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.