Question

sodium - 24 has a half - life of 15 hours.
how many grams of a 900 g sample will remain after 90 hours?
7.03125 g
7.5 g
14.0625 g
28.125 g

Explanation:

Step1: Calculate the number of half - lives

The formula for the number of half - lives \(n=\frac{t}{T}\), where \(t = 90\) hours (total time) and \(T=15\) hours (half - life).
\(n=\frac{90}{15}=6\)

Step2: Use the radioactive decay formula

The formula for the remaining mass \(m = m_0\times(\frac{1}{2})^n\), where \(m_0 = 900\) g (initial mass) and \(n = 6\) (number of half - lives).
\(m=900\times(\frac{1}{2})^6\)

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Answer:

14.0625 g