13.30 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 in a fission reactor.

Hint: The energy released by the nuclear reaction can be found by \(E=\Delta mc^2\).
Step 1: Find the energy released by 1kg of Hydrogen.
(a) Amount of hydrogen, m=1 kg=1000 g
1 mole, i.e., 1 g of hydrogen H11contains6.023×1023 atoms.
1000gofH11contains6.023×1023×1000atoms
Withinthesun,fourH11nucleicombineandformoneH24enucleus.Inthisprocess,26MeVofenergyisreleased
Hence,theenergyreleasedfromthefusionof1kgH11is:
E1=6.023×1023×26×1034=39.1495×1026MeV
Step 2: Find the energy released by 1 kg of Uranium.
(b)AmountofU92235=1kg=1000g
1moleof,i.e.,235gofU92235contains6.023×1023atoms.
1000gofU92235contains6.023×1023×1000235atoms
ItisknownthattheamountofenergyreleasedinthefissionooneatomofU92235is200MeV
Hence, the energyreleasedfromthefissionof1kgofU92235is:
E2=6×1023×1000×200235
=5.106×1026MeV
E1E1=39.1495×10265.106×1026=7.678
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.