Edge 2022: Potassium-40 Decay Calculation

How much potassium-40 will remain after 1.022 x 10¹⁰ years from a 500.3-g sample?

A) approximately 1.95 g

B) approximately 3.91 g

C) approximately 62.54 g

D) approximately 71.47 g

Answer:

(A) approximately 1.95 g

Explanation:

In this case, we are dealing with the decay of potassium-40 over a period of 1.022 x 10¹⁰ years from a 500.3-g sample. The half-life of potassium-40 is 1.277 x 10⁹ years.

To calculate how much potassium-40 will remain, we need to determine the number of half-lives that have passed. By dividing the total time elapsed (1.022 x 10¹⁰ years) by the half-life of potassium-40 (1.277 x 10⁹ years), we get 8, which represents the number of half-lives.

Next, we calculate the remaining mass of potassium-40 by multiplying the initial mass (500.3 g) by (1/2)^8, which equals approximately 1.95 g. Therefore, the correct answer is approximately 1.95 g of potassium-40 remaining after 1.022 x 10¹⁰ years.