Question

the half - life of a radioactive element, such as carbon - 14, is the time it takes for half of the atoms of the element to decay. how many half - life periods have passed if a fossil contains 1/32 of the original amount of carbon - 14?
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Explanation:

Step1: Set up the formula

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N\) is the final amount, \(N_0\) is the initial amount, and \(n\) is the number of half - life periods. We know \(N=\frac{1}{32}N_0\).

Step2: Substitute into the formula

Substitute \(N=\frac{1}{32}N_0\) into \(N = N_0\times(\frac{1}{2})^n\). We get \(\frac{1}{32}N_0=N_0\times(\frac{1}{2})^n\). Divide both sides by \(N_0\) (since \(N_0
eq0\)), so \(\frac{1}{32}=(\frac{1}{2})^n\).

Step3: Rewrite \(\frac{1}{32}\)

We know that \(\frac{1}{32}=\frac{1}{2^5}\), and \(\frac{1}{2^5}=(\frac{1}{2})^5\).

Answer:

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