Answer :
Final answer:
The amount of time it will take for only 1 mg of Polonium-218 to remain from a starting quantity of 16 mg, given a half-life of 3.0 minutes, is roughly 12 minutes.
Explanation:
The half-life is the time it takes for half the atoms of a radioactive substance to decay. In this case, we are given a half-life of 3.0 minutes for polonium-218. If we start with 16 mg of polonium-218 and want to determine how long it takes until only 1 mg is remaining, we can use the formula for exponential decay.
The formula we are going to use is: [tex]N = N_{0} * (1/2)^{(t/T)}[/tex] where: N is the final amount remaining after the time period, N0 is the initial quantity, T is the half-life and t is the elapsed time.
Putting the values into the equation we get, [tex]1 = 16 * (1/2)^{(t/3)}[/tex].
Here, our goal is to solve for 't', the amount of elapsed time. With some algebra, we get t = 3 * log(1/16) / log(0.5), which equates to approximately 12 minutes. Therefore, for 1 mg of polonium-218 to remain from an initial quantity of 16 mg, about 12 minutes must pass.
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