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?

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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