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Question
Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression 3–t. After how many half-lives will the fraction be `1/243` of the original?
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Solution
Given, t half-lives = 3–t
So, `1/243 = 3^-t`
⇒ `1/3^5 = 1/3^t` ...`[because 3 xx 3 xx 3 xx 3 xx 3 = 3^5 "and" a^-m = 1/a^m]`
On comparing both sides, we get
t = 5 half-lives
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