Question

complete these sentences by selecting the correct answers from the drop - down menus. after one half - life, % of the atoms will change to a stable isotope and % will remain radioactive. after three half - lives, % of the atoms will change to a stable isotope and % will remain radioactive.

Explanation:

Step1: Understand half - life concept

The half - life is the time it takes for half of the radioactive atoms in a sample to decay into a stable isotope.

Step2: After one half - life

If we start with 100% of radioactive atoms, after one half - life, 50% of the atoms will change to a stable isotope and 50% will remain radioactive.

Step3: After three half - lives

The fraction of remaining radioactive atoms after \(n\) half - lives is \((\frac{1}{2})^n\). For \(n = 3\), \((\frac{1}{2})^3=\frac{1}{8}=0.125 = 12.5\%\) remain radioactive. So the percentage of atoms that change to a stable isotope is \(100 - 12.5=87.5\%\).

Answer:

After one half - life: 50% of the atoms will change to a stable isotope and 50% will remain radioactive.
After three half - lives: 87.5% of the atoms will change to a stable isotope and 12.5% will remain radioactive.