A sample of a radioactive isotope is found to have lost 26.6% of its original activity after 3.21 days.What is the rate constant for decay of this isotope?

Question

Quizplus · Accepted Answer

The decay of a radioactive isotope can be described by the equation N = N0 * e^(-kt), where N is the remaining quantity of the substance, N0 is the initial quantity, k is the decay constant, and t is the time. Given that 26.6% of the isotope has decayed, 73.4% remains. Setting N/N0 = 0.734 and t = 3.21 days, we can solve for k. Rearranging the equation gives k = -ln(N/N0) / t = -ln(0.734) / 3.21 ≈ 0.096 d−1.

A Sample of a Radioactive Isotope Is Found to Have