Radioactive Decay of Potassium-40

How much of a 24-gram sample of potassium-40 will remain after 3.75 billion years?

Based on the data, what is the final amount of the potassium-40 sample after 3.75 billion years?

Answer:

After 3.75 billion years, only 3 grams of the 24-gram sample of potassium-40 will remain.

Radioactive decay is a natural process that occurs over time. In the case of potassium-40, it decays to argon-40 with a half-life of 1.25 billion years. This means that half of the original sample will have decayed in that time frame.

Using the radioactive decay formula N = N0 * (1/2)^(t/T), where N0 is the initial amount of the radioactive substance, N is the final amount, t is the time that has passed, and T is the half-life of the substance, we can calculate how much of the potassium-40 sample will remain after 3.75 billion years.

Plugging in the given values, we get N = 24 g * (1/2)^3.75 billion years / 1.25 billion years. Simplifying the equation, we get N = 3 grams. Therefore, only 3 grams of the original 24-gram sample of potassium-40 will remain after 3.75 billion years.