Question

The half-life of radium-226 is 1590 years. if a sample contains 100 mg, how many mg will remain after 1000 years?

Answer 1

Answer:

$a=64.7mg$

Explanation:

Hello,

In this case, we need to remember that for the required time for a radioactive nuclide as radium-226 to decrease to one half its initial amount we are talking about its half-life. Furthermore, the amount of remaining radioactive material as a function of the half-lives is computed as follows:

$a=a_0(\frac{1}{2} )^{\frac{t}{t_{1/2}} }$

Therefore, for an initial amount of 100 mg with a half-life of 1590 years, after 1000 years, we have:

$a=100mg(\frac{1}{2} )^{\frac{1000years}{1590years} }\\\\a=64.7mg$

Best regards.