Question

how much of a radioactive kind of tellurium will be left after 12 months if the half - life is 2 months and you start with 864,640 grams?

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Explanation:

Step1: Determine the number of half - lives

The half - life of tellurium is 2 months, and the time elapsed is 12 months. To find the number of half - lives \(n\), we use the formula \(n=\frac{\text{total time}}{\text{half - life}}\). So \(n = \frac{12}{2}=6\).

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. Here, \(N_0 = 864640\) grams and \(n = 6\).

First, calculate \((\frac{1}{2})^6=\frac{1}{64}\).

Then, find \(N\) by multiplying \(N_0\) by \(\frac{1}{64}\): \(N=864640\times\frac{1}{64}\).

We can calculate \(864640\div64\): \(864640\div64 = 13510\).

Answer:

13510