# Solve the following exponential application problem involving half life of a substance.Plutonium-239 has a half-life of 24,000 years. A rule of thumb is that radioactive wastes are virtually...

Solve the following exponential application problem involving half life of a substance.

Plutonium-239 has a half-life of 24,000 years. A rule of thumb is that radioactive wastes are virtually harmless after 10 half-lives. How long must 1 gram of Plutonium-239 be securely stored before it is virtually harmless.

I think you use the equation A= A02-t/k , but I don't know what to plug in and how to solve.

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### 1 Answer

If it is given that radioactive wastes have to be stored for a duration of time equal to 10 half-lives, that is the period for which it has to be securely stored before it is harmless.

A half life is the duration of time over which a substance degrades so that only half of the initial amount is left at the end of the duration. 10 half-lives would leave behind an amount equal to 1/2^10 of the initial amount.

As far as your question goes, if you need to find how long to store the plutonium if it has to be stored for 10 half lives, the answer is obtained by simply multiplying the half life by 10. Here, as the half life is 24000 years we get 24000*10 = 240,000 years.

**The required duration that the Plutonium 239 has to be stored for is 240,000 years.**