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 3^{5}.

⇒

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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