In a nuclear reactor, ²³⁵ U undergoes fission liberating 200 MeV of energy. The reactor has a 10 % efficiency and produces 1000 MW power. If the reactor is to function for 10 yr , then find the total mass of uranium required.

Step-by-step solution

Total energy produced by the reactor in time t=10 yr . aligned E & =1000 10^6 10 3.15 10^7 ~J & =3.15 10¹⁷ ~J aligned aligned & Efficiency = output energy input energy & Input energy caused by fission = output energy efficiency aligned = 3.15 10¹⁷ (10 / 100) =3.15 10¹⁸ ~J Energy produced by one fission of ²³⁵ U =200 MeV aligned & =200 1.6 10⁻¹³ ~J & =3.2 10⁻¹¹ ~J aligned Therefore, number of fissions required = total energy energy per fission = 3.15 10¹⁸ 3.2 10⁻¹¹ =9.8 10²⁸ Hence, mass of uranium required is given