Question

These exercises use the radioactive decay model. The half-life of radium-226 is 1600years. Suppose we have a 22 -mg sample. How much of the sample will remain after 4000 years?

Answer 1

Approximately 3.89 mg of the 22-mg sample will remain after 4000 years.

Step-by-step explanation:

The half-life of radium-226 is 1600 years. To find out how much of the sample will remain after 4000 years, we can use the formula for radioactive decay:

Amount remaining = Initial amount * (1/2)^(number of half-lives)

First, we need to find the number of half-lives that have passed in 4000 years. Since the half-life of radium-226 is 1600 years, we divide 4000 by 1600 to get 2.5. This means that 2.5 half-lives have passed.

Now we can calculate the amount remaining:

Amount remaining = 22 mg * (1/2)^2.5

Amount remaining = 22 mg * 0.1768

Amount remaining = 3.89 mg

After 4000 years, approximately 3.89 mg of the 22-mg sample will remain.