Explanation:
Formula to calculate how many particles are left is as follows.
N = [tex]N_{0} (\frac{1}{2}
)^{l}[/tex]
where, [tex]N_{0}[/tex] = number of initial particles
l = number of half lives
As it is given that number of initial particles is [tex]128 \times 10^{10}[/tex] and number of half-lives is 3.
Hence, putting the given values into the above equation as follows.
N = [tex]N_{0} (\frac{1}{2})^{l}[/tex]
= [tex]128 \times 10^{10}(\frac{1}{2})^{3}[/tex]
= [tex]16 \times 10^{10}[/tex]
or, [tex]1.6 \times 10^{11}[/tex]
Thus, we can conclude that [tex]1.6 \times 10^{11}[/tex] particles of radioactive nuclei remain in the given sample.
In five hours we've gone through 5 half lives so the answer is:
particles
