Question

A 5000-Ci ⁶0Co source used for cancer therapy is considered too weak to be useful when its activity falls to 3500 Ci. How long after its manufacture does this happen?

a) 10 years
b) 20 years
c) 30 years
d) 40 years

Answer 1

A cobalt-60 source used for cancer therapy has a half-life of 5.27 years. When its activity falls to 3500 Ci from 5000 Ci, it takes approximately 1.77 years after manufacture.

Step-by-step explanation:

A cobalt-60 source used for cancer therapy has a half-life of 5.27 years. In a given cobalt-60 source, both the amount of material and the intensity of the radiation emitted are cut in half every 5.27 years. When the activity of the source falls to 3500 Ci from its initial activity of 5000 Ci, we can calculate how long it takes for this to happen by using the concept of half-life. We can use the formula:

Final activity = Initial activity * (1/2)^(number of half-lives)

3500 = 5000 * (1/2)^(number of half-lives)

Solving this equation, we find that the number of half-lives is approximately 0.338. Since each half-life is 5.27 years, we can multiply the number of half-lives by the length of a half-life to find the time it takes for the activity to fall to 3500 Ci. Therefore, the time after manufacture when this happens is approximately 1.77 years.