Radium has a half-life of 1580 years. If a sample contains 1g of radium now, how much radium will there be:

Question

a) In 500 years b) In 3000 years c) 1000 years ago

I know that this is a half life question but am not sure what the formula is and how to solve part a, b, and c. Can somebody please show me the steps?

Answer 1

Let $D$ be the rate of decay. Then we have that:

$$e^{1580D}=\frac 12$$

You can use this to find $D=\frac{-\ln(2)}{1580}$

Then you simply need to plug in $D$ for $e^{500D}$ etc