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  • Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of 235U in a fission reactor.

Q. 13.30 Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of 235U in a fission reactor.

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(a) _{1}^{1}\textrm{H} _{1}^{1}\textrm{H}+_{1}^{1}\textrm{H}+_{1}^{1}\textrm{H}+_{1}^{1}\textrm{H}\rightarrow _{2}^{4}\textrm{He}

The above fusion reaction releases the energy of 26 MeV

Number of Hydrogen atoms in 1.0 kg of Hydrogen is 1000NA

Therefore 250NA such reactions would take place

The energy released in the whole process is E1

\\=250\times 6.023\times 10^{23}\times 26\times 10^{6}\times 1.6\times 10^{-19}\\=6.2639\times 10^{14}\ J

(b) The energy released in fission of one _{92}^{235}\textrm{U} atom is 200 MeV

Number of _{92}^{235}\textrm{U} atoms present in 1 kg of _{92}^{235}\textrm{U} is N

\\N=\frac{1000\times 6.023\times 10^{23}}{235}\\ N=2.562\times 10^{24}

The energy released on fission of N atoms is E2

\\E=2.562\times 10^{24}\times 200\times 10^{6}\times 1.6\times 10^{-19}\\ E=8.198\times 10^{13}J

\frac{E_{1}}{E_{2}}=\frac{6.2639\times 10^{14}}{8.198\times 10^{13}}\approx 8

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