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

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=(A)/(2) \ a t \ t=1590 \\&\Rightarrow (1)/(2)=e^(1590n) \Rightarrow n=(\ln (1 / 2))/(1590)=-0.00043594162\end{aligned}`

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