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Assume a quantity of a radioactive substance. If $3 − t$ expression is used to find the quantity of the substance that remains after t half-lives, then how many half-lives will it take for the fraction to equal $1243$ the initial value?

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answer is C.

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Detailed Solution

It is given that

3 − t

expression is used to find the quantity of the substances that remains after t half-lives.

∴ 1243 = 3 − t

Apply the law of exponent

x − m = 1 x m .

⇒ 1243 = 1 3 t

⇒ 135 = 1 3 t ∴ 35 = 243

By comparing the powers, we get,

5 = t

Therefore after 5 half-lives, the fraction will be

1243

of the initial value.
Hence option (3) is correct.

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