Question

The half-life of Radium-226 is 1590 years. If a sample contains 400 mg, how many mg will remain after 2000 years?

Answer 1

Answer:

167.27 mg.

Step-by-step explanation:

We have been given that the half-life of Radium-226 is 1590 years and a sample contains 400 mg.

We will use half life formula to solve our given problem.

$N(t)=N_0*(\frac{1}{2})^{\frac{t}{t/2}$, where N(t)= Final amount after t years, $N_0$= Original amount, t/2= half life in years.

Now let us substitute our given values in half-life formula.

$N(2000)=400*(\frac{1}{2})^{\frac{2000}{1590}$

$N(2000)=400*(0.5)^{1.2578616352201258}$    

$N(2000)=400*0.4181633028874878239$

$N(2000)=167.26532115499512956\approx 167.27$

Therefore, the remaining amount of Radium-226 after 2000 years will be 167.27 mg.