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?
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.
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
