a 60 - g sample of radioactive isotope is measured after two half - lives have passed. what pair of…

a 60 - g sample of radioactive isotope is measured after two half - lives have passed. what pair of percentages describes the sample after two half - lives?\n50% unchanged and 50% stable\n25% unchanged and 75% stable\n12.5% unchanged and 87.5% stable\n75% unchanged and 25% stable

a 60 - g sample of radioactive isotope is measured after two half - lives have passed. what pair of percentages describes the sample after two half - lives?\n50% unchanged and 50% stable\n25% unchanged and 75% stable\n12.5% unchanged and 87.5% stable\n75% unchanged and 25% stable

Answer

Explanation:

Step1: Recall half - life concept

The amount of a radioactive isotope remaining after $n$ half - lives is given by the formula $N = N_0\times\left(\frac{1}{2}\right)^n$, where $N_0$ is the initial amount and $n$ is the number of half - lives.

Step2: Calculate remaining fraction

Here, $n = 2$. So the fraction of the radioactive isotope remaining is $\left(\frac{1}{2}\right)^2=\frac{1}{4}=0.25 = 25%$.

Step3: Calculate stable fraction

The fraction that has decayed (become stable) is $1 - 0.25=0.75 = 75%$.

Answer:

25% unchanged and 75% stable