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The half life of a radioactive element is 3 days - Leaving Cert Physics - Question i - 2007

Question i

The half life of a radioactive element is 3 days. What fraction of a sample of the radioactive element will remain after 9 days?

Worked Solution & Example Answer:The half life of a radioactive element is 3 days - Leaving Cert Physics - Question i - 2007

Step 1

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Answer

To find out how many half-lives have occurred in 9 days, we divide the total time by the half-life duration:

$ext{Number of half-lives} = \frac{9 \text{ days}}{3 \text{ days}} = 3$

This indicates that 3 half-lives have passed.

Step 2

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Answer

The remaining fraction after each half-life can be calculated using the formula:

$ext{Remaining fraction} = \left(\frac{1}{2}\right)^n$

Where $n$ is the number of half-lives. Therefore, after 3 half-lives:

$ext{Remaining fraction} = \left(\frac{1}{2}\right)^3 = \frac{1}{8}$

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