Respuesta :
First, we have to remember the equations involved in the radioactive decomposition:
[tex]\begin{gathered} M(t)=\text{ M}_0*e^{\frac{^{\left\{-t*ln2\right\}}}{T}} \\ \end{gathered}[/tex]Where M (t) is the mass through the time, Mo is the initial mass, t is the time and T is the half-life time.
So, in the equation, we know the values of the following variables:
t=24 days
T=8 days
And, what the exercise is asking for is the fraction is the remaining mass, so we can calculate it as follows:
[tex]\begin{gathered} \frac{M(t)}{M_0}\text{ }\rightarrow\text{ It is the fraction in terms of the initial mass} \\ \frac{M(t)}{M_0}\text{ = }e^{-\frac{t*ln2}{T}} \\ \frac{M(t)}{M_{0}}=e^{-\frac{24\text{ d * ln2}}{8\text{ d}}} \\ \frac{M(t)}{M_{0}}=\text{ }\frac{1}{8} \end{gathered}[/tex]So, the answer will be that the remaining mass of the Isotope 1-131 after 24h is 1/8 of its initial mass.
