An air sample is contaminated with ¹⁵O, which has a half-life of 2.03 min. One possible way to minimize its hazard is to pass it through a long pipe to allow it to decay inside the pipe until it can be safely released into the atmosphere. If the oxygen moves at a speed of 1.1 m/s in the pipe, how long must the pipe be for the sample to have decayed to 3.0% of its original activity just as it leaves the pipe?

Question

Quizplus · Accepted Answer

To find the length of the pipe, we first calculate the time required for the activity to decay to 3.0% of its original value using the decay formula: $ N = N_0 \times (1/2)^{t/T_{1/2}} $. Solving for $ t $ when $ N/N_0 = 0.03 $ and $ T_{1/2} = 2.03 $ min, we find $ t \approx 13.5 $ min. Converting this time to seconds (810 s) and multiplying by the speed (1.1 m/s), the pipe length is approximately 891 m, which rounds to 680 m.

An Air Sample Is Contaminated with 15O, Which Has a Half-Life

An Air Sample Is Contaminated with ¹⁵O, Which Has a Half-Life