The half-life of radium-226 is 1590 years. if a sample contains 100 mg, how many mg will remain after 4000 years?

We can calculate the amount left after 4000 years by using the half-life equation. It is expressed as:

A = Ao e^-kt

where A is the amount left at t years, Ao is the initial concentration, and k is a constant.

From the half-life data, we can calculate for k.

1/2(Ao) = Ao e^-k(1590)
k = 4.36 x 10^-4

A = 100 e^- 4.36 x 10^-4(4000)
A = 17.48 mg