A radioactive isotope decays at a rate proportional to its

Chapter 11, Problem 11.13

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A radioactive isotope decays at a rate proportional to its concentration. If the concentration of an isotope is C (mg/L), then its rate of decay may be expressed as rd[mg/(L's)1 = kC where k is a constant. 568 Chapter 11 Balances on Transient Processes Encyclopedia reactor-batch Equipment Encyclopedia reactor Equipment -batch (a) A volume V(L) of a solution of a radioisotope whose concentration is Cl(mg/L) is placed in a closed vessel. Write a balance on the isotope in the vessel and integrate it to prove that the half-life tl/2 of the isotope-by definition, the time required for the isotope concentration to decrease to half of its initial value-equals (In 2)/ k. (b) The half-life of 56Mn is 2.6 h. A batch of this isotope that was used in a radiotracing experiment has been collected in a holding tank. The radiation safety officer declares that the activity (which is proportional to the isotope concentration) must decay to 1% of its present value before the solution can be discarded. How long will this take?