A lunar research station needs a continuous electrical power of for its operation

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

Problem

A lunar research station needs a continuous electrical power of

5\,\mathrm{MW}

for its operation. The station plans to use a compact

^{235}\mathrm{U}

fission reactor that works at an overall efficiency of

25\%

. Take the energy released per fission to be

200\,\mathrm{MeV}

and Avogadro’s number

N_A = 6.02\times10^{23}\,\text{mol}^{-1}

. Atomic mass of

^{235}\mathrm{U}

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

and

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

. (i) Calculate the total electrical energy required in one terrestrial day

(24\,\text{h})

. (ii) Determine the number of fission events that must occur in the core during this period. (iii) Compute the mass of

^{235}\mathrm{U}

that will be consumed in the same period.