Discussion
If N is the initial number of atoms in a radioactive sample, then the number of atoms decayed after the five half life periods is
Answer: A
The number decayed is \(\frac{31}{32}N\).
After each half-life the remaining number halves, so after five half-lives
\[ \begin{aligned} N_{left} &= N\left(\tfrac{1}{2}\right)^{5} = \frac{N}{32} \\ N_{decayed} &= N - \frac{N}{32} = \frac{31}{32}N \end{aligned} \]
\(\frac{N}{32}\) is the number left, the main trap, and \(\frac{15}{16}N\) and \(\frac{7}{8}N\) are the decayed fractions after four and three half-lives.
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