A plasma discharge device is invented to purify polluted air by ionizing and filtering it. This device requires an electrical input power of at least 40 kW continuously for its useful lifetime of 40 years. IT is proposed to power this air cleaner with the disintegration energy from the following reaction:
238^Pu decays to: 234^U + 4^He
which is a half-life of 87.7 years. If this decay reaction is the only source of energy available to this device, determine the initial mass of 238^Pu required so that it has sufficient power for its entire useful lifetime.