Question

How many half-lives must elapse until (a) 90% and (b) 99% of a radioactive sample of atoms has decayed?

Short answer

Use the expression for the activity of the sample present after time t to calculate the age of the sample.

The activity of the sample present after time t is,

Step-by-step solution

R=Ree-λr

The expression for disintegration constant related to the half-life of the radium sample is,

$\lambda =\frac{0.693}{T_{1/2}}$

$t=-\frac{T_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}In\left({\displaystyle \frac{K}{R_0}}\right)}{0.693}$