The steel compression ring for the piston of an automobile e

The steel compression ring for the piston of an automobile engine has a mass of 40 g. The ring is irradiated with neutrons until it has an activity of 2.5 Ci of ^59Fe (T_1/2 =44.529 d) distributed uniformly throughout The ring is installed in an engine and removed 30 days later If the 22 L of crankcase oil has an average activity due to ^59 Fe of 0.023 d/s per cubic centimeter, what mass (g) of steel was worn off the piston ring?

Solution

Initial total activity = 2.5 uci

Activity after 30 days (T_1/2 = 44.529 d)

                      = 2.5* exp(-0.693*30/44.529)

                      = 1.567 uci = 1.567* 3.7e+4 d/s = 5.78e+4 d/s

Activity found in the oil = 0.023 d/s per cc

Total activity in the oil = 0.023*22000 = 506 d/s

Mass of steel worn out = 40*506/5.78e+4

                                    = 0.3502 gms