Question

1. a sample of radioactive fermium has a mass of 12 g. if the half - life is 4.5 days, what mass is left after 13.5 days?

Explanation:

Step1: Calculate the number of half - lives

The formula for the number of half - lives \(n=\frac{t}{T}\), where \(t = 13.5\) days (time elapsed) and \(T=4.5\) days (half - life).
\(n=\frac{13.5}{4.5}=3\)

Step2: Use the radioactive decay formula

The radioactive decay formula is \(m = m_0\times(\frac{1}{2})^n\), where \(m_0 = 12\) g (initial mass) and \(n = 3\) (number of half - lives).
\(m=12\times(\frac{1}{2})^3\)

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Answer:

\(1.5\) g