The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to $

Question

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to $\frac{1}{16}$ of its initial value?

Accepted Answer

The activity $A$ after $n$ half-lives is given by $A = A_0 (\frac{1}{2})^n$. Given $\frac{A}{A_0} = \frac{1}{16} = (\frac{1}{2})^4$, so $n = 4$. Total time $t = n 	imes T_{1/2} = 4 	imes 20 = 80$ minutes.

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