Final answer:
The question relates to the radioactive decay of Cobalt-60 used in cancer therapy, and requires calculating when its activity level falls below a certain threshold. Through the use of the half-life formula and decay constant, we can determine the timeframe in which the 5000-Ci source decreases to 3500 Ci.
Step-by-step explanation:
The question concerns the concept of radioactive decay, which is a significant topic in physics, particularly when applied to the medical field for treatments like cancer therapy. To determine when a 5000-Ci 60 Co source used for treating terminally ill patients becomes insufficient for use—at an activity level below 3500 Ci—we need to calculate its decay using the half-life formula.
The half-life of Cobalt-60 is about 5.26 years. We can use the formula for exponential decay A(t) = A0e-λt, where A(t) is the activity at time t, A0 is the initial activity, and λ is the decay constant. The decay constant can be found using the formula λ = ln(2)/half-life. After calculating the decay constant, we can solve for t when A(t) = 3500 Ci by rearranging the formula to t = -ln(A(t)/A0)/λ. This calculation will give us the time it takes for the source to be considered too weak to be useful for cancer therapy in terminally ill patients.