AU ²³⁵ nuclear reactor generates energy at a rate of 3.70 10^7 ~J / s . Each fission liberates 185 MeV useful energy. If the reactor has to operate for 144 10^4 ~s , then, the mass of the fuel needed is (Assume Avogadro's number .=6 10²³ ~mol ⁻¹, 1 eV =1.6 10⁻¹⁹ ~J )

Step-by-step solution

In 1 ~s , energy generated is 3.7 10^7 ~J In 144 10^4 ~s , energy generated is =3.7 10^7 144 10^4 ~J Also energy released in one fission is aligned & =185 meV & =185 10^6 1.6 10⁻¹⁹ ~J aligned Number of fission = 3.7 10^7 144 10^4 185 10^6 1.6 10⁻¹⁹ =1.8 10²⁴ of U ²³⁵ atoms. Mass contained in 1.8 10²⁴ atoms of U²³⁵ is = 235 1.8 10²⁴ 6.023 10²³ =702.3 ~g =0.70 ~kg