There will be zero radioactive atoms left
Explanation:
The amount of radioactive atoms left of a radioactive sample after a certain time t is given by the equation
[tex]N(t) = N_0 (\frac{1}{2})^{-\frac{t}{\tau}}[/tex]
where
N(t) is the number of radioactive atoms left after time t
[tex]N_0[/tex] is the initial number of radioactive atoms
[tex]\tau[/tex] is the half-life of the sample
In this problem we have:
[tex]N_0 = 800[/tex] (initial number of radioactive atoms)
[tex]t=14 \tau[/tex] (we want to evaluate the number of atoms left after 14 half-lives)
Substituting, we find:
[tex]N(14\tau) = (800)(\frac{1}{2})^{-\frac{14\tau}{\tau}}=0.049[/tex]
This means that there will be zero atoms left, since atoms can't be split in fractional parts.
Learn more about radioactive decay:
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