Question

The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?

Answer 1

Answer: 129.33 g

Step-by-step explanation:

$Let p=A \cdot e^{n t} \\ (p= present amount, A= initial amount, n= decay rate, t= time)$

$\begin{aligned}&\Rightarrow \text { Given } p=\frac{A}{2} \ a t \ t=1590 \\&\Rightarrow \frac{1}{2}=e^{1590n} \Rightarrow n=\frac{\ln (1 / 2)}{1590}=-0.00043594162\end{aligned}$

$If A=200 \mathrm{mg} and t=1000 then, \begin{aligned}P &=200 e^{\left(\frac{\ln \left(1/2\right)}{1590}\right) \cdot 1000} \text \\\\&=129.33 \text { grams}\end{aligned}$