64 g is initial amount of a radioactive substance left after 4 half-lives have passed.
What is Half life?
Half life is the time in which the amount of a radioactive substance remains halve of its initial amount. For example, half life of carbon-14 is 5730 years. It means if we have 4 grams of carbon-14 then it will remain 2 grams after 5730 years.
For the given problem, we have to calculate initial amount of a radioactive, if 4.0 grams left after 4 half-lives have passed.
The formula used for this is:
[tex]\frac{A}{A^{0} } = \frac{1^n}{2^n}[/tex]
where, A0 is the initial amount and A is final amount and n is the number of half-lives.
Let's plug in the values in the formula.
[tex]\frac{4}{A^{0} } = \frac{1^4}{2^4}[/tex]
[tex]A^{0} = 64 g[/tex]
Hence, 64 g is initial amount of a radioactive substance left after 4 half-lives have passed.
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