Q. 1405.0( 1 Vote )

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.

A. What fraction of substance remains after 7 half-lives?

B. After how many half-lives will the fraction be of the original?

Answer :

Given that the fraction of radioactive substance that remains after t half-lives can be found by the expression 3-t.


A. Here, t = 7


Fraction of substance that remains after 7 half-lives = 3-7


We know by laws of exponents, a-n =


3-7 = =


of radioactive substance remains after 7 half-lives.


B. Fraction of substance that remains after t half-lives =


But fraction of radioactive substance that remains after t half-lives = 3-t


3-t =


243 can also be written as 35.



We know that by laws of exponents, .


3-t = 3-5


As bases are equal, we equate the powers.


-t = -5


t = 5


After 5 half-lives the fraction will be of the original.


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