Final answer:
1.00 g of mass converted to electric energy at 38.0% efficiency would last approximately 18.97 seconds.
Step-by-step explanation:
To calculate how long 1.00 g of mass converted to electric energy would last at 38.0% efficiency, we need to convert the mass to energy using Einstein's equation (E=mc²). The energy generated would be (1.00 g) x (2.99792458 × 10^8 m/s)² = 8.9875 x 10^13 J. Since the efficiency is 38.0%, we multiply the energy by 0.38 to get the usable energy, which is 3.415 x 10^13 J. Since the power usage per month is 500 kW.h, we can convert it to joules by multiplying by 3.6 x 10^6 J/kW.h. This gives us 1.8 x 10^12 J. Finally, we can calculate the time the energy would last by dividing the usable energy by the power usage, which is (3.415 x 10^13 J) / (1.8 x 10^12 J) = 18.97 seconds.