Answer:
The amount of Radium-226 remaining after 2000 years is approximately 209.08 mg.
Explanation:
We can use the formula for exponential decay to solve this problem. The formula is:
N = N0 * (1/2)^(t/T)
where N is the amount of substance remaining after time t, N0 is the initial amount of substance, T is the half-life of the substance, and t is the time elapsed.
In this case, we are given that the half-life of Radium-226 is 1590 years, and that we start with an initial amount of 500 mg. We want to find the amount remaining after 2000 years.
Substituting the given values into the formula, we get:
N = 500 * (1/2)^(2000/1590)
Evaluating the expression, we get:
N ≈ 209.08
So the amount of Radium-226 remaining after 2000 years is approximately 209.08 mg.