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About 185 MeV of usable energy is releas...

About 185 MeV of usable energy is released is the neutron induced fissioning of a `""_(92)^(235)U` nucleus. If the reactor using `""_(92)^(235)U` as fuel continuously generates 100 MW of power, how long will it take for 1 kg of the uranium to be used up?

Text Solution

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Number of fission occurring/s to give an energy output of 100 MW `(=10^(8)Js^(-1))`.
= `(10^(8)Js^(-1))/(185xx10^(6)xx1.6xx10^(-19)J)`
= `3.378xx10^(18)` fission `s^(-1)`
Number of nuclei contained in 1 kg of `""^(235)U`
= `(1kg)/(235kg//kmol)xx6.023xx10^(26)("nuclei")/(k "mol")`
= `2.563xx10^(24)` nuclei
Time taken to exhaust 1 kg of `""^(235)U`
= `(2.563xx10^(24))/(3.378xx10^(18))`second
8.78 days.
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