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(C) In the fusion reaction,$4$ hydrogen nuclei release $26.7 \ MeV$ of energy.Energy released per hydrogen nucleus $= \frac{26.7}{4} \ MeV$.Number of

Vedclass · Accepted Answer

$7.62$

Vedclass · Answer

(C) In the fusion reaction,$4$ hydrogen nuclei release $26.7 \ MeV$ of energy.Energy released per hydrogen nucleus $= \frac{26.7}{4} \ MeV$.Number of hydrogen nuclei in $2 \ kg = \frac{2000 \ g}{1 \ g/mol} 	imes N_{A} = 2000 \ N_{A}$.Total energy $E_{H} = 2000 \ N_{A} 	imes \frac{26.7}{4} \ MeV = 500 	imes 26.7 \ N_{A} \ MeV = 13350 \ N_{A} \ MeV$.In the fission reaction,$1$ nucleus of ${ }^{235} U$ releases $200 \ MeV$ of energy.Number of uranium nuclei in $2 \ kg = \frac{2000 \ g}{235 \ g/mol} 	imes N_{A} = \frac{2000}{235} \ N_{A}$.Total energy $E_{U} = \frac{2000}{235} \ N_{A} 	imes 200 \ MeV = \frac{400000}{235} \ N_{A} \ MeV \approx 1702.13 \ N_{A} \ MeV$.The ratio $\frac{E_{H}}{E_{U}} = \frac{13350 \ N_{A}}{1702.13 \ N_{A}} \approx 7.84$.Given the options,the closest value is $7.62$.

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