Question 289033
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Using the definition of half life, the amount{{{A(n)}}} remaining after {{{n}}} half-lives is {{{A(n)=A(0)((1/2)^n)}}}, where {{{A(0)}}} is the initial amount.<br>
In this problem, the number of half-lives is {{{1000/5730}}}.<br>
With an initial amount of 3 grams, the amount remaining after that many half-lives is<br>
{{{A(3)=(3)((1/2)^(1000/5730))}}}<br>
= 2.658186689....<br>
Remember that radioactive decay is a statistical process; that mathematical answer is only approximately correct<br>