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?

Answer 1

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.