An experimental reactor core contains uranium enriched to in by number

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

An experimental reactor core contains uranium enriched to

90\%

^{235}\text{U}

by number, the remainder being

^{238}\text{U}

. During a two-hour test run the plant delivers

5.0\times10^{8}\,\text{J}

of electrical energy at an overall efficiency of

35\%

(from fission energy to electricity). Assume

200\,\text{MeV}

is liberated in each fission of

^{235}\text{U}

and that only

^{235}\text{U}

undergoes fission. (i) Calculate the number of fission events occurring per second during the test run. (ii) Determine the mass of

^{235}\text{U}

consumed in the test. (iii) If the plant efficiency were increased to

45\%

, by what percentage would the mass of

^{235}\text{U}

consumed during an identical two-hour run decrease?