• # question_answer Calculate and compare the energy released by (i) fusion of 1 kg of hydrogen deep with in Sun and (ii) the fission of 1kg of ${}^{235}U$ in a fission reactor.

(i) In Sun, four hydrogen nuclei fuse to form a helium nucleus with release of 26 MeV energy. $\therefore$ 1 g of hydrogen contains $=\text{ }6.023\times {{10}^{23}}$ nuclei $\therefore$ Energy released by fusion of 1 kg (= 1000 g) of hydrogen, ${{E}_{1}}=\frac{6.023\times {{10}^{23}}\times 26\times {{10}^{3}}}{4}$ $=39\times {{10}^{26}}$ MeV (ii) Energy released in one fission of $_{92}^{235}U$ nucleus =200 MeV Mass of uranium = 1 kg = 1000 g We know that, 235 g of ${}^{235}U$ has $6.023\times {{10}^{23}}$ atoms or nuclei. $\therefore$ Energy released in fission of 1 kg of ${{U}^{235}},$ ${{E}_{2}}=\frac{6.023\times {{10}^{23}}\times 1000\times 200}{235}=5.1\times {{10}^{26}}$ MeV $\therefore \frac{{{E}_{1}}}{{{E}_{2}}}=\frac{39\times {{10}^{26}}}{5.1\times {{10}^{26}}}=7.65\approx 8$ Thus, the energy released in fusion is 8 times the energy released in fission.