Question 22 The half-life of Radium- 226 is 1590 years. If a sample contains $200 \mathrm{mg}$, how many mg will remain after 2000 years? Question Help: $D$ Post to forum Submit Question

Step 1 ：Given that the initial amount of Radium-226 is \(N_0 = 200\) mg.

Step 2 ：The time that has passed is \(t = 2000\) years.

Step 3 ：The half-life of Radium-226 is \(h = 1590\) years.

Step 4 ：We can calculate the final amount of Radium-226 using the formula \(N = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{h}}\).

Step 5 ：Substituting the given values into the formula, we get \(N = 200 \times \left(\frac{1}{2}\right)^{\frac{2000}{1590}}\).

Step 6 ：Solving the above expression, we get \(N \approx 83.63\).

Step 7 ：So, after 2000 years, approximately \(\boxed{83.63}\) mg of Radium-226 will remain.