A nuclear explosion is designed to deliver `1 MW` of heat energy, how many fission events must be required in a second to attain this power level. If this explosion is designed with a nuclear fuel consisting of uranium `235` to run a reactor at this power level for one year, then calculate the amount of fuel needed. You can assume that the calculate the amount of energy released per fission event is `200 MeV`.

Options

A. 1kg
B. 0.01kg
C. 3.84 kg
D. 0.384 kg

Answer

D

Explanation

Energy released per fission is
`E=200 Me V=200xx1.6xx10^(-11)J`
Total energy required to run aa 1 MW reactor for one year is
`=10^(6)Js6(-1)xx(365xx60xx60xx)=3.15xx10^(13)J`
energy SO, total number of `U^(235)` are contained in 235 g of `U^(235)`
`therefore Mass of U^(235) containing 9.84xx10^(23) atoms is`
`M=(235)/(6.02xx10^(22)xx9.84xx10^(23))=34kg=0.384 kg`