Chapter 30, Problem 41P

To determine

Fraction of radioactive sample left after 5 half-lives

Answer to Problem 41P

Solution:

3.125%

Explanation of Solution

Given Info:

Some fraction of radioactive sample is left after every half-life.

In every half-life the number of radioactive atoms gets multiplied by ½.

$\begin{array}{l}\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n\\ \frac{N}{N_0}={\left(\frac{1}{2}\right)}^n={\left(\frac{1}{2}\right)}^5\\ =\frac{1}{32}=3.125\%\end{array}$