How Much Potassium-40 Isotope Will Remain After 2.5 Billion Years?
Calculating Remaining Potassium-40 Isotope
A rock sample contains 80g of a potassium-40 (K10) isotope with a half-life of 1.25 billion years. We need to determine how much of the potassium-40 isotope will remain after 2.5 billion years have passed.
Given data:
Original mass of K-40 before decay = 80 g
Half-life of Potassium-40 = 1.25 billion years
Time taken by the decay = 2.5 billion years
Formula: Remaining mass = Original mass × (1/2)^n
where n is the number of half-lives
Calculations:
Number of half lives, n = Time taken ÷ half-life
= 2.5 billion years ÷ 1.25 billion years
= 2
Remaining mass = 80 g × (0.5)^2
= 80 g × 0.25
= 20 g
Therefore, the mass of K-40 isotope that will remain after 2.5 billion years is 20 g.
3. A rock sample contains 80g of a potassium-40 (K10) isotope with a half-life of 1.25 billion years. How much of the potassium-40 isotope will remain after 2.5 billion years have passed? A. 0g B. 10g C. 20g D. 80g
Answer: 20 g Explanation: We are given the original mass of K-40, the half-life of Potassium-40, and the time taken by the decay. By calculating the number of half-lives and using the formula for remaining mass, we find that 20 g of the potassium-40 isotope will remain after 2.5 billion years.