Both nuclear fission and nuclear fusion are considered for large-scale energy generation

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Both nuclear fission and nuclear fusion are considered for large-scale energy generation. The fusion reaction

^2_1\text{H}+^3_1\text{H}\rightarrow {}^4_2\text{He}+n

releases

17.6\,\text{MeV}

of energy per event. Assume molar masses

M_{^2\!H}=2\,\text{g\,mol}^{-1}

M_{^3\!H}=3\,\text{g\,mol}^{-1}

and

M_{^{235}\!U}=235\,\text{g\,mol}^{-1}

. Use

N_A = 6.022\times10^{23}\,\text{mol}^{-1}

and

1\,\text{eV}=1.6\times10^{-19}\,\text{J}

. (i) A mixture contains equal numbers of deuterium and tritium nuclei. Calculate the energy obtainable when a total mass of

1.0\,\text{g}

of this mixture undergoes complete fusion. (ii) Determine the energy released when

1.0\,\text{g}

^{235}\text{U}

undergoes complete fission, each fission event releasing

200\,\text{MeV}

. (iii) Find the ratio of the energies obtained per gram from the fusion fuel and from

^{235}\text{U}

, respectively. Comment briefly on the result.