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.

Answer:

(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.