The radioactive isotope \({ }^{238} \mathrm{Pu},\) used in pacemakers, decays by
emitting an alpha particle with a half-life of 86 yr. (a) Write an equation
for the decay process. (b) The energy of the emitted alpha particle is \(9.0
\times 10^{-13} \mathrm{~J}\), which is the energy per decay. Assume that all
the alpha particle energy is used to run the pacemaker, calculate the power
output at \(t=0\) and \(t=10 \mathrm{yr}\). Initially \(1.0 \mathrm{mg}\) of \({
}^{238} \mathrm{Pu}\) was present in the pacemaker (Hint: After \(10
\mathrm{yr}\), the activity of the isotope decreases by 8.0 percent. Power is
measured in watts or \(\mathrm{J} / \mathrm{s}\).).