a fission reactor.

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#### Solution

**(a)** Amount of hydrogen, m = 1 kg = 1000 g

1 mole, i.e., 1 g of hydrogen `(""_1^1"H")` contains 6.023 × 10^{23} atoms.

∴ 1000 g of `""_1^1"H"` contains 6.023 × 10^{23} × 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 × 10^{23} 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.

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