Estiamte the minium amount of `._(235)^(92)U` that needs to undergo fission in order to run a `1000 MW` power reactor per year of continuous operartion. Assume an efficiency of about `33` percent.

Explanation

For `1000 MW` ouptput , the total power generation is `3000 MW`, of which `2000 W=MW` is rejected as "waste" heat. Thus the total energy released in year `(3 xx 10^(7)s)` from fission is about `(3 xx 10^(9)) (3 xx 10^(7))~~10^(17)` If each fission releases `200 MeV` of energy, the number of fission required is
`((10^(17))/(2xx10^(8))(1.6 xx10^(-19)) ~~3~~10^(27)`fissions The mass of a single uranium atom is about `(235 u)(1.66 xx10^(-27) kg//u) ~~4.5 xx10^(-25) kg`, so that mass needed is `((10^(17)))/((2xx10^(8))(1.6xx10^(-19)))` approxeapproxfission` or about a ton. Since .`_(92)^(235)U` is only a fraction of normal uranium, and even when requiremnet for uranium is of the order of tens of tons.