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The half-life of a radioactive material is the amount of time it takes for 50% of its radioactivity to decrease. If a particular material has a half-life of 32 years, then what percent will remain radioactive after 80 years?

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Final answer:

After 80 years, approximately 12.5% of the radioactive material with a half-life of 32 years will remain.

Step-by-step explanation:

The half-life of a radioactive material is the amount of time it takes for 50% of its radioactivity to decay.

If a material has a half-life of 32 years, we can determine how much of it remains after 80 years by calculating the number of half-lives that have passed and then applying the decay process sequentially for each half-life.


After the first 32 years, half of the material remains (50% of the original).

After the second 32 years (64 years in total), this amount is halved again, resulting in 25% of the original amount.

After 80 years, which encompasses two full half-lives and an additional fraction of a half-life (80 - 64 = 16 years), the further reduction of the remaining material is accounted for.

We can summarize the process as follows:

First half-life (32 years): 50% remains.

Second half-life (64 years): 50% of 50% remains = 25%.

For the next 16 years: halfway between the 2nd and 3rd half-life, we need to halve the remaining percentage once more to find how much remains after 80 years.

So, 25% / 2 = 12.5% of the original material remains radioactive.

Therefore, after 80 years, approximately 12.5% of the radioactive material remains.

User Barry Irvine
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