Calculate and compare the energy released by (a) fusion of 1.0kg of hydrogen deep within the sun, and (b) the fission of 1.0kg of `U^(235)` in a fission reactor.

Explanation

(a) Amount of hydrogen, m=1 kg=1000g
1 mole, i.e, 1g of hydrogen `(""_(1)^(1)H)` contains `6.023xx10^(23)` atoms.
`therefore` 1000g of `""_(1)^(1)H` contains `6.023xx10^(23)xx1000` 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)=(6.023xx10^(23)xx26xx10^(3))/(4)`
`=39.1495xx10^(26) MeV`
(b) Amount of `""_(92)^(235)U=1 kg=1000g`
1 mole,i.e.,235 g of `""_(92)^(235)U` contains `6.023xx10^(23)` atoms.
`therefore`1000 g of `""_(92)^(235)U` contains `(6.023xx10^(23)xx1000)/(235)"atoms"`
It is known that the amount of enegy released in the fission of one atom of `""_(92)^(235)U` is 200MeV.
Hence, energy released from the fission of 1 kg of `""_(92)^(235)U` is :
`E_(2)=(6xx10^(23)xx1000xx200)/(235)`
`=5.106 xx10^(26)MeV`
`therefore (E_(1))/(E_(2))=(39.1495xx10^(26))/(5.06xx10^(26))=7.67~~8`
Therefore, the energy released in the fusion of 1 kg hydrogen is nearly 8 times the energy released in the fission of 1 kg of uranium.