Example

If Radium has a half life of 1620 yrs, how long will it take to decay to 20% of its original radioactivity?

**t _{½} = **1620

**[A] _{0 }**= 100%

**[A] **= 20%

To find t we need to know k, therefore we use equation (2) first;

kt_{½} = ln2

k = 0.693/1620 = 4.28
x 10^{^-4}

We can now use equation (1) to find t;

kt = ln{[A]_{0}/[A]}

kt = ln(100/20) = 1.609

t = 1.609/4.28 x 10^{^-4 }
= **3760.4 yrs**