A uranium reactor generates thermal energy at a rate of 300 MW . Determine the amount of ²³⁵ U consumed every second, given that the average energy released per fission is 200 MeV .

Step-by-step solution

Power generated, P = 300 MW = 300 10^6 J/s Energy released per fission, E = 200 MeV = 200 10^6 1.6 10⁻¹⁹ J = 3.2 10⁻¹¹ J Number of fissions per second, n = P E = 300 10^6 3.2 10⁻¹¹ = 9.375 10¹⁸ Mass of one ²³⁵ U atom, m = 235 6.022 10²³ g Mass of ²³⁵ U consumed per second = n m = 9.375 10¹⁸ 235 6.022 10²³ g Mass consumed 3.65 10⁻³ g = 3.65 mg 3.7 mg