Potassium-40 () is a naturally occurring radioactive isotope possessing a natural abundance of among — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
Potassium-40 ($^{40}K$) is a naturally occurring radioactive isotope possessing a natural abundance of $0.012\%$ among all stable potassium isotopes. If a medical patient ingests exactly $250\text{ mg}$ of pure elemental Potassium ($K$), calculate the total mass of the radioactive $^{40}K$ isotope ingested, and express your exact answer in micrograms ($\mu\text{g}$).
💡 Solution & Explanation
The total mass of elemental Potassium ingested is $250\text{ mg}$. The natural isotopic abundance indicates that out of any macroscopic mass of potassium, exactly $0.012\%$ of that mass consists of the $^{40}K$ isotope. Mass of $^{40}K = \text{Total Mass} \times \frac{\text{Percentage Abundance}}{100}$. Mass of $^{40}K = 250\text{ mg} \times \frac{0.012}{100} = 250 \times 0.00012\text{ mg} = 0.03\text{ mg}$. To convert milligrams (mg) to micrograms ($\mu\text{g}$), multiply by $1000$. $0.03\text{ mg} = 0.03 \times 1000\text{ }\mu\text{g} = 30\text{ }\mu\text{g}$.