Estimate the percentage of radioactive material that remains in a sample after 5 years if the half-life of the material is 299 days.Round to the nearest hundredth of a percent.

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for radioactive decay:

N = N0 * (1/2)^(t/T)

where N is the amount of radioactive material remaining after time t, N0 is the initial amount of radioactive material, T is the half-life, and ^(t/T) represents the number of half-life periods that have passed.

In this case, we know that T = 299 days, and we want to know the amount of material remaining after 5 years, or 1825 days. We can use the formula and plug in these values:

N = N0 * (1/2)^(1825/299) = 0.0145N0

This means that only 1.45% of the original radioactive material remains after 5 years. Therefore, the best choice is C) 1.45%.

Estimate the Percentage of Radioactive Material That Remains in a Sample