The original mass is m₀ = 1 μg.
The decay equation is
[tex]m(t) = m_{0} e^{-kt}[/tex]
where
m = mass remaining after time t,
k = constant.
Let
t = t₁ = time for half-life.
Then
[tex] \frac{m_{0}}{2} =m_{0} e^{-kt_{1}} \\\\ -kt_{1} = ln(1/2) \\\\ t_{1} = 0.6931/k[/tex]
When t = 5 half-lives, then
t = 5*(0.6931/k) = 3.4657/k
The mass remaining is
[tex]m = m_{0} e^{-k( \frac{3.4657}{k})} =m_{0} e^{-3.4657} = 0.0313m_{0}[/tex]
The mass remaining after 5 half-lives is
0.0313 μg
Answer: 0.0313 μg
