Question

how much of a radioactive kind of bismuth will be left after 8 minutes if the half - life is 2 minutes and you start with 79,360 grams?

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Explanation:

Step1: Determine the number of half - lives

The half - life is 2 minutes and the total time passed is 8 minutes. To find the number of half - lives \(n\), we use the formula \(n=\frac{\text{total time}}{\text{half - life}}\).
So \(n = \frac{8}{2}=4\).

Step2: Use the radioactive decay formula

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount, \(n\) is the number of half - lives, and \(N\) is the remaining amount.
We know that \(N_0 = 79360\) grams and \(n = 4\).
Substitute these values into the formula: \(N=79360\times(\frac{1}{2})^4\).
First, calculate \((\frac{1}{2})^4=\frac{1}{16}\).
Then, \(N = 79360\times\frac{1}{16}\).
\(79360\div16 = 4960\).

Answer:

4960