NASA is designing a robotic spacecraft to visit Neptune. The probe will use the radioactive isotope Plutonium-238(Pu-238) as a power source. One gram of Pu-238 generates 0.56 watts of thermal power and has a half-life of 87.7 years. The generator that converts thermal power to electrical power for the probe's instruments operates at 6% efficiency (i.e. 1 watt of thermal power generates 0.06 watts of electrical power). The instruments on the spacecraft require 85 watts of electrical power and need to operate for 19 years to complete the mission.
a. How many whole grams of Pu-238 are required to complete the mission?
b. Discuss how a different generator, operating at 7% efficiency, would affect the amount of Pu-238 required to complete the mission. Use algebra to back up your claim.
c. Suppose NASA wants the mission to last 25 years and has only 2500 grams of Pu-238 available for the probe. To what operating efficiency must the engineers design the generator? Round your answer to the nearest tenth of a percent.
help with this problem is greatly appreciated, thank you!
