The Decay of Potassium-40 (K-40) into Argon-40 (Ar-40)

Understanding Potassium-40 Decay Process

Potassium-40 (K-40) is a radioactive isotope that undergoes decay into argon-40 (Ar-40) over time. The decay process involves the emission of beta particles. One key aspect of radioactive decay is the concept of half-life, which is the time it takes for half of the original amount of the radioactive isotope to decay.

The Decay of 20 Grams of K-40 After 1.25 Billion Years

If we start with 20 grams of K-40 and wait for 1.25 billion years, the amount of K-40 would be reduced to 10 grams due to radioactive decay. This means that half of the original amount of K-40 has decayed into Ar-40.

Calculating the Remaining Amount of K-40 After 5 Billion Years

Now, let's calculate how much of the original K-40 would remain after 5 billion years. Since the half-life of K-40 is 1.25 billion years, and we are looking at 5 billion years in total, we can divide the total time by the half-life to find out how many half-lives have passed.

5 billion years / 1.25 billion years/half-life = 4 half-lives

After 4 half-lives, the amount of K-40 would be reduced to:

20 grams / 2 (1st half-life) / 2 (2nd half-life) / 2 (3rd half-life) / 2 (4th half-life) = 1.25 grams

Therefore, after 5 billion years, only 1.25 grams of the original 20 grams of K-40 would remain.