Half-Life Practice

1. A scientist begins with $100.0$ grams of a radioactive isotope. After exactly $12$ days have passed, only $25.0$ grams remain.

   What is the half-life of this isotope?

2. Many volcanic rocks contain potassium, which allows scientists to date them using the radioactive decay of ${K-40}$. This is how scientists discovered that the Galápagos Islands were only $3$ million years old.

   
   

   La Cumbre volcano on Isla Fernandina

   Potassium-$40$ has a half-life of $1.25$ billion years.

   If you start with $8.0$ grams of ${K-40}$, how many grams will remain after $2.5$ billion years?

   Choose 1 answer:

   1. $0$ grams
   2. $2.0$ grams
   3. $4.0$ grams

   4. $16.0$ grams

3. The following graph shows three different radioisotopes decaying over a period of $10$ seconds.

   
   

   Rank the isotopes from shortest to longest half-life.

   • Isotope C
   • Isotope A
   • Isotope B

4. A nuclear lab has produced $0.50$ moles of a pure radioisotope. The graph below shows it decaying over the course of $36$ hours.

   
   

   What is the approximate half-life of this radioisotope?

   Choose 1 answer:

   1. $1$ hour
   2. $3$ hours
   3. $6$ hours
   4. $12$ hours

Source: Khan Academy, https://www.khanacademy.org/science/hs-chemistry/x2613d8165d88df5e:nuclear-chemistry-hs/x2613d8165d88df5e:half-life-and-radiometric-dating/e/apply-half-life-and-radiometric-dating
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