Question

The radioactive Isotope 1- 131 has a half-life of 8 days. What fraction of a sample of 1_(131 will remain after 24 daysA . 1 /4B. 1/16C . 1/8D, 1/2

Answer 1

First, we have to remember the equations involved in the radioactive decomposition:

`\begin{gathered} M(t)=\text{ M}_0*e^{\frac{^{\left\{-t*ln2\right\}}}{T}} \\ \end{gathered}`

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:

`\begin{gathered} (M(t))/(M_0)\text{ }\rightarrow\text{ It is the fraction in terms of the initial mass} \\ (M(t))/(M_0)\text{ = }e^{-(t*ln2)/(T)} \\ (M(t))/(M_(0))=e^{-\frac{24\text{ d * ln2}}{8\text{ d}}} \\ (M(t))/(M_(0))=\text{ }(1)/(8) \end{gathered}`

So, the answer will be that the remaining mass of the Isotope 1-131 after 24h is 1/8 of its initial mass.