Chapter 20, Problem 16STP

To determine

To predict that whether the tracer will be traceable or not after 24 hours which has half-life of 2 hours.

Explanation of Solution

Give info:

Half-life of radioactive tracer = 2 hours

Introduction:

Half-life is the amount of time it takes for half the lives in a sample of an isotope to decay.

Following figure showing the proportion of decaying nuclei left after each half-life.

It can be clearly seen from above figure that after each half-life the number of remaining undecayed nuclei are decreasing rapidly.

Corresponding to 24 hours the number of half-lives are 12 since the tracer have half-life of 2 hours. Hence, after 12 half-lives there will be no remaining undecayed nuclei for tracing and tracer cannot be traceable after 24 hours.

Conclusion:

Thus, tracer cannot be traceable after 24 hours. Since its half-life is only 2 hours the whole sample would be decayed before 24 hours.