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Iodine-131 is a radioactive isotope. After 20.8 days, 41.1% of a sample 131I remains. What is the half life of 131I?

Need a way to do it on scientific calculator, please.

User Razican
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The half-life of \(^{131}I\) is approximately 15.87 days.

The half-life (\(t_{1/2}\)) of a radioactive isotope is the time it takes for half of a sample of that isotope to decay. The relationship between the remaining fraction (\(R\)) and the number of half-lives (\(n\)) can be expressed using the formula:

\[ R = \left( \frac{1}{2} \right)^n \]

In this case, after 20.8 days, 41.1% of the sample remains. The remaining fraction (\(R\)) is 0.411.

\[ 0.411 = \left( \frac{1}{2} \right)^n \]

Now, solve for \(n\):

\[ n = \frac{\log(0.411)}{\log(1/2)} \]

\[ n \approx 1.31 \]

Since \(n\) is the number of half-lives, and we know that after 20.8 days, 1.31 half-lives have passed, we can find the half-life (\(t_{1/2}\)):

\[ t_{1/2} = \frac{20.8}{1.31} \]

\[ t_{1/2} \approx 15.87 \, \text{days} \]

So, the half-life of \(^{131}I\) is approximately 15.87 days.

User Kamil P
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