A nuclear reactor generates power at a steady rate of 1000 MW . What is the mass converted into energy during 1 hour of its operation, in milligrams?

Step-by-step solution

The total energy produced by the reactor in 1 hour is calculated using the relation between energy, power, and time: E = P t Given P = 1000 MW = 10^9 W and t = 1 hour = 3600 s : E = 10^9 3600 = 3.6 10¹² J According to the mass-energy equivalence principle, E = mc^2 . The mass m converted into energy is: m = E c^2 m = 3.6 10¹² (3 10^8)^2 m = 3.6 10¹² 9 10¹⁶ m = 0.4 10⁻⁴ kg = 4 10⁻⁵ kg To convert this mass into milligrams: 1 kg = 10^3 g = 10^6 mg m = 4 10⁻⁵ 10^6 mg = 40 mg Answer: 40