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.