Chapter 3.6, Problem 25PE

The isotope of plutonium ${}^{\text{238}}\text{Pu}$ is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 2.0 kg of ${}^{\text{238}}\text{Pu}$ .

a. If the half-life of ${}^{\text{238}}\text{Pu}$ is 87.7 yr, write a function of the form $Q\left(t\right)=Q_0{e}^{-kt}$ to model the quantity $Q\left(t\right){\text{ of }}^{238}\text{Pu}$ left after t years.

b. If 1.6 kg of ${}^{\text{238}}\text{Pu}$ is required to power the spacecraft’s data transmitter, for how long after launch would scientists be able to receive data? Round to the nearest year.