Question

the half-life of a radioactive kind of thallium is 5 minutes. how much will be left after 20 minutes, if you start with 933,392 grams of it?
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Explanation:

Step1: Determine number of half - lives

The half - life is 5 minutes and the total time is 20 minutes. To find the number of half - lives \(n\), we use the formula \(n=\frac{\text{total time}}{\text{half - life}}\). So \(n = \frac{20}{5}=4\).

Step2: Use the half - life formula

The formula for the amount of a radioactive substance remaining after \(n\) half - lives is \(A = A_0\times(\frac{1}{2})^n\), where \(A_0\) is the initial amount and \(A\) is the amount remaining. Here, \(A_0 = 933392\) grams and \(n = 4\). So \(A=933392\times(\frac{1}{2})^4\).
First, calculate \((\frac{1}{2})^4=\frac{1}{16}\). Then \(A = 933392\times\frac{1}{16}\).
\(933392\div16 = 58337\).

Answer:

58337