An interesting application of nuclear decay is the radioisotope thermoelectric generator, or RTG. In such a device, energy from radioactive decay is initially converted to heat in a manner similar to the decay heat discussed in Section 14.6. The heat is then converted to electrical energy using thermocouples in what is known as the Seebeck effect. The RTG is a long-lived source of low levels of electrical energy and has been used to power various space probes, including Cassini, which orbited Saturn for 13 years before ending its mission in 2017. The most commonly used isotope in RTGs is ²³⁸Pu. 

(a) Write a nuclear equation for the alpha decay of ²³⁸Pu.

(b) The energy output from the decay of ²³⁸Pu is about 0.54 kW per kilogram of plutonium. Suppose the fuel for a particular RTG is 7.8 kg of ²³⁸PuO₂, and that the conversion of heat to electrical energy is about 6.5% efficient. Estimate the electrical power output in watts for such an RTG.