A mixture used in a fusion research facility contains equal numbers of deuterium…

PHYSICS · Multi-part · CBSE · Physics · Nuclei · Nuclei

Problem

A mixture used in a fusion research facility contains equal numbers of deuterium nuclei

(^2_1\mathrm{H})

and tritium nuclei

(^3_1\mathrm{H})

. Each fusion reaction

^2_1\mathrm{H}+^3_1\mathrm{H}\rightarrow ^4_2\mathrm{He}+^1_0\mathrm{n}

releases

17.6\,\mathrm{MeV}

of energy. (i) Calculate the energy released, in joules, in a single fusion reaction. Use

1\,\mathrm{eV}=1.602\times10^{-19}\,\mathrm{J}

. (ii) Determine the number of fusion reactions required to generate

1.0\,\mathrm{GWh}

of energy. (iii) Given that the molar masses of deuterium gas

\mathrm{D_2}

and tritium gas

\mathrm{T_2}

are

4.0\,\mathrm{g\,mol^{-1}}

and

6.0\,\mathrm{g\,mol^{-1}}

respectively, find the total mass of the D–T mixture needed to supply

1.0\,\mathrm{GWh}

of energy. (Assume the mixture contains

50\%

deuterium atoms and

50\%

tritium atoms by number.)