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Question 139

A half-life is the amount of time that it takes for a radioactive substance to decay one-half of its original quantity.
Suppose radioactive decay causes 300 grams of a substance to decrease 300×23 grams after 3 half-lives. Evaluate 300×23 to determine how many grams of the substance is left.
Explain why the expression 300×2n can be used to find the amount of the substance that remains after n half-lives.


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Solution

Since, 300 g of a substance decreases to 300×23g after 3 half-lives.

Similarly, 300 g of a substance would decrease to 300×2ng after n half-lives.

So, we have to evaluate :
300×23
=300×23
=3008 [23=8]
=37.5 g


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